#pragma rtGlobals=1		// Use modern global access method.
#pragma ModuleName=LatticeSym
#pragma version = 3.35
#include "MaterialsLocate"								// used to find the path to the materials files
//
//	remember to execute    InitLatticeSymPackage()
//
//	with version 2.0, added a text description to the crystalStructure structure
//
//	with version 3.0, fixed up and changed the symmetry operators, I now think that they are right
//	with version 3.1, only compute symmetry operations as needed
//	with version 3.2, fixed Trigonal, now can use rhombohedral axes
//	with version 3.3, fixed lowestAllowedHKL() made alpha, beta & gamma non-zero 


Menu "Analysis"
	SubMenu "Lattice"
		"Set Crystal Structure...",MakeLatticeParametersPanel("")
		help={"Define the crystal structure and lattice to be used"}
		"Show Crystal Structure",showCrystalStructure()
		help={"Shows the crystal structure and lattice that is currently defined"}
		"Load a new Crystal Structure",LoadCrystal("")
		help={"load a rystal structure from a fie"}
		"d[hkl]",/Q,get_dhkl(NaN,NaN,NaN,T=NaN)
		help={"show d-spacing for the hkl reflection"}
		"F[structure, hkl)]",getFstruct(NaN,NaN,NaN)
		help={"Crude Structure Factor using current lattice"}
		"angle between two hkl's",angleBetweenHKLs(NaN,NaN,NaN,  NaN,NaN,NaN)
	End
End

Static Constant STRUCTURE_ATOMS_MAX=20	// max number of atom types in a material structure (for Si only need 1)
Strconstant PresetLatticeStructures = "FCC:225;BCC:229;Diamond:227;Simple Cubic:221;Hexagonal:194;Wurtzite (B4):186;Sapphire:167;Triclinic:1;other"
//OverRide Strconstant PresetLatticeStructures = "\"FCC:225;BCC:229;Diamond:227;Simple Cubic:221;Hexagonal:194;Wurtzite (B4):186;Sapphire:167;Triclinic:1;other\""


// =========================================================================
// =========================================================================
//	Start of setting particular lattice constants

Function MakeLatticeParametersPanel(strStruct)
	String strStruct									// optional passed value of geo structure, this is used if passed
	if (strlen(WinList("LatticeSet",";","WIN:64")))	// window alreay exits, bring it to front
		DoWindow/F LatticeSet
		return 0
	endif
	NewPanel /K=1 /W=(675,60,895,425)
	DoWindow/C LatticeSet
	FillLatticeParametersPanel(strStruct,"LatticeSet",0,0)
End

// prompts the user for lattice info, and set local structure.  Store the information in a structure string in current datafolder
Function setLattice()
	String strName=""
	Variable SpaceGroup									//Space Group number, from International Tables
	Variable a,b,c,alpha,bet,gam
	String desc

	STRUCT crystalStructure xtal
	xtal.a = 0
	FillCrystalStructDefault(xtal)						//fill the lattice structure with default values
	a = xtal.a			;	b = xtal.b		;	c = xtal.c
	alpha = xtal.alpha	;	bet = xtal.beta	;	gam = xtal.gam
	SpaceGroup = xtal.SpaceGroup
	desc = xtal.desc

	if (GetLatticeConstants(xtal,SpaceGroup,strName,a,b,c,alpha,bet,gam,desc))
		return 1
	endif
	xtal.Unconventional00 = NaN
	updateCrystalStructureDefaults(xtal)
	return 0
End


Function showCrystalStructure()						// prints the structure that is currently being used
	STRUCT crystalStructure xtal
	if (FillCrystalStructDefault(xtal))					//fill the lattice structure with test values
		DoAlert 0, "no crystal structure found"
		return 1
	endif
	String str, sym = getSymString(xtal.SpaceGroup)
	sprintf str, "'%s'  %d atoms,  #%d   %s\r%.9g, %.9g, %.9gnm,\r%g¡, %g¡, %g¡",xtal.desc,xtal.N,xtal.SpaceGroup,sym,xtal.a,xtal.b,xtal.c,xtal.alpha,xtal.beta,xtal.gam
	DoAlert 1,str+"\r\tprint all details to history too?"
	if (V_flag==1)
		print_crystalStructure(xtal)					// prints out the value in a crystalStructure structure
	else
		printf "currently using  '%s'  lattice is  #%d   %s     %.9gnm, %.9gnm, %.9gnm,   %g¡, %g¡, %g¡\r",xtal.desc,xtal.SpaceGroup,sym,xtal.a,xtal.b,xtal.c,xtal.alpha,xtal.beta,xtal.gam
		if (!(xtal.alphaT<=0))
			printf "coefficient of thermal expansion is %g\r",xtal.alphaT
		endif
	endif
	return 0
End


Structure crystalStructure		// structure definition for a crystal lattice
	char desc[100]				// name or decription of this crystal
	double a,b,c					// latticde constants, length (nm)
	double alpha,beta,gam			// angles (degree)
	int16 SpaceGroup				// Space Group number from international tables, allowed range is [1, 230]
	double  a0,  b0,  c0			// direct lattice from constants { a[], b[], c[] }
	double  a1,  b1,  c1
	double  a2,  b2,  c2
	double  as0,  bs0,  cs0		// reciprocal lattice { a*[], b*[], c*[] }
	double  as1,  bs1,  cs1		// a*,b*,c* already have the 2PI in them
	double  as2,  bs2,  cs2
	double Vc						// volume of cell, triple product of (a[]xb[]).c
	double density					// calculated density (g/cm^3)
	double	alphaT					// coef of thermal expansion, a = ao*(1+alphaT*(TempC-22.5))
	int16 N						// number of atoms described here
	Struct atomTypeStructure atom[STRUCTURE_ATOMS_MAX]
	double Unconventional00,Unconventional01,Unconventional02	// transform matrix for an unconventional unit cel
	double Unconventional10,Unconventional11,Unconventional12
	double Unconventional20,Unconventional21,Unconventional22
	char hashID[66]				// hash function for this strucutre (needs to hold at least 64 chars)
EndStructure
//
Structure atomTypeStructure	// definines one type of atom in a crystal structure
	char name[60]				// label for this atom, usually starts with atomic symbol
	int16 Zatom					// Z of the atom
	double x						// fractional coord along x lattice vector
	double y
	double z
	double occ						// occupancy
	double Debye					// Debye-Waller factor
EndStructure

Function print_crystalStructure(xtal)			// prints out the value in a crystalStructure
	STRUCT crystalStructure &xtal				// this sruct is printed in this routine
	Variable i,N=xtal.N
	if (strlen(xtal.desc))
		printf "'%s'   \t",xtal.desc
	else
		printf "\t\t\t"
	endif
	printf "Space Group = %d   %s       Vc = %g (nm^3)",xtal.SpaceGroup, getSymString(xtal.SpaceGroup),xtal.Vc
	if (xtal.density>0)
		printf "       density = %g (g/cm^3)",xtal.density
	endif
	if (!(xtal.alphaT<=0))
		printf "     coefficient of thermal expansion is %g\r",xtal.alphaT
	else
		printf "\r"
	endif
	printf "lattice constants  { %.15gnm, %.15gnm, %.15gnm,   %.15g¡, %.15g¡, %.15g¡ }\r",xtal.a,xtal.b,xtal.c,xtal.alpha,xtal.beta,xtal.gam
//	printf "lattice constants  { %.16gnm, %.16gnm, %.16gnm,   %.16g¡, %.16g¡, %.16g¡ }\r",xtal.a,xtal.b,xtal.c,xtal.alpha,xtal.beta,xtal.gam
	if (N<1)
		print "No Atoms Defined"
	else
		Variable mult
		reMakeAtomXYZs(xtal)
		printf "atom locations:\r"
		for (i=0;i<xtal.N;i+=1)
			printf "     %s (Z=%g)\t\t{%g,  %g,  %g}",xtal.atom[i].name,xtal.atom[i].Zatom,xtal.atom[i].x,xtal.atom[i].y,xtal.atom[i].z
			if (xtal.atom[i].occ != 1)
				printf "    occ = %g",xtal.atom[i].occ
			endif
			if (xtal.atom[i].Debye > 0)
				printf "    Debye-Waller = %g",xtal.atom[i].Debye
			endif
			mult = DimSize($("root:Packages:Lattices:atom"+num2istr(i)),0)
			if (mult>1)
				printf "\t\tmultiplicity = %d",mult
			endif
			printf "\r"
		endfor
	endif
	if (numtype(xtal.Unconventional00)==0)					// Unconventional exists, transform the lattice by it
		printf "\rusing an Uncoventional Cell, the transform is:\r"
		printf "\t\t%+6.3f\t\t%+6.3f\t\t%+6.3f\r",xtal.Unconventional00,xtal.Unconventional01,xtal.Unconventional02
		printf "\tT =\t%+6.3f\t\t%+6.3f\t\t%+6.3f\r",xtal.Unconventional10,xtal.Unconventional11,xtal.Unconventional12
		printf "\t\t%+6.3f\t\t%+6.3f\t\t%+6.3f\r",xtal.Unconventional20,xtal.Unconventional21,xtal.Unconventional22
	endif
	printf "\r"
	printf "				a				b				c   (nm)\r"
	printf "direct		%+10.7f\t%+10.7f\t%+10.7f\r",xtal.a0,xtal.b0,xtal.c0
	printf "lattice		%+10.7f\t%+10.7f\t%+10.7f\r",xtal.a1,xtal.b1,xtal.c1
	printf "			%+10.7f\t%+10.7f\t%+10.7f\r",xtal.a2,xtal.b2,xtal.c2
	printf "\r				a*				b*				c*  (1/nm)\r"
	printf "recip	\t%+10.6f\t%+10.6f\t%+10.6f\r",xtal.as0,xtal.bs0,xtal.cs0
	printf "lattice	\t%+10.6f\t%+10.6f\t%+10.6f\r",xtal.as1,xtal.bs1,xtal.cs1
	printf "		\t%+10.6f\t%+10.6f\t%+10.6f\r",xtal.as2,xtal.bs2,xtal.cs2
//	print "hash id = ",xtal.hashID
End

// gets lattice constants for known structures via dialogs,  it uses Space Group numbers from the International Tables
// known structures are:
//	FCC			225
//	BCC			229
//	Diamond		227
//	Simple Cubic	221
//	Hexagonal		194
//	Sapphire		167
//	Triclinic		1
Static Function GetLatticeConstants(xtal,SpaceGroup,structureName,a,b,c,alpha,bet,gam,desc)
	STRUCT crystalStructure &xtal						// this sruct is set in this routine
	Variable SpaceGroup									// same as for Internationl tables
	String structureName									// see structures below for list of valid names
	Variable a,b,c,alpha,bet,gam							// lattice constants, lengths in nm angles in degrees
	String desc											// description of lattice (i.e. the name)
	a = numtype(a)||a<=0 ? 0.405 : a					// default is aluminum
	b = numtype(b)||b<=0 ? a : b
	c = numtype(c)||c<=0 ? a : c
	alpha = numtype(alpha)||alpha<=0 ? 90 : alpha	// for invalid angles, use 90¡
	bet = numtype(bet)||bet<=0 ? 90 : bet
	gam = numtype(gam)||gam<=0 ? 90 : gam
	//	Cubic			[195,230]	//	a
	//	Hexagonal		[168,194]	//	a,c
	//	Trigonal		[143,167]	//	a,alpha
	//	Tetragonal		[75,142]		//	a,c
	//	Orthorhombic	[16,74]		//	a,b,c
	//	Monoclinic		[3,15]			//	a,b,c,gamma
	//	Triclinic		[1,2]			//	a,b,c,alpha,beta,gamma
	String item="",structures="FCC:225;BCC:229;Diamond:227;Simple Cubic:221;Hexagonal:194;Wurtzite (B4):186;Sapphire:167;Triclinic:1;other"
	if (strlen(xtal.desc)>0 && xtal.SpaceGroup==SpaceGroup)
		structures = xtal.desc+":"+num2istr(SpaceGroup)+";"+structures
	endif
	Variable i,N=ItemsInList(structures)
	if (SpaceGroup>=1 && SpaceGroup<=230)			// valid SpaceGroup number
		structureName = ""
		for(i=0;i<N;i+=1)
			item = StringFromList(i,structures)
			if (SpaceGroup==str2num(StringFromList(1,item,":")))
				structureName = StringFromList(0,item,":")
			endif
		endfor
		if (strlen(structureName)<1)
			DoAlert 0, "unknown structure number "+num2str(SpaceGroup)
		endif
	endif
	if (strlen(structureName)>1)						// a structureName passed
		SpaceGroup = -1
		for(i=0;i<N;i+=1)
			item = StringFromList(i,structures)
			if (stringmatch(structureName,StringFromList(0,item,":")))
				SpaceGroup = str2num(StringFromList(1,item,":"))
			endif
		endfor
		if (SpaceGroup<1)
			DoAlert 0, "unknown structure name '"+structureName+"'"
		endif
	endif
	item = structureName+":"+num2istr(SpaceGroup)
	Prompt item, "lattice structure", popup, structures
	DoPrompt/HELP="" "lattice structure",item
	if (V_flag)
		return 1
	endif
	if (stringmatch(item,"other"))
		Prompt SpaceGroup,"Space Group number from International Tables [1,230]"
		DoPrompt "Space Group",SpaceGroup
		if (V_flag)
			return 1
		endif
	else
		SpaceGroup=str2num(StringFromList(1,item,":"))
		structureName = StringFromList(0,item,":")
	endif
	if (!(1<=SpaceGroup && SpaceGroup<=230))
		return 1
	endif

	Prompt a, "a (nm)"
	Prompt b, "b (nm)"
	Prompt c, "c (nm)"
	Prompt alpha, "alpha (¡)"
	Prompt bet, "beta (¡)"
	Prompt gam, "gamma (¡)"

	if (SpaceGroup>=195)			// Cubic
		DoPrompt/HELP="" "Cubic lattice constants",a
		b=a;  c=a
		alpha=90;  bet=90;  gam=90
	elseif(SpaceGroup>=168)		// Hexagonal
		c = (a==c) ? 3*a : c
		DoPrompt/HELP="" "Hexagonal lattice constants",a,c
		b = a
		alpha=90;  bet=90;  gam=120
	elseif(SpaceGroup>=143)		// Trigonal, use the rhmbohedral cell
		DoPrompt/HELP="" "Trigonal lattice constants (rhombohedral cell)",a,alpha
		b=a  ;  c=a
		bet=alpha;  gam=alpha
//	elseif(SpaceGroup>=143)		// Trigonal, use the hexagonal cell
//		c = (a==c) ? 3*a : c
//		DoPrompt/HELP="" "Trigonal lattice constants",a,c
//		b = a
//		alpha=90;  bet=90;  gam=120
	elseif(SpaceGroup>=75)			// Tetragonal
		DoPrompt/HELP="" "Tetragonal lattice constants",a,c
		b = a
		alpha=90;  bet=90;  gam=90
	elseif(SpaceGroup>=16)			// Orthorhombic
		DoPrompt/HELP="" "Orthorhombic lattice constants",a,b,c
		alpha=90;  bet=90;  gam=90
	elseif(SpaceGroup>=3)			// Monoclinic
		DoPrompt/HELP="" "Monoclinic lattice constants",a,b,c,gam
//		alpha=90;  bet=90
		alpha=90;  gam=90
	else								// Triclinic
		DoPrompt/HELP="" "Triclinic lattice constants",a,b,c,alpha,bet,gam
	endif

	xtal.a = a			;	xtal.b = b		;	xtal.c = c	// put values into structure
	xtal.alpha = alpha	;	xtal.beta = bet	;	xtal.gam = gam
	xtal.SpaceGroup=SpaceGroup
	xtal.Unconventional00=NaN
	ForceLatticeToStructure(xtal)
	return 0
End
//
// forces lattice constants to match the Space Group number (e.g. for cubic, forces b and c to be a, and all angles 90)
Static Function ForceLatticeToStructure(xtal)
	STRUCT crystalStructure &xtal					// this sruct is set in this routine

	Variable SpaceGroup=xtal.SpaceGroup			// local value for convienence
	if (SpaceGroup!=limit(SpaceGroup,1,230))		// invalid SpaceGroup, it must be in range [1,230]
		DoAlert 0, "invalid Space Group number "+num2str(SpaceGroup)
		return 1
	endif
	//	Cubic			[195,230]	//	a
	//	Hexagonal		[168,194]	//	a,c
	//	Trigonal		[143,167]	//	a,alpha
	//	Tetragonal		[75,142]		//	a,c
	//	Orthorhombic	[16,74]		//	a,b,c
	//	Monoclinic		[3,15]			//	a,b,c,gamma
	//	Triclinic		[1,2]			//	a,b,c,alpha,beta,gamma
	Variable usingHexAxes = (abs(90-xtal.alpha)+abs(90-xtal.beta)+abs(120-xtal.gam))<1e-9

	if (SpaceGroup>=195)				// Cubic
		xtal.b = xtal.a
		xtal.c = xtal.a
		xtal.alpha=90;  xtal.beta=90;  xtal.gam=90
	elseif(SpaceGroup>=168)			// Hexagonal
		xtal.b = xtal.a
		xtal.alpha=90;  xtal.beta=90;  xtal.gam=120
	elseif(SpaceGroup>=143)			// Trigonal, use rhomohedral cell, unless obviously the hexagonal cell
		if (usingHexAxes)				// use hexagonal
			xtal.b = xtal.a
			xtal.alpha=90  ;  xtal.beta=90  ;  xtal.gam=120
		else								// use rhombohedral
			xtal.b = xtal.a
			xtal.c = xtal.a
			xtal.beta = xtal.alpha
			xtal.gam = xtal.alpha
		endif
		//	xtal.b = xtal.a
		//	xtal.alpha=90;  xtal.beta=90;  xtal.gam=120
	elseif(SpaceGroup>=75)			// Tetragonal
		xtal.b = xtal.a
		xtal.alpha=90;  xtal.beta=90;  xtal.gam=90
	elseif(SpaceGroup>=16)			// Orthorhombic
		xtal.alpha=90;  xtal.beta=90;  xtal.gam=90
	elseif(SpaceGroup>=3)				// Monoclinic
//		xtal.alpha=90;  xtal.beta=90
		xtal.alpha=90;  xtal.gam=90
//	else									// Triclinic
	endif

	String str
	if (xtal.a<=0 || xtal.b<=0 || xtal.c<=0 || numtype(xtal.a+xtal.b+xtal.c))	// check for valid a,b,c
		sprintf str,"invalid, (a,b,c) = (%g,%g,%g)",xtal.a,xtal.b,xtal.c
		DoAlert 0, str
		return 1
	endif
	Variable alpha=xtal.alpha,bet=xtal.beta,gam=xtal.gam
	if (alpha<=0 || bet<=0 || gam<=0 || alpha>=180 || bet>=180 || gam>=180 || numtype(alpha+bet+gam))	// check for valid angles
		sprintf str,"invalid, (alpha,beta,gam) = (%g,%g,%g)",alpha,bet,gam
		DoAlert 0, str
		return 1
	endif
	setDirectRecip(xtal)								// update Vc, direct and recip, density, and also calculates atom positions
	return 0
End
//
Static Function setDirectRecip(xtal)					// set direct and recip lattice vectors from a,b,c,..., also calculates Vc & density
	STRUCT crystalStructure &xtal

	Variable a=xtal.a, b=xtal.b, c=xtal.c
	Variable sa = sin((xtal.alpha)*PI/180), ca = cos((xtal.alpha)*PI/180)
	Variable cb = cos((xtal.beta)*PI/180), cg = cos((xtal.gam)*PI/180)
	Variable phi = sqrt(1.0 - ca*ca - cb*cb - cg*cg + 2*ca*cb*cg)	// = Vc/(a*b*c)
	xtal.Vc = a*b*c * phi								// volume of unit cell
	Variable pv = (2*PI) / (xtal.Vc)				// used for scaling
	Variable a0,a1,a2,  b0,b1,b2,  c0,c1,c2		//components of the direct lattice vectors
	a0=a*phi/sa	; a1=a*(cg-ca*cb)/sa	; a2=a*cb
	b0=0			; b1=b*sa				; b2=b*ca
	c0=0			; c1=0					; c2=c
	xtal.a0=a0		; xtal.a1=a1	; xtal.a2=a2
	xtal.b0=b0		; xtal.b1=b1	; xtal.b2=b2
	xtal.c0=c0		; xtal.c1=c1	; xtal.c2=c2
	xtal.as0=(b1*c2-b2*c1)*pv	; xtal.as1=(b2*c0-b0*c2)*pv	; xtal.as2=(b0*c1-b1*c0)*pv	// (b x c)*2¹/Vc
	xtal.bs0=(c1*a2-c2*a1)*pv	; xtal.bs1=(c2*a0-c0*a2)*pv	; xtal.bs2=(c0*a1-c1*a0)*pv	// (c x a)*2¹/Vc
	xtal.cs0=(a1*b2-a2*b1)*pv	; xtal.cs1=(a2*b0-a0*b2)*pv	; xtal.cs2=(a0*b1-a1*b0)*pv	// (a x b)*2¹/Vc

	if (numtype(xtal.Unconventional00)==0 && xtal.Unconventional00>-100 && xtal.Unconventional00<100)
		Make/N=(3,3)/O/D root:Packages:Lattices:Unconventional
		Wave Unconventional=root:Packages:Lattices:Unconventional
		Unconventional[0][0]=xtal.Unconventional00;	Unconventional[0][1]=xtal.Unconventional01;	Unconventional[0][2]=xtal.Unconventional02
		Unconventional[1][0]=xtal.Unconventional10;	Unconventional[1][1]=xtal.Unconventional11;	Unconventional[1][2]=xtal.Unconventional12
		Unconventional[2][0]=xtal.Unconventional20;	Unconventional[2][1]=xtal.Unconventional21;	Unconventional[2][2]=xtal.Unconventional22
	else
		KillWaves/Z root:Packages:Lattices:Unconventional
	endif

	xtal.density = densityOfCrystalStructure(xtal)
	return 0
End

Function densityOfCrystalStructure(xtal)				// returns the density (g/cm^3)
	STRUCT crystalStructure &xtal						// this sruct is filled  by this routine
	Variable NA=6.02214199e23						// Avagadro's number
	String amuList										// atomic mass of all of the elements
	amuList   = "1.00794;4.002602;6.941;9.012182;10.811;12.0107;14.0067;15.9994;18.9984032;20.1797;22.98977;24.305;"
	amuList += "26.981538;28.0855;30.973761;32.065;35.453;39.948;39.0983;40.078;44.95591;47.867;50.9415;51.9961;"
	amuList += "54.938049;55.845;58.9332;58.6934;63.546;65.409;69.723;72.64;74.9216;78.96;79.904;83.798;85.4678;87.62;"
	amuList += "88.90585;91.224;92.90638;95.94;98;101.07;102.9055;106.42;107.8682;112.411;114.818;118.71;121.76;"
	amuList += "127.6;126.90447;131.293;132.90545;137.327;138.9055;140.116;140.90765;144.24;145;150.36;151.964;157.25;"
	amuList += "158.92534;162.5;164.93032;167.259;168.93421;173.04;174.967;178.49;180.9479;183.84;186.207;190.23;"
	amuList += "192.217;195.078;196.96655;200.59;204.3833;207.2;208.98038;209;210;222;223;226;227;232.0381;231.03588;"
	amuList += "238.02891;237;244;243;247;247;251;252;257;258;259;262;261;262;266;264;277;268" 
	String name
	Variable amu											// atomic mass of all atoms in cell
	Variable m, N=xtal.N
	reMakeAtomXYZs(xtal)
	for (m=0,amu=0; m<N; m+=1)						// for each atom type
		name="root:Packages:Lattices:atom"+num2istr(m)
		Wave ww = $name
		amu += str2num(StringFromList(xtal.atom[m].Zatom-1,amuList))*DimSize(ww,0) * xtal.atom[m].occ
	endfor
	return (amu/NA)/(xtal.Vc * 1e-21)				// grams / cm^3
End

Function get_dhkl(h,k,l,[T])
	Variable h,k,l
	Variable T											// Temperature, only used if 
	STRUCT crystalStructure xtal
	if (FillCrystalStructDefault(xtal))				//fill the lattice structure with test values
		DoAlert 0, "no lattice structure found"
		return NaN
	endif
	Variable alphaTbad = !(abs(xtal.alphaT)<0.1)	// if  |alphaT| > 0.1 then it must be wrong
	if (numtype(h+k+l))
		h = numtype(h) ? 0 : h
		k = numtype(k) ? 0 : k
		l = numtype(l) ? 2 : l
		Prompt h,"H"
		Prompt k,"K"
		Prompt l,"L"
		Prompt T,"Temperature, standard is 22.5, (C)"
		Variable askForT = (!ParamIsDefault(T) && !alphaTbad)
		if (askForT)
			DoPrompt "(hkl)",h,k,l,T
		else
			DoPrompt "(hkl)",h,k,l
		endif
		if (V_flag)
			return NaN
		endif
	endif
	if (numtype(h+k+l))
		return NaN
	endif
	Variable d, usingT = !alphaTbad && numtype(T)==0
	if (usingT)											// both alphaT and T are valid
		d = dSpacing(xtal,h,k,l,T=T)
	else
		d = dSpacing(xtal,h,k,l)
	endif
	if (ItemsInList(GetRTStackInfo(0))<2)
		Variable places = placesOfPrecision(xtal.a)
		if (usingT)										// both alphaT and T are valid
			printf "d['%s' (T=%g),  (%s)] = %.9g nm\r",xtal.desc,T,hkl2str(h,k,l),roundSignificant(d,places)
		else
			printf "d['%s',  (%s)] = %.9g nm\r",xtal.desc,hkl2str(h,k,l),roundSignificant(d,places)
		endif
	endif
	return d
End
//
Function dSpacing(xtal,h,k,l,[T])		// returns d-spacing for the hkl (nm)
	STRUCT crystalStructure &xtal		// this sruct is set in this routine
	Variable h,k,l
	Variable T
	Variable xx,yy,zz
	xx = h*xtal.as0 + k*xtal.bs0 + l*xtal.cs0
	yy = h*xtal.as1 + k*xtal.bs1 + l*xtal.cs1
	zz = h*xtal.as2 + k*xtal.bs2 + l*xtal.cs2
	Variable d = 2*PI/sqrt(xx*xx + yy*yy + zz*zz)
	if (abs(xtal.alphaT)<0.1 && !ParamIsDefault(T))	// do if T passed, and valid alphaT
		T = limit(T,-273.15,Inf)				// limit T to > absolute zero
		d = d*(1+xtal.alphaT*(T-22.5))		// apply temperature correction
	endif
	return d
End

// returns d-spacing (nm) given (hkl) and lattice constants, just a local utility
Function dSpacingFromLatticeConstants(h,k,l,a,b,c,alpha,bet,gam)
	Variable h,k,l
	Variable a,b,c,alpha,bet,gam							// lattice constants, lengths in nm angles in degrees

	STRUCT crystalStructure xtal						// this sruct is only used locally
	xtal.a = a			;	xtal.b = b		;	xtal.c = c	// put values into structure
	xtal.alpha = alpha	;	xtal.beta = bet	;	xtal.gam = gam
	xtal.SpaceGroup=1
	ForceLatticeToStructure(xtal)

	Variable k0,k1,k2, d					// 	k =  {k0,k1,k2} = h*as + k*bs + l*cs
	k0 = h*xtal.as0 + k*xtal.bs0 + l*xtal.cs0
	k1 = h*xtal.as1 + k*xtal.bs1 + l*xtal.cs1
	k2 = h*xtal.as2 + k*xtal.bs2 + l*xtal.cs2
	d = 2*PI/sqrt(k0*k0 + k1*k1 + k2*k2)	// d = 2*pi/|k|
	return d
End


Function angleBetweenHKLs(h1,k1,l1,  h2,k2,l2)		// find angle between (h1,k1,l1) and (h2,k2,l2)
	Variable h1,k1,l1,h2,k2,l2
	if (numtype(h1+k1+l1+h2+k2+l2) && ItemsInList(GetRTStackInfo(0))<2 )
		h1 = numtype(h1) ? 0 : h1
		k1 = numtype(k1) ? 0 : k1
		l1 = numtype(l1) ? 2 : l1
		h2 = numtype(h2) ? 1 : h2
		k2 = numtype(k2) ? 1 : k2
		l2= numtype(l2) ? 1 : l2
		String hklStr1, hklStr2
		sprintf hklStr1,"%g %g %g",h1,k1,l1
		sprintf hklStr2,"%g %g %g",h2,k2,l2
		Prompt hklStr1,"(hkl) of the first Q"
		Prompt hklStr2,"(hkl) of the second Q"
		DoPrompt "hkl max & font size",hklStr1,hklStr2
		if (V_flag)
			return 1
		endif
		sscanf hklStr1, "%g %g %g",h1,k1,l1
		sscanf hklStr2, "%g %g %g",h2,k2,l2
	endif

	STRUCT crystalStructure xtal
	if (FillCrystalStructDefault(xtal))					//fill the lattice structure with current values
		DoAlert 0, "No Lattice, please set one"
		return 1
	endif
	Make/N=3/O/D hkl_angleBetweenHKLs1, hkl_angleBetweenHKLs2
	Wave q1=hkl_angleBetweenHKLs1, q2=hkl_angleBetweenHKLs2
	q1[0] = h1*xtal.as0+k1*xtal.bs0+l1*xtal.cs0		// q1 =  recip x hkl1
	q1[1] = h1*xtal.as1+k1*xtal.bs1+l1*xtal.cs1
	q1[2] = h1*xtal.as2+k1*xtal.bs2+l1*xtal.cs2
	q2[0] = h2*xtal.as0+k2*xtal.bs0+l2*xtal.cs0		// q2 =  recip x hkl2
	q2[1] = h2*xtal.as1+k2*xtal.bs1+l2*xtal.cs1
	q2[2] = h2*xtal.as2+k2*xtal.bs2+l2*xtal.cs2
	normalize(q1)
	normalize(q2)
	Variable angle = acos(limit(MatrixDot(q1,q2),-1,1))
	angle *= 180/PI
	KillWaves hkl_angleBetweenHKLs1, hkl_angleBetweenHKLs2
	if (ItemsInList(GetRTStackInfo(0))<2)
		printf "angle between (%s) and (%s) is %g¡\r",hkl2str(h1,k1,l1),hkl2str(h2,k2,l2),angle
	endif
	return angle
End


Function FillCrystalStructDefault(xtal)				//fill the crystal structure with 'current' values
	STRUCT crystalStructure &xtal					// returns 0 if something set, 1 is nothing done

	String strStruct=StrVarOrDefault(":crystalStructStr","")// set to values in current directory
	if (strlen(strStruct)<1)
		strStruct=StrVarOrDefault("root:Packages:Lattices:crystalStructStr","")	// try the default values
	endif
	if (strlen(strStruct)>1)
		StructGet/S/B=2 xtal, strStruct				// found structure information, load into xtal
	else
		LoadPackagePreferences/MIS=1 "LatticeSym","LatticeSymPrefs",1,xtal
		if (V_flag)
			return 1									// did nothing, nothing found
		endif
	endif
	setDirectRecip(xtal)								// ensure that these are set
	return 0
End


Function updateCrystalStructureDefaults(xtal)
	STRUCT crystalStructure &xtal						// returns 0 if something set, 1 is nothing done

	String strStruct
	xtal.hashID = ""										// re-set hash function to identify associated waves
	StructPut/S xtal, strStruct
	xtal.hashID = hash(strStruct,1)

	// save as defaults for further use
	if (exists(":crystalStructStr")==2)				// use the global in this data folder
		SVAR crystalStructStr=:crystalStructStr
	elseif (exists("root:Packages:Lattices:crystalStructStr")==2)	// use the global in the Packages
		SVAR crystalStructStr=root:Packages:Lattices:crystalStructStr
	else
		String/G crystalStructStr						// no global, make one in this data folder
	endif
	StructPut/S/B=2 xtal, crystalStructStr				// and write them to the global
	SavePackagePreferences/FLSH=1 "LatticeSym","LatticeSymPrefs",1,xtal
	return 0
End

//	End of setting particular lattice constants
// =========================================================================
// =========================================================================


// =========================================================================
// =========================================================================
//	Start of lattice set panel

Function/T FillLatticeParametersPanel(strStruct,hostWin,left,top)
	String strStruct									// optional passed value of xtal structure, this is used if passed
	String hostWin									// name of home window
	Variable left, top									// offsets from the left and top

	NewDataFolder/O root:Packages:Lattices:PanelValues	// ensure that the needed data folders exist
	Variable new = !(NumVarOrDefault("root:Packages:Lattices:PanelValues:SpaceGroup",-1)>0)
	String/G root:Packages:Lattices:PanelValues:desc
	Variable/G root:Packages:Lattices:PanelValues:SpaceGroup
	Variable/G root:Packages:Lattices:PanelValues:a
	Variable/G root:Packages:Lattices:PanelValues:b
	Variable/G root:Packages:Lattices:PanelValues:c
	Variable/G root:Packages:Lattices:PanelValues:alpha
	Variable/G root:Packages:Lattices:PanelValues:beta
	Variable/G root:Packages:Lattices:PanelValues:gam
	Variable/G root:Packages:Lattices:PanelValues:alphaT
	Variable/G root:Packages:Lattices:PanelValues:dirty
	NVAR SpaceGroup=root:Packages:Lattices:PanelValues:SpaceGroup
	SVAR desc=root:Packages:Lattices:PanelValues:desc
	NVAR a=root:Packages:Lattices:PanelValues:a
	NVAR b=root:Packages:Lattices:PanelValues:b
	NVAR c=root:Packages:Lattices:PanelValues:c
	NVAR alpha=root:Packages:Lattices:PanelValues:alpha
	NVAR beta=root:Packages:Lattices:PanelValues:beta
	NVAR gam=root:Packages:Lattices:PanelValues:gam
	NVAR alphaT=root:Packages:Lattices:PanelValues:alphaT
	NVAR dirty=root:Packages:Lattices:PanelValues:dirty

	Variable/G root:Packages:Lattices:PanelValues:h
	Variable/G root:Packages:Lattices:PanelValues:k
	Variable/G root:Packages:Lattices:PanelValues:l
	Variable/G root:Packages:Lattices:PanelValues:dspace_nm
	Variable/G root:Packages:Lattices:PanelValues:Fr
	Variable/G root:Packages:Lattices:PanelValues:Fi
	String/G root:Packages:Lattices:PanelValues:crystalStructStr
	SVAR crystalStructStr = root:Packages:Lattices:PanelValues:crystalStructStr

	STRUCT crystalStructure xtal
	if (strlen(strStruct))								// start using the passed values
		StructGet/S/B=2 xtal, strStruct					// found passed structure information, load into xtal
		dirty = 1
		crystalStructStr = strStruct
	elseif(new)											// no old values present, use usual defaults
		FillCrystalStructDefault(xtal)
		a=xtal.a  ;  b=xtal.b  ;  c=xtal.c
		alpha=xtal.alpha  ;  beta=xtal.beta  ;  gam=xtal.gam
		SpaceGroup=xtal.SpaceGroup
		alphaT=xtal.alphaT
		desc=xtal.desc
		dirty = 0
		StructPut/S xtal, strStruct
	endif

	SetWindow kwTopWin,userdata(LatticePanelName)=hostWin+"#LatticePanel"
	NewPanel/K=1/W=(left,top,left+221,top+465)/HOST=$hostWin
	ModifyPanel frameStyle=0, frameInset=0
	RenameWindow #,LatticePanel
	SetVariable setDesc,pos={4,13},size={211,18},title="name"
	SetVariable setDesc,help={"description of this lattice"},fSize=12,proc=LatticePanelParamProc
	SetVariable setDesc,limits={-inf,inf,0},value= root:Packages:Lattices:PanelValues:desc
	PopupMenu popLatticeStructure,pos={44,41},size={116,20},proc=LatticePanelPopMenuProc
	PopupMenu popLatticeStructure,font="Baskerville Semibold",fSize=12,fStyle=1
//	PopupMenu popLatticeStructure,mode=5,popvalue="Hexagonal:194",value= #PresetLatticeStructures
//	PopupMenu popLatticeStructure,mode=5,value= #PresetLatticeStructures
	PopupMenu popLatticeStructure,mode=5,value= #"PresetLatticeStructures"
	SetVariable set_SpaceGroup,pos={45,67},size={110,18},proc=LatticePanelParamProc,title="structure"
	SetVariable set_SpaceGroup,fSize=12,format="%d",userdata(oldValue)=num2istr(SpaceGroup)
	SetVariable set_SpaceGroup,limits={1,230,0},value= root:Packages:Lattices:PanelValues:SpaceGroup
	TitleBox structureTitle,pos={25,95},size={82,15},title="\\JC"
	TitleBox structureTitle,fSize=16,frame=0,anchor= LC
	SetVariable set_a_nm,pos={45,125},size={128,18},proc=LatticePanelParamProc,title="a (nm)"
	SetVariable set_a_nm,fSize=12,format="%.7f"
	SetVariable set_a_nm,limits={0,inf,0},value= root:Packages:Lattices:PanelValues:a
	SetVariable set_b_nm,pos={45,145},size={128,18},proc=LatticePanelParamProc,title="b (nm)"
	SetVariable set_b_nm,fSize=12,format="%.7f"
	SetVariable set_b_nm,limits={0,inf,0},value= root:Packages:Lattices:PanelValues:b
	SetVariable set_c_nm,pos={45,165},size={128,18},proc=LatticePanelParamProc,title="c (nm)"
	SetVariable set_c_nm,fSize=12,format="%.7f"
	SetVariable set_c_nm,limits={0,inf,0},value= root:Packages:Lattices:PanelValues:c
	SetVariable set_alpha,pos={45,195},size={100,17},proc=LatticePanelParamProc,title="a°"
	SetVariable set_alpha,font="Symbol",fSize=14,format="%.5f"
	SetVariable set_alpha,limits={0,180,0},value= root:Packages:Lattices:PanelValues:alpha
	SetVariable set_beta,pos={45,215},size={100,17},proc=LatticePanelParamProc,title="b°"
	SetVariable set_beta,font="Symbol",fSize=14,format="%.5f"
	SetVariable set_beta,limits={0,180,0},value= root:Packages:Lattices:PanelValues:beta
	SetVariable set_gamma,pos={45,235},size={100,17},proc=LatticePanelParamProc,title="g°"
	SetVariable set_gamma,font="Symbol",fSize=14,format="%.5f"
	SetVariable set_gamma,limits={0,180,0},value= root:Packages:Lattices:PanelValues:gam
	Button buttonLatticeSave,pos={35,265},size={150,20},proc=LatticePanelButtonProc,title="Save"
	Button buttonLatticeSave,help={"Save these values as the current values"}
	Button buttonLatticeRevert,pos={35,290},size={150,20},proc=LatticePanelButtonProc,title="Revert"
	Button buttonLatticeRevert,help={"revert to the current default"}
	Button buttonLatticeFromFile,pos={35,315},size={150,20},proc=LatticePanelButtonProc,title="Load from a file"
	Button buttonLatticeFromFile,help={"Fill the values in this panel from a file"}
	Button buttonPrintLattice,pos={35,340},size={150,20},proc=LatticePanelButtonProc,title="Print Lattice to History"
	Button buttonPrintLattice,help={"print lattice values to the history"}

	SetVariable h_LatticeVar,pos={12,391},size={60,15},proc=LatticePanelParamProc,title="H",font="Lucida Grande",fSize=12
	SetVariable h_LatticeVar,value= root:Packages:Lattices:PanelValues:h
	SetVariable k_LatticeVar,pos={84,391},size={60,15},proc=LatticePanelParamProc,title="K",font="Lucida Grande",fSize=12
	SetVariable k_LatticeVar,value= root:Packages:Lattices:PanelValues:k
	SetVariable L_LatticeVar,pos={156,391},size={60,15},proc=LatticePanelParamProc,title="L",font="Lucida Grande",fSize=12
	SetVariable L_LatticeVar,value= root:Packages:Lattices:PanelValues:l
	ValDisplay d_LatticeDisp,pos={57,412},size={123,17},title="d (nm)=",font="Lucida Grande",fSize=12,format="%.7f"
	ValDisplay d_LatticeDisp,limits={0,0,0},barmisc={0,1000},value=#"root:Packages:Lattices:PanelValues:dspace_nm"
	ValDisplay d_LatticeDisp,help={"d-spacing (nm) calculated using the lattice"},frame=0
	ValDisplay Fr_3atticeDisp,pos={20,435},size={80,17},title="F =",value= #"root:Packages:Lattices:PanelValues:Fr"
	ValDisplay Fr_3atticeDisp,font="Lucida Grande",fSize=12,format="%.3f",limits={0,0,0},barmisc={0,1000}
	ValDisplay Fr_3atticeDisp,help={"d-spacing (nm) calculated using the lattice"},frame=0
	ValDisplay Fi_3atticeDisp,pos={104,435},size={80,17},title="+i",value= #"root:Packages:Lattices:PanelValues:Fi"
	ValDisplay Fi_3atticeDisp,font="Lucida Grande",fSize=12,format="%.3f",limits={0,0,0},barmisc={0,1000}
	ValDisplay Fi_3atticeDisp,help={"d-spacing (nm) calculated using the lattice"},frame=0

	LatticePanelParamProc("set_SpaceGroup",SpaceGroup,"","")
	return "#LatticePanel"
End
//
Function LatticePanelPopMenuProc(ctrlName,popNum,popStr) : PopupMenuControl
	String ctrlName
	Variable popNum
	String popStr
	Variable SpaceGroup = str2num(StringFromList(1, popStr,":"))
//	String subWin = "microPanel#LatticePanel"
	String subWin = GetUserData("","","LatticePanelName")
	if (numtype(SpaceGroup))		// other, Space Group number is manually supplied
		SetVariable set_SpaceGroup,noedit=0	,frame=1,fstyle=0,win=$subWin	// enable
	else	
		SetVariable set_SpaceGroup,noedit=1	,frame=0,fstyle=2,win=$subWin	// disable Space Group number
		NVAR num = root:Packages:Lattices:PanelValues:SpaceGroup
		num = SpaceGroup
		NVAR dirty=root:Packages:Lattices:PanelValues:dirty
		dirty = 1
	endif
	LatticePanelParamProc("set_SpaceGroup",SpaceGroup,"","")
End
//
Function LatticePanelParamProc(ctrlName,varNum,varStr,varName) : SetVariableControl
	String ctrlName
	Variable varNum
	String varStr
	String varName

	String subWin = GetUserData("","","LatticePanelName")
	NVAR a=root:Packages:Lattices:PanelValues:a
	NVAR b=root:Packages:Lattices:PanelValues:b
	NVAR c=root:Packages:Lattices:PanelValues:c
	NVAR alpha=root:Packages:Lattices:PanelValues:alpha
	NVAR beta=root:Packages:Lattices:PanelValues:beta
	NVAR gam=root:Packages:Lattices:PanelValues:gam
	NVAR alphaT=root:Packages:Lattices:PanelValues:alphaT
	NVAR SpaceGroup=root:Packages:Lattices:PanelValues:SpaceGroup
	NVAR dirty=root:Packages:Lattices:PanelValues:dirty
	if (stringmatch(ctrlName,"set_SpaceGroup"))
		if (!(1<=varNum && varNum<=230))
			return 1
		endif
		dirty = dirty || (varNum!=str2num(GetUserData(subWin,"set_SpaceGroup","oldValue")))
		SetVariable set_SpaceGroup, userdata(oldValue)=num2istr(varNum),win=$subWin
		Variable i, usingHexAxes = (abs(90-alpha)+abs(90-beta)+abs(120-gam))<1e-9
		for (i=ItemsInList(PresetLatticeStructures)-1;i>=0;i-=1)
			if (varNum==str2num(StringFromList(1,StringFromList(i,PresetLatticeStructures),":")))
				break
			endif
		endfor
		if (i>=0)		// if varNum is in the list, then change back to the popup menu
			PopupMenu popLatticeStructure,mode=(i+1), win=$subWin
			SetVariable set_SpaceGroup,noedit=1	,frame=0,fstyle=2,win=$subWin	// disable Space Group number
		else
			PopupMenu popLatticeStructure,mode=ItemsInList(PresetLatticeStructures), win=$subWin	// set to 'other'
		endif
		String titleStr="\\JC"
		if (varNum>=195)												// Cubic, a
			SetVariable set_a_nm,noedit=0,frame=1,win=$subWin	// enable
			SetVariable set_b_nm,noedit=1,frame=0,win=$subWin	// disable
			SetVariable set_c_nm,noedit=1,frame=0,win=$subWin
			SetVariable set_alpha,noedit=1,frame=0,win=$subWin
			SetVariable set_beta,noedit=1,frame=0,win=$subWin
			SetVariable set_gamma,noedit=1,frame=0,win=$subWin
			b=a  ;  c=a  ;  alpha=90 ; beta=90 ; gam=90
			titleStr += "Cubic"
		elseif (varNum>=168)											// Hexagonal, a, c
			SetVariable set_a_nm,noedit=0,frame=1,win=$subWin	// enable
			SetVariable set_c_nm,noedit=0,frame=1,win=$subWin
			SetVariable set_b_nm,noedit=1,frame=0,win=$subWin	// disable
			SetVariable set_alpha,noedit=1,frame=0,win=$subWin
			SetVariable set_beta,noedit=1,frame=0,win=$subWin
			SetVariable set_gamma,noedit=1,frame=0,win=$subWin
			b=a ; alpha=90 ; beta=90 ; gam=120
			titleStr += "Hexagonal"
		elseif (varNum>=143)											// Trigonal, a, alpha
			SetVariable set_a_nm,noedit=0,frame=1,win=$subWin	// enable
			SetVariable set_alpha,noedit=0,frame=1,win=$subWin
			SetVariable set_b_nm,noedit=1,frame=0,win=$subWin	// disable
			SetVariable set_c_nm,noedit=1,frame=0,win=$subWin
			SetVariable set_beta,noedit=1,frame=0,win=$subWin
			SetVariable set_gamma,noedit=1,frame=0,win=$subWin
			if (usingHexAxes)										// obviously using hexagonal
				b=a
				alpha=90  ;  beta=90  ;  gam=120
			else														// use rhombohedral
				b=a  ;  c=a
				beta=alpha  ;  gam=alpha
			endif
			//	b=a  ;  c=a  ;  beta=90 ; gam=90
			titleStr += "Trigonal"
		elseif (varNum>=75)											// Tetragonal, a, c
			SetVariable set_a_nm,noedit=0,frame=1,win=$subWin	// enable
			SetVariable set_c_nm,noedit=0,frame=1,win=$subWin
			SetVariable set_b_nm,noedit=1,frame=0,win=$subWin	// disable
			SetVariable set_alpha,noedit=1,frame=0,win=$subWin
			SetVariable set_beta,noedit=1,frame=0,win=$subWin
			SetVariable set_gamma,noedit=1,frame=0,win=$subWin
			b=a ; alpha=90 ; beta=90 ; gam=90
			titleStr += "Tetragonal"
		elseif (varNum>=16)											// Orthorhombic, a, b, c
			SetVariable set_a_nm,noedit=0,frame=1,win=$subWin	// enable
			SetVariable set_b_nm,noedit=0,frame=1,win=$subWin
			SetVariable set_c_nm,noedit=0,frame=1,win=$subWin
			SetVariable set_alpha,noedit=1,frame=0,win=$subWin	// disable
			SetVariable set_beta,noedit=1,frame=0,win=$subWin
			SetVariable set_gamma,noedit=1,frame=0,win=$subWin
			alpha=90 ; beta=90 ; gam=90
			titleStr += "Orthorhombic"
		elseif (varNum>=3)											// Monoclinic, a, b, c, gamma
			SetVariable set_a_nm,noedit=0,frame=1,win=$subWin	// enable
			SetVariable set_b_nm,noedit=0,frame=1,win=$subWin
			SetVariable set_c_nm,noedit=0,frame=1,win=$subWin
			SetVariable set_beta,noedit=0,frame=1,win=$subWin
			SetVariable set_alpha,noedit=1,frame=0,win=$subWin	// disable
			SetVariable set_gamma,noedit=1,frame=0,win=$subWin
//			alpha=90 ; beta=90
			alpha=90 ; gam=90
			titleStr += "Monoclinic"
		else																// Triclinic, a, b, c, alpha, beta, gamma
			SetVariable set_a_nm,noedit=0,frame=1,win=$subWin	// enable all
			SetVariable set_b_nm,noedit=0,frame=1,win=$subWin
			SetVariable set_c_nm,noedit=0,frame=1,win=$subWin
			SetVariable set_alpha,noedit=0,frame=1,win=$subWin
			SetVariable set_beta,noedit=0,frame=1,win=$subWin
			SetVariable set_gamma,noedit=0,frame=1,win=$subWin
			titleStr += "Triclinic"
		endif
		titleStr += "   \\F'Courier'"+getSymString(varNum)
		titleStr = minus2bar(titleStr)									// change all minuses to a bar over following character
		TitleBox structureTitle,title=titleStr,win=$subWin

	elseif (!(stringmatch(ctrlName,"h_LatticeVar")||stringmatch(ctrlName,"k_LatticeVar")||stringmatch(ctrlName,"L_LatticeVar")))
		dirty = 1
		//	Cubic			[195,230]	//	a
		//	Hexagonal		[168,194]	//	a,c
		//	Trigonal		[143,167]	//	a,alpha
		//	Tetragonal		[75,142]		//	a,c
		//	Orthorhombic	[16,74]		//	a,b,c
		//	Monoclinic		[3,15]			//	a,b,c,gamma
		//	Triclinic		[1,2]			//	a,b,c,alpha,beta,gamma
		if (SpaceGroup>=195)			// Cubic, a
			b=a  ;  c=a
		elseif (SpaceGroup>=168)		// Hexagonal, a, c
			b=a
		elseif (SpaceGroup>=143)		// Trigonal, a, alpha
			b=a  ;  c=a  ;  beta=alpha ; gam=alpha
		elseif (SpaceGroup>=75)			// Tetragonal, a, c
			b=a
		endif
	endif

	NVAR h=root:Packages:Lattices:PanelValues:h, k=root:Packages:Lattices:PanelValues:k, l=root:Packages:Lattices:PanelValues:l
	NVAR dspace_nm=root:Packages:Lattices:PanelValues:dspace_nm
	NVAR Fr=root:Packages:Lattices:PanelValues:Fr, Fi=root:Packages:Lattices:PanelValues:Fi


	STRUCT crystalStructure xtal			// returns 0 if something set, 1 is nothing done
	FillCrystalStructDefault(xtal)			//fill the crystal structure with 'current' values
	dspace_nm = dSpacing(xtal,h,k,l)
	Variable/C Fc = Fstruct(xtal,h,k,l)
	Fr = real(Fc)
	Fi = imag(Fc)

	// set buttons to enable/disable, based upon 'dirty'
	if (dirty)
		Button buttonLatticeSave disable=0,fColor=(57346,65535,49151),title="Save  (Needed)",win=$subWin
		Button buttonLatticeRevert disable=0,fColor=(65535,65534,49151),win=$subWin
	else
		Button buttonLatticeSave disable=2,fColor=(0,0,0),title="Saved",win=$subWin
		Button buttonLatticeRevert disable=2,fColor=(0,0,0),win=$subWin
	endif
	return 0
End
//
Function LatticePanelButtonProc(ctrlName) : ButtonControl
	String ctrlName

	SVAR desc=root:Packages:Lattices:PanelValues:desc
	NVAR SpaceGroup=root:Packages:Lattices:PanelValues:SpaceGroup
	NVAR a=root:Packages:Lattices:PanelValues:a
	NVAR b=root:Packages:Lattices:PanelValues:b
	NVAR c=root:Packages:Lattices:PanelValues:c
	NVAR alpha=root:Packages:Lattices:PanelValues:alpha
	NVAR beta=root:Packages:Lattices:PanelValues:beta
	NVAR gam=root:Packages:Lattices:PanelValues:gam
	NVAR alphaT=root:Packages:Lattices:PanelValues:alphaT
	NVAR dirty = root:Packages:Lattices:PanelValues:dirty
	SVAR crystalStructStr = root:Packages:Lattices:PanelValues:crystalStructStr
	STRUCT crystalStructure xtal
	StructGet/S/B=2 xtal, crystalStructStr				// pre-load with current information

	if (stringmatch(ctrlName,"buttonLatticeRevert"))		// close window, do not save numbers
		FillCrystalStructDefault(xtal)						//fill the lattice structure with default values
		a=xtal.a  ;  b=xtal.b  ;  c=xtal.c
		alpha=xtal.alpha  ;  beta=xtal.beta  ;  gam=xtal.gam
		SpaceGroup=xtal.SpaceGroup
		alphaT = xtal.alphaT
		desc = xtal.desc
		dirty = 0
		SetVariable set_SpaceGroup, userdata(oldValue)=num2istr(SpaceGroup),win=$ GetUserData("","","LatticePanelName")
		LatticePanelParamProc("set_SpaceGroup",SpaceGroup,"","")
		StructPut/S xtal, crystalStructStr
	elseif (stringmatch(ctrlName,"buttonLatticeSave") && dirty)
		xtal.a = a  ;  xtal.b = b  ;  xtal.c = c
		xtal.alpha = alpha  ;  xtal.beta = beta  ;  xtal.gam = gam
		xtal.SpaceGroup = SpaceGroup
		xtal.alphaT = alphaT
		xtal.desc = desc
		ForceLatticeToStructure(xtal)
		updateCrystalStructureDefaults(xtal)
		dirty = 0
		LatticePanelParamProc("set_SpaceGroup",SpaceGroup,"","")
	elseif (stringmatch(ctrlName,"buttonLatticeFromFile"))
		if (readCrystalStructure(xtal,""))
			DoAlert 0,"nothing read"
		endif
		a=xtal.a  ;  b=xtal.b  ;  c=xtal.c
		alpha=xtal.alpha  ;  beta=xtal.beta  ;  gam=xtal.gam
		SpaceGroup=xtal.SpaceGroup
		desc=xtal.desc
		alphaT=xtal.alphaT
		dirty = 1
		StructPut/S xtal, crystalStructStr
		LatticePanelParamProc("set_SpaceGroup",SpaceGroup,"","")
	elseif (stringmatch(ctrlName,"buttonPrintLattice"))	// print shown lattice parameters to the history
		xtal.a = a  ;  xtal.b = b  ;  xtal.c = c
		xtal.alpha = alpha  ;  xtal.beta = beta  ;  xtal.gam = gam
		xtal.SpaceGroup = SpaceGroup
		xtal.desc = desc
		xtal.alphaT = alphaT
		ForceLatticeToStructure(xtal)
		print " "
		print_crystalStructure(xtal)
	endif
	return 0
End

//	End of lattice set panel
// =========================================================================
// =========================================================================


// =========================================================================
// =========================================================================
//	Start of reading/writing lattice paremeters to a file

Function LoadCrystal(fname)
	String fname
	STRUCT crystalStructure xtal					// this sruct is filled  by this routine
	readCrystalStructure(xtal,fname)
End


//Function testReadCrystal()
//	STRUCT crystalStructure xtal					// this sruct is filled  by this routine
//	readCrystalStructure(xtal,"")
//	print_crystalStructure(xtal)
//End
Function readCrystalStructure(xtal,fname)
	STRUCT crystalStructure &xtal					// this sruct is filled  by this routine
	String fname

	PathInfo materials
	if (strlen(S_path)<1)							// make it if it does not exist
		NewPath/Z materials, ParseFilePath(1,FunctionPath("MaterialsAreHere"),":",1,0)
	endif
	PathInfo materials
	if (strlen(S_path)<1)							// make it if it does not exist
		PathInfo Igor
		NewPath/Z materials, S_path+"User Procedures:materials"
	endif
	String list = keyStrFromFile(fname,"CrystalStructure","materials")
	if (strlen(list)<1)									// try old style
		return read_cri_fileOLD(xtal,fname)
	endif

	Variable a,b,c,alpha,bet,gam, SpaceGroup, alphaT
	sscanf StringByKey("latticeParameters",list,"="), "{ %g, %g, %g, %g, %g, %g }"  , a,b,c,alpha,bet,gam
	if (V_flag!=6)
		return 1
	endif
	SpaceGroup = str2num(StringByKey("SpaceGroup",list,"="))
	if (numtype(SpaceGroup))
		return 1
	endif
	String unit = StringByKey("lengthUnit",list,"=")
	if (stringmatch(unit,"Ang*") || stringmatch(unit,"�*"))
		a*= 10  ;  b*= 10  ;  c*= 10
	endif
	alphaT = str2num(StringByKey("latticeAlphaT",list,"="))

	xtal.a = a  ;  xtal.b = b  ;  xtal.c = c
	xtal.alpha = alpha  ;  xtal.beta = bet  ;  xtal.gam = gam
	xtal.SpaceGroup = SpaceGroup
	xtal.alphaT = !(alphaT>0) ? 0 : alphaT
	ForceLatticeToStructure(xtal)

	xtal.desc = StringByKey("structureDesc",list,"=")
	if (strlen(xtal.desc)==0)
		xtal.desc = StringByKey("latticeDesc",list,"=")
	endif
	Variable N=0
	Variable i,xx,yy,zz, occ,Debye=0
	String str,item
	do
		item = StringByKey("AtomDesctiption"+num2istr(N+1),list,"=")
		sscanf item, "{%s %g %g %g %g}",str,xx,yy,zz,occ
		if (V_flag!=5)
			sscanf item, "{%s %g %g %g}",str,xx,yy,zz
			if (V_flag!=4)
				break
			endif
			occ = 1
		endif
		xtal.atom[N].name = str
		xtal.atom[N].Zatom = ZfromLabel(str)
		xtal.atom[N].x = xx
		xtal.atom[N].y = yy
		xtal.atom[N].z = zz
		xtal.atom[N].occ = occ
		xtal.atom[N].Debye = Debye
		N += 1
	while(strlen(str) && N<STRUCTURE_ATOMS_MAX-1)
	xtal.N = N

	xtal.Unconventional00=NaN;  xtal.Unconventional01=NaN;  xtal.Unconventional02=NaN	// transform matrix for an unconventional unit cel
	xtal.Unconventional10=NaN;  xtal.Unconventional11=NaN;  xtal.Unconventional12=NaN	// default to a conventional cell
	xtal.Unconventional20=NaN;  xtal.Unconventional21=NaN;  xtal.Unconventional22=NaN
	str = StringByKey("Unconventional",list,"=")
	if (strlen(str))										// found an $Unconventional tag
		Variable u00,u10,u20, u01,u11,u21, u02,u12,u22
		sscanf str,"{ {%g,%g,%g}, {%g,%g,%g}, {%g,%g,%g} }",u00,u10,u20, u01,u11,u21, u02,u12,u22
		if (V_flag==9 && numtype(u00+u10+u20+u01+u11+u21+u02+u12+u22)==0)
			xtal.Unconventional00 = u00;	xtal.Unconventional01 = u01;	xtal.Unconventional02 = u02
			xtal.Unconventional10 = u10;	xtal.Unconventional11 = u11;	xtal.Unconventional12 = u12
			xtal.Unconventional20 = u20;	xtal.Unconventional21 = u21;	xtal.Unconventional22 = u22
 		endif
	endif

	updateCrystalStructureDefaults(xtal)
	if (N<1)
		printf "Failed to Load Crystal Structure from '%s'\r",StringByKey("keyStrFileName",list,"=")
		return 1
	else
		printf "Loaded Crystal Structure from '%s'     using units of '%s'\r",StringByKey("keyStrFileName",list,"="),unit
	endif
	return 0
End
//
Function read_cri_fileOLD(xtal,fname)
	STRUCT crystalStructure &xtal					// this sruct is filled  by this routine
	String fname

	Variable f
	Open/R/M="the .cri file"/T=".cri" f as fname
	if (f==0)
		return 1
	endif

	Variable SpaceGroup, a,b,c,alpha,bet,gam
	String line

	FReadLine f, line
	xtal.desc = ReplaceString("\r",line,"")
	FReadLine f, line
	SpaceGroup = str2num(line)
	if (!(SpaceGroup>=1 && SpaceGroup<=230))
		Close f
		return 1
	endif
	xtal.SpaceGroup = SpaceGroup

	FReadLine f, line
	sscanf line, "%g %g %g  %g %g %g",a,b,c,alpha,bet,gam
	if (V_flag!=6)
		Close f
		return 1
	endif
	xtal.a = a
	xtal.b = b
	xtal.c = c
	xtal.alpha = alpha
	xtal.beta = bet
	xtal.gam = gam

	FReadLine f, line
	Variable N = str2num(line)
	if (!(N>=1 && N<=STRUCTURE_ATOMS_MAX))
		Close f
		return 1
	endif
	xtal.N = N
	Variable i,xx,yy,zz, occ
	String str
	for (i=0;i<N;i+=1)
		FReadLine f, line

		sscanf line, "%s %g %g %g %g",str,xx,yy,zz,occ
		if (V_flag!=5)
			sscanf line, "%s %g %g %g",str,xx,yy,zz
			if (V_flag!=4)
				Close f
				return 1
			endif
			occ = 1
		endif
		xtal.atom[i].name = str
		xtal.atom[i].Zatom = ZfromLabel(str)
		xtal.atom[i].x = xx
		xtal.atom[i].y = yy
		xtal.atom[i].z = zz
		xtal.atom[i].occ = occ
	endfor
	Close f
	if (ItemsInList(GetRTStackInfo(0))<2)
		printf "read structure from file  '%s'\r",S_fileName
	endif
	xtal.Unconventional00=NaN;  xtal.Unconventional01=NaN;  xtal.Unconventional02=NaN	// transform matrix for an unconventional unit cel
	xtal.Unconventional10=NaN;  xtal.Unconventional11=NaN;  xtal.Unconventional12=NaN	// default to a conventional cell
	xtal.Unconventional20=NaN;  xtal.Unconventional21=NaN;  xtal.Unconventional22=NaN
	ForceLatticeToStructure(xtal)					// set recip and direct and makes lattice constants valid
	updateCrystalStructureDefaults(xtal)
	return 0
End
//
Static Function ZfromLabel(symb)		// returns Z for an atomic symbol (NOT case sensitive), used for the atomic strucure factor
	String symb				// atomic symbol
	String symbols = "H;He;Li;Be;B;C;N;O;F;Ne;Na;Mg;Al;Si;P;S;Cl;Ar;"
	symbols += "K;Ca;Sc;Ti;V;Cr;Mn;Fe;Co;Ni;Cu;Zn;Ga;Ge;As;Se;Br;Kr;"
	symbols += "Rb;Sr;Y;Zr;Nb;Mo;Tc;Ru;Rh;Pd;Ag;Cd;In;Sn;Sb;Te;I;Xe;"
	symbols += "Cs;Ba;La;Ce;Pr;Nd;Pm;Sm;Eu;Gd;Tb;Dy;Ho;Er;Tm;Yb;Lu;"
	symbols += "Hf;Ta;W;Re;Os;Ir;Pt;Au;Hg;Tl;Pb;Bi;Po;At;Rn;Fr;Ra;Ac;Th;Pa;U;"
	symbols += "Np;Pu;Am;Cm;Bk;Cf;Es;Fm;Md;No;Lr;Rf;Db;Sg;Bh;Hs;Mt"
	symb = symb[0,1]
	symb[0,0] = UpperStr(symb[0,0])		// ensure first char is upper case
	symb[1,1] = LowerStr(symb[1,1])		// and second character is lower
	Variable c=char2num(symb[1,1])
	if (c<97 || c>122)
		symb = symb[0,0]
	endif
	Variable iz = WhichListItem(symb,symbols)+1
	return ((iz>0) ? iz : NaN)
End
//
//Function testRead()
//	STRUCT crystalStructure xtal					// this sruct is filled  by this routine
//	read_cri_fileOLD(xtal,"")
//	print_crystalStructure(xtal)
//End
//	Al2O3 crystal (hexagonal axis)
//	   167
//	   0.47580   0.47580   1.2991  90.00000  90.00000 120.00000
//	     2
//	Al001    0.00000   0.00000   0.35230   1.00000
//	O0001    0.30640   0.00000   0.25000   1.00000
//
//Function ReadLatticeFromKeyFile(fileName,path,xtal)	// read in the geometry structure from a keyword file
//	String fileName										// full path name to the file
//	String path											// name of an Igor path to use
//	STRUCT crystalStructure &xtal						// the structure to fill from the file
//
//	Variable tempPath = 0
//	if (strlen(path)<1)
//		path = "userMaterials"
//		PathInfo userMaterials
//		if (V_flag)
//		else
//			PathInfo Igor
//			NewPath/Z/Q userMaterials,S_path+"User Procedures:materials:"
//			tempPath = !V_flag
//			if (V_flag)
//				path = "home"							// no materials folder, just look in home
//			endif
//		endif
//	endif
//	String list = keyStrFromFile(fileName,"LatticeFile",path)// read in all of the tagged values into a keyword list
//	if (strlen(list)<1)
//		return 1
//	endif
//	if (tempPath)
//		KillPath/Z $path
//	endif
//
//	Variable a,b,c,alpha,beta,gam, SpaceGroup, alphaT
//	sscanf StringByKey("latticeParameters",list,"="), "{ %g, %g, %g, %g, %g, %g }"  , a,b,c,alpha,beta,gam
//	if (V_flag!=6)
//		return 1
//	endif
//	SpaceGroup = str2num(StringByKey("SpaceGroup",list,"="))
//	if (numtype(SpaceGroup))
//		return 1
//	endif
//	String unit = StringByKey("lengthUnit",list,"=")
//	if (stringmatch(unit,"Ang*"))
//		a*= 10  ;  b*= 10  ;  c*= 10
//	endif
//	alphaT = str2num(StringByKey("latticeAlphaT",list,"="))
//
//	xtal.a = a  ;  xtal.b = b  ;  xtal.c = c
//	xtal.alpha = alpha  ;  xtal.beta = beta  ;  xtal.gam = gam
//	xtal.SpaceGroup = SpaceGroup
//	xtal.desc = StringByKey("latticeDesc",list,"=")
////	xtal.alphaT = !(alphaT>0) ? 0 : alphaT
//	xtal.alphaT = !(abs(alphaT)<0.1) ? 0 : alphaT	// alphaT can be negative, but it must be small
//	ForceLatticeToStructure(xtal)
//	printf "Loaded lattice information from '%s'     using units of '%s'\r",StringByKey("keyStrFileName",list,"="),unit
//	return 0
//End
Static Function/S keyStrFromFile(fname,ftype,path)	// read in all of the tagged values from a file into a keyword list
	String fname									// full path name to file with tagged geometry values
	String ftype									// the required file identifier, included as a tag (ftype is optional)
	String path									// name of Igor path

	Variable refNum
	String fullName=""

	PathInfo/S materials
	GetFileFolderInfo/P=$path/Q/Z fname
	fullName = S_Path
	if (!V_isFile)
		Open/D/M="file with a lattice keyword list"/P=$path/R/T=".xtl" refNum as fname
		fullName = S_fileName
	endif
	if (strlen(fullName)<1)
		return ""
	else
		Open/P=$path/R/Z=1 refNum as fullName
		fullName = S_fileName
	endif
	if (strlen(fullName)<1 || !refNum)
		return ""
	endif
// the above 12 lines should not be necessary, the /Z=2 switch does not work right

	String tagStr,valStr,line
	if (strlen(ftype))							// an ftype is present, so check the file
		FReadLine refNum, line
		extractTagValueFromLine(line,tagStr,valStr)	// check both ways
		if (!stringmatch(tagStr,ftype) && !(stringmatch(tagStr,"filetype") && stringmatch(valStr,ftype)))
			printf "The file must start with '%s', but the first line is '%s'\r",ftype,line
			Close refNum
			return ""
		endif
	endif

	String list = ReplaceStringByKey("keyStrFileName","",fullName,"=")
	Variable i,dollar = char2num("$")
	do
		FReadLine refNum, line
		extractTagValueFromLine(line,tagStr,valStr)
		if (strlen(tagStr))
			// check if tag is already in list, only take the first instance of a tag, not the last
			if (keyInList(tagStr,list,"=",""))	// check if this key is already in list
				continue
			endif
			list = ReplaceStringByKey(tagStr,list,valStr,"=")
		endif
	while (strlen(line))							// go until EOF
	Close refNum
	return list
End
//
Static Function extractTagValueFromLine(line,tagStr,valStr)
	String line										// input line, presumably starting with a %tag
	String &tagStr								// returned
	String &valStr								// returned
	tagStr = ""										// init both to empty
	valStr = ""

	if (char2num(line)!=char2num("$"))		// if it does not starts with a $, do not process
		return 0
	endif

	Variable i = strsearch(line,"//",0)			// strip off comments
	if (i>=0)
		line = line[0,i-1]
	endif
	for (i=0;char2num(line[i+1])>32;i+=1)	// find end of tag, it ends with a space or lower
	endfor
	tagStr = ReplaceString(";",line[1,i],":")
	tagStr = ReplaceString("=",tagStr,"_")
	if (strlen(tagStr)<1)
		return 1
	endif

	for (i=i+1;char2num(line[i])<=32;i+=1)	// find first non-white space
	endfor
	valStr = line[i,Inf]							// value associated with tagStr

	for (i=strlen(valStr)-1;char2num(valStr[i])<=32 && i>0;i-=1)	// strip off trailing whitespace
	endfor
	valStr = ReplaceString(";",valStr[0,i],":")
	valStr = ReplaceString("=",valStr,"_")
	return 1
End

//	End of of reading/writing lattice paremeters to a file
// =========================================================================
// =========================================================================


// =========================================================================
// =========================================================================
//	Start of crystal symmetry stuff

Static Constant TRICLINIC=0,MONOCLINIC=1,ORTHORHOMBIC=2,TETRAGONAL=3,TRIGONAL=4,HEXAGONAL=5,CUBIC=6
Static Constant P_CENTER=0,F_CENTER=1,B_CENTER=2,RHOMBOHEDRAL=3,C_CENTER=4,A_CENTER=5
Static Constant FCC=225,BCC=229,DIA=227,SIMPLE_CUBIC=221,SAPPHIRE=167	// generic Space Group numbers


Function/C getFstruct(h,k,l)				// user interface to getting F for current crystal structure
	Variable h,k,l
	if (numtype(h+k+l))
		h = numtype(h) ? 0 : h
		k = numtype(k) ? 0 : k
		l = numtype(l) ? 2 : l
		Prompt h,"H"
		Prompt k,"K"
		Prompt l,"L"
		DoPrompt "(hkl)",h,k,l
		if (V_flag)
			return cmplx(NaN,NaN)
		endif
		if (numtype(h+k+l))
			return cmplx(NaN,NaN)
		endif
	endif
	STRUCT crystalStructure xtal					// this sruct is filled  by this routine
	FillCrystalStructDefault(xtal)

	Variable/C Fc = Fstruct(xtal,h,k,l)
	Variable Freal=real(Fc),Fimag=imag(Fc)
	printf "F('%s', %d %d %d) = %g %s i%g,      |F|^2 = %g\r",xtal.desc,h,k,l,real(Fc),SelectString(imag(Fc)<0,"+","-"),abs(imag(Fc)),magsqr(Fc)
	return Fc
End


Function/C Fstruct(xtal,h,k,l)
	STRUCT crystalStructure &xtal						// this sruct is filled  by this routine
	Variable h,k,l

	Variable SpaceGroup=xtal.SpaceGroup
	if (!(SpaceGroup>=1 || SpaceGroup<=230) || numtype(h+k+l))
		return cmplx(NaN,NaN)	// bad inputs
	endif
	Variable latticeCentering								// lattice centering, ie face centered, body centered, ...
	Variable multiplicity=1
	Variable/C zero=cmplx(0,0)
	Variable usingHexAxes = (abs(90-xtal.alpha)+abs(90-xtal.beta)+abs(120-xtal.gam))<1e-9
	String sym											// symmetry symbol
	Variable system = latticeSystem(SpaceGroup)
	sym = getSymString(SpaceGroup)					// get sym[]
	latticeCentering = strsearch("PFIRCA",sym[0,0],0)	// takes on number [0,5]
	switch (latticeCentering)
		case F_CENTER:
			if (!ALLOW_FC(h,k,l))
				return zero
			endif
			multiplicity = 4
			break
		case B_CENTER:
			if (!ALLOW_BC(h,k,l))
				return zero
			endif
			multiplicity = 2
			break
		case C_CENTER:
			if (!ALLOW_CC(h,k,l))
				return zero
			endif
			multiplicity = 2
			break
		case A_CENTER:
			if (!ALLOW_AC(h,k,l))
				return zero
			endif
			multiplicity = 2
			break
		case RHOMBOHEDRAL:
			if (usingHexAxes)
				if (!ALLOW_RHOM_HEX(h,k,l))
					return zero
				endif
			endif
			break							// using rhombohedral axes
	endswitch
	if (system==HEXAGONAL)
		if (!ALLOW_HEXAGONAL(h,k,l)) 
			return zero
		endif
	endif

	Variable Freal=0,Fimag=0
	Variable na,i
	Variable  arg
	Variable fatom
	String name
	Variable m,N=xtal.N
	reMakeAtomXYZs(xtal)

	if (N>0)
		for (m=0;m<N;m+=1)
			name="root:Packages:Lattices:atom"+num2istr(m)
			Wave ww = $name
			fatom = xtal.atom[m].Zatom * xtal.atom[m].occ
			na = DimSize(ww,0)
			for (i=0;i<na;i+=1)
				arg = 2*PI*(h*ww[i][0]+k*ww[i][1]+l*ww[i][2])
				Freal += fatom*cos(arg)
				Fimag += fatom*sin(arg)
			endfor
		endfor
	else
		Freal = 1
		Fimag = 0
	endif

	if (system==HEXAGONAL || (usingHexAxes && system==TRIGONAL))
		arg = 2*PI*((h+2*k)/3 + l*0.5)		// heagnal has atoms at (0,0,0) and (1/3, 2/3, 1/2)
		Variable Fr=1. + cos(arg), Fi=sin(arg)
		Variable rr=Freal, ii=Fimag
		Freal = rr*Fr - ii*Fi
		Fimag = rr*Fi + ii*Fr
		//  for hexagonal:
		//	h+2k=3n,		l=even;		F = 4*f			1
		//	h+2k=3n±1,	l=odd;		F = sqrt(3)*f   sqrt(3)/4
		//	h+2k=3n±1,	l=even;		F = f			1/4
		//	h+2k=3n,		l=odd; 		F = 0			0
	endif

	Freal = abs(Freal)<1e-8 ? 0 : Freal*multiplicity
	Fimag = abs(Fimag)<1e-8 ? 0 : Fimag*multiplicity
	return cmplx(Freal,Fimag)
End
//
Function reMakeAtomXYZs(xtal)
	STRUCT crystalStructure &xtal				// this sruct is filled  by this routine
	String wnote=ReplaceStringByKey("ID","",xtal.hashID,"="), name
	Wave ww = root:Packages:Lattices:atom0
	if (WaveExists(ww))							// if first atom has correct hash, assume the rest are OK too
		if (stringmatch(StringByKey("ID",note(ww),"="),xtal.hashID))
			return 0								// waves have correct hash, so return
		endif
	endif
	Variable m
	for (m=0;m<xtal.N;m+=1)					// loop over each atom type
		name="root:Packages:Lattices:atom"+num2istr(m)
		Wave ww = $name
		Make/N=3/O/D $name
		Wave ww = $name
		positionsOfOneAtomType(xtal.SpaceGroup,xtal.atom[m].x,xtal.atom[m].y,xtal.atom[m].z,ww)
		wnote = ReplaceStringByKey("atomType",wnote,xtal.atom[m].name,"=")
		wnote = ReplaceNumberByKey("Zatom",wnote,xtal.atom[m].Zatom,"=")
		wnote = ReplaceNumberByKey("occupy",wnote,xtal.atom[m].occ,"=")
		Note/K ww, wnote
	endfor
	return 0
End
//Function reMakeAtomXYZs(xtal)
//	STRUCT crystalStructure &xtal				// this sruct is filled  by this routine
//	String wnote=ReplaceStringByKey("ID","",xtal.hashID,"="), name
//	Variable m, OK
//	for (m=0;m<xtal.N;m+=1)					// loop over each atom type
//		name="root:Packages:Lattices:atom"+num2istr(m)
//		Wave ww = $name
//		OK = 0
//		if (WaveExists(ww))
//			OK = stringmatch(StringByKey("ID",note(ww),"="),xtal.hashID)
//		endif
//		if (!OK)									// cached arrays do not match the hashID in crystalStructure
//			Make/N=3/O/D $name
//			Wave ww = $name
//			positionsOfOneAtomType(xtal.SpaceGroup,xtal.atom[m].x,xtal.atom[m].y,xtal.atom[m].z,ww)
//			wnote = ReplaceStringByKey("atomType",wnote,xtal.atom[m].name,"=")
//			wnote = ReplaceNumberByKey("Zatom",wnote,xtal.atom[m].Zatom,"=")
//			wnote = ReplaceNumberByKey("occupy",wnote,xtal.atom[m].occ,"=")
//			Note/K ww, wnote
//		endif
//	endfor
//End
//
//Function testFstruct(h,k,l)
//	Variable h,k,l
//	STRUCT crystalStructure xtal				// this sruct is filled  by this routine
////	readCrystalStructure(xtal,"Macintosh HD:Users:tischler:Desktop:new sym calc:al2o3.cri")
////	readCrystalStructure(xtal,"Macintosh HD:Users:tischler:Desktop:new sym calc:si.cri")
////	readCrystalStructure(xtal,"")
////	readCrystalStructure(xtal,"silicon.xtl")
//	FillCrystalStructDefault(xtal)
//
//	Variable/C Fc = Fstruct(xtal,h,k,l)
//	printf "F(%d %d %d) = %g %s i%g,      |F| = %g\r",h,k,l,real(Fc),SelectString(imag(Fc)<0,"+","-"),abs(imag(Fc)),sqrt(magsqr(Fc))
//End
//
Static Function positionsOfOneAtomType(SpaceGroup,xx,yy,zz,xyz)
	Variable SpaceGroup	//Space Group number, from International Tables
	Variable xx,yy,zz		// fractional coords of this kind of atom
	Wave xyz				// list of all equiv posiitions for this atom in fractional coords

	SetSymOpsForSpaceGroup(SpaceGroup)			// ensure existance of symmetry op mats and vecs
	Wave mats = $("root:Packages:Lattices:SymOps:equivXYZM"+num2istr(SpaceGroup))
	Wave bvecs = $("root:Packages:Lattices:SymOps:equivXYZB"+num2istr(SpaceGroup))
	if (!WaveExists(mats) || !WaveExists(bvecs))
		Abort"Unable to get symmetry operations in positionsOfOneAtomType()"
	endif
	Make/N=(3,3)/O/D matTemp_					// temp utiliity waves
	Make/N=3/O/D vecTemp_, vecTempIn_
	Wave mat=matTemp_, bv=vecTemp_, in=vecTempIn_
	Variable m,Neq=NumberByKey("numSymOps", note(mats),"=")
	Redimension/N=(Neq,3) xyz
	in = {xx,yy,zz}
	xyz = NaN
	Variable dup, i,N
	// printf "atom at  %.5f, %.5f, %.5f\r",in[0],in[1],in[2]
	for (m=0,N=0;m<Neq;m+=1)
		mat = mats[m][p][q]
		bv = bvecs[m][p]
		MatrixOp/O rrTemp_ = mat x in + bv
		Wave rr = rrTemp_
		rr += abs(floor(rr))						// translate back in to unit cell, so value in [0,1)
		rr = mod(rr,1)
		for (i=0,dup=0;i<N;i+=1)					// reject duplicates positions
			if (abs(xyz[i][0]-rr[0])+abs(xyz[i][1]-rr[1])+abs(xyz[i][2]-rr[2])<1e-9)
				dup = 1
				break
			endif
		endfor
		if (!dup)									// not a duplicate, so add to the list of positions
			// printf "atom at  %.5f, %.5f, %.5f\r",rr[0],rr[1],rr[2]
			xyz[N][] = rr[q]
			N += 1
		endif
	endfor
	Redimension/N=(N,3) xyz						// remove extra space (since no duplicates)

	Wave Unconventional=root:Packages:Lattices:Unconventional
	if (WaveExists(Unconventional))					// Unconventional exists, transform all the fractional coords
		Wave vec = vecTemp_
		for (i=0;i<N;i+=1)
			vec = xyz[i][p]
			MatrixOp/O vec = Unconventional x vec
			xyz[i][] = vec[q]
		endfor
	endif
	KillWaves/Z matTemp_, vecTemp_, vecTempIn_, rrTemp_
	return N
End


Function allowedHKL(h,k,l,xtal)
	Variable h,k,l
	STRUCT crystalStructure &xtal
	Variable/C Fc = Fstruct(xtal,h,k,l)
	return (magsqr(Fc)/(xtal.N)^2 > 0.01)
End


// returns info about the symmetry of a structure
// sym holds the symmetry info on return, and xyz holds the atom positions.  It returns the number of atom positions put in xyz
// which is always at least 1.  If you call with a bad wave ref for xyz, then it only returns the sym string, and the returned value is 0
Function/S getSymString(SpaceGroup)
	Variable SpaceGroup					//Space Group number, from International Tables
	if (SpaceGroup<1 || SpaceGroup>230)
		return ""							// invalid SpaceGroup number
	endif

	// there are 230 items in this list
	String symms="P1;P-1;P2:b;P21:b;C2:b1;Pm:b;Pc:b1;"
	symms += "Cm:b1;Cc:b1;P2/m:b;P21/m:b;C2/m:b1;P2/c:b1;"
	symms += "P21/c:b1;C2/c:b1;P222;P2221;P21212;P212121;"
	symms += "C2221;C222;F222;I222;I212121;Pmm2;Pmc21;"
	symms += "Pcc2;Pma2;Pca21;Pnc2;Pmn21;Pba2;Pna21;"
	symms += "Pnn2;Cmm2;Cmc21;Ccc2;Amm2;Abm2;Ama2;Aba2;"
	symms += "Fmm2;Fdd2;Imm2;Iba2;Ima2;Pmmm;Pnnn:1;Pccm;"
	symms += "Pban:1;Pmma;Pnna;Pmna;Pcca;Pbam;Pccn;Pbcm;"
	symms += "Pnnm;Pmmn:1;Pbcn;Pbca;Pnma;Cmcm;Cmca;Cmmm;"
	symms += "Cccm;Cmma;Ccca:1;Fmmm;Fddd:1;Immm;Ibam;Ibca;"
	symms += "Imma;P4;P41;P42;P43;I4;I41;P-4;I-4;"
	symms += "P4/m;P42/m;P4/n:1;P42/n:1;I4/m;I41/a:1;P422;"
	symms += "P4212;P4122;P41212;P4222;P42212;P4322;P43212;"
	symms += "I422;I4122;P4mm;P4bm;P42cm;P42nm;P4cc;"
	symms += "P4nc;P42mc;P42bc;I4mm;I4cm;I41md;I41cd;"
	symms += "P-42m;P-42c;P-421m;P-421c;P-4m2;P-4c2;P-4b2;"
	symms += "P-4n2;I-4m2;I-4c2;I-42m;I-42d;P4/mmm;P4/mcc;"
	symms += "P4/nbm:1;P4/nnc:1;P4/mbm;P4/mnc;P4/nmm:1;P4/ncc:1;"
	symms += "P42/mmc;P42/mcm;P42/nbc:1;P42/nnm:1;P42/mbc;P42/mnm;"
	symms += "P42/nmc:1;P42/ncm:1;I4/mmm;I4/mcm;I41/amd:1;"
	symms += "I41/acd:1;P3;P31;P32;R3:H;P-3;R-3:H;P312;"
	symms += "P321;P3112;P3121;P3212;P3221;R32:H;P3m1;P31m;"
	symms += "P3c1;P31c;R3m:H;R3c:H;P-31m;P-31c;P-3m1;P-3c1;"
	symms += "R-3m:H;R-3c:H;P6;P61;P65;P62;P64;P63;P-6;"
	symms += "P6/m;P63/m;P622;P6122;P6522;P6222;P6422;P6322;"
	symms += "P6mm;P6cc;P63cm;P63mc;P-6m2;P-6c2;P-62m;P-62c;"
	symms += "P6/mmm;P6/mcc;P63/mcm;P63/mmc;P23;F23;I23;P213;"
	symms += "I213;Pm-3;Pn-3:1;Fm-3;Fd-3:1;Im-3;Pa-3;Ia-3;"
	symms += "P432;P4232;F432;F4132;I432;P4332;P4132;I4132;"
	symms += "P-43m;F-43m;I-43m;P-43n;F-43c;I-43d;Pm-3m;"
	symms += "Pn-3n:1;Pm-3n;Pn-3m:1;Fm-3m;Fm-3c;Fd-3m:1;Fd-3c:1;"
	symms += "Im-3m;Ia-3d;"
	return StringFromList(SpaceGroup-1,symms)	// set the symmetry symbol
End


Static Function latticeSystem(SpaceGroup)
	Variable SpaceGroup				//Space Group number, from International Tables
	if (SpaceGroup>230)
		return -1					  	 // invalid
	elseif (SpaceGroup>=195)
		return CUBIC
	elseif (SpaceGroup>=168)
		return HEXAGONAL
	elseif (SpaceGroup>=143)
		return TRIGONAL				// Trigonal, (using the hexagonal cell axes)
	elseif (SpaceGroup>=75)
		return TETRAGONAL
	elseif (SpaceGroup>=16)
		return ORTHORHOMBIC
	elseif (SpaceGroup>=3)
		return MONOCLINIC
	elseif  (SpaceGroup>0)
		return TRICLINIC
	endif
	return -1							// invalid
End



//	#define ALLOW_FC(H,K,L) (!(((H)+(K))%2) && !(((K)+(L))%2))		// H,K,L all even or all odd
//	#define ALLOW_BC(H,K,L) (!(((H)+(K)+(L))%2))					// !mod(round(h+k+l),2)
//	#define ALLOW_CC(H,K,L) (!((H)+(K))%2)							// !mod(round(h+k),2)
//	#define ALLOW_AC(H,K,L) (!((K)+(L))%2)							// !mod(round(k+l),2)
//	#define ALLOW_RHOM_HEX(H,K,L) (((-(H)+(K)+(L))%3)==0 || (((H)-(K)+(L))%3)==0)   // allowed are -H+K+L=3n or H-K+L=3n
//	#define ALLOW_HEXAGONAL(H,K,L) ((((H)+2*(K))%3) || !((L)%2))   // forbidden are: H+2K=3N with L odd
//
Static Function ALLOW_FC(h,k,l)				// for face-centered, hkl must be all even or all odd
	Variable h,k,l
	return !mod(h+k,2) && !mod(k+l,2)
End
//
Static Function ALLOW_BC(h,k,l)				// for body-centered, !mod(round(h+k+l),2)
	Variable h,k,l
	return !mod(round(h+k+l),2)
End
//
Static Function ALLOW_CC(h,k,l)				// for C-centered, !mod(round(h+k),2)
	Variable h,k,l
	return !mod(round(h+k),2)
End
//
Static Function ALLOW_AC(h,k,l)				// for A-centered, !mod(round(k+l),2)
	Variable h,k,l
	return !mod(round(k+l),2)
End
//
Static Function ALLOW_RHOM_HEX(h,k,l)		// for rhombohedral hexagonal, allowed are -H+K+L=3n or H-K+L=3n
	Variable h,k,l
	return !mod(-h+k+l,3) || !mod(h-k+l,3)
End
//
Static Function ALLOW_HEXAGONAL(h,k,l)		// for hexagonal, // forbidden are: H+2K=3N with L odd
	Variable h,k,l
	return mod(h+2*k,3) || !mod(l,2)
End

//	End of crystal symmetry stuff
// =========================================================================
// =========================================================================

// =========================================================================
// =========================================================================
//	Start of some utility routines

// changes hkl[3] to the lowest order hkl, ignores whether a reflection is allowed, just removes common factors
Function lowestOrderHKL(h,k,l)
	Variable &h,&k,&l							// these hkl are returned with all common factors removed
	Variable maxDiv								// max possible divisor
	Variable i
	maxDiv = max(abs(h),abs(k))				// the maximum divisor cannot be bigger than the smallest of hkl
	maxDiv = max(maxDiv,abs(l))
	for (i=maxDiv;i>=2;i-=1)					// check all divisorts in range [2, maxDiv]
		if (mod(h,i) || mod(k,i) || mod(l,i))	// i is not a factor of h, k, and l
			continue
		endif
		h /= i
		k /= i
		l /= i
	endfor
End


// changes hkl[3] to the lowest order allowed hkl (ie for FCC, 0,0,12 -> 002 not 001
Function lowestAllowedHKL(h,k,l,SpaceGroup)
	Variable &h,&k,&l
	Variable SpaceGroup					// number denoting Space Group, see "#define" for FCC, BCC, etc.

	STRUCT crystalStructure xtal			// temporary crystal structure

	xtal.SpaceGroup = SpaceGroup
	xtal.alpha=80 ; xtal.beta=80 ; xtal.gam=80	// just needed to prevent errors
	xtal.a=1
	xtal.b=1
	xtal.c=1
	ForceLatticeToStructure(xtal)
	xtal.N = 1
	xtal.atom[0].x = 0
	xtal.atom[0].y = 0
	xtal.atom[0].z = 0
	xtal.atom[0].Zatom = 1				// Z of the atom
	xtal.atom[0].occ = 1

	Variable i
	Variable hh=h, kk=k, ll=l
	lowestOrderHKL(hh,kk,ll)			// remove all common factors

	for (i=1;i<16;i+=1)					// never need more than 16 to reach an allowed reflection
		h = i*hh							// try each of the multiples to reach an allowed reflection
		k = i*kk
		l = i*ll
		if (allowedHKL(h,k,l,xtal))
			return 0
		endif
	endfor
	return 0
End


Function/S hkl2str(h,k,l)				// format h,k,l into a string of acceptable minimal length
	Variable h,k,l
	if (numtype(h+k+l))
		return "(NaN,NaN,NaN)"
	endif
	String hkl
	if (abs(mod(h,1))+abs(mod(k,1))+abs(mod(l,1)) > 1e-6)	// hkl are non-integers
		sprintf hkl,"%g, %g, %g",h,k,l
	elseif (k<0 || l<0)
		sprintf hkl,"%.0f, %.0f, %.0f",h,k,l
	elseif (abs(h)<10 && k<10 && l<10)
		sprintf hkl,"%.0f%.0f%.0f",h,k,l
	else
		sprintf hkl,"%.0f %.0f %.0f",h,k,l
	endif
	return hkl
End


Function/T minus2bar(str)		// change an Igor string that has minuses to one using a bar over following character
	String str
	String bs
	Variable i
	for (i=0; i<=9 && strsearch(str,"-",0)>=0; i+=1)
		sprintf bs, "\\[%d\\SÑ\\M\\X%d",i,i
		str = ReplaceString("-",str,bs,0,1)
	endfor
	return str
End


Static Function placesOfPrecision(a)		// number of significant figures in a number
	Variable a
	a = roundSignificant(abs(a),17)
	Variable i
	for (i=1;i<18;i+=1)
		if (abs(a-roundSignificant(a,i))/a<1e-15)
			break
		endif
	endfor
	return i
End

//	End of utility
// =========================================================================
// =========================================================================


//
//	================================================================================
//
//			This section creates the wave definitions used in    InitLatticeSymPackage()
//



Function InitLatticeSymPackage()								// used to initialize this package
	NewDataFolder/O root:Packages
	NewDataFolder/O root:Packages:Lattices
	NewDataFolder/O root:Packages:Lattices:SymOps
End



//
//	================================================================================
//
//			This section is for making the matricies for the symmetry operations for Space Groups
//



Static Function SetSymOpsForSpaceGroup(SpaceGroup)		// make the symmetry operations mats and vecs (if needed), returns number of operations
	Variable SpaceGroup
	Wave mats = $("root:Packages:Lattices:SymOps:equivXYZM"+num2istr(SpaceGroup))
	Wave bvecs = $("root:Packages:Lattices:SymOps:equivXYZB"+num2istr(SpaceGroup))
	Variable numSymOps
	if (WaveExists(mats) && WaveExists(bvecs))				// check if they exist
		numSymOps = NumberByKey("numSymOps",note(mats),"=")
		return numtype(numSymOps) ? 0 : numSymOps		// do not re-make, just return number of operations
	endif
	if (SpaceGroup<1 || 230<SpaceGroup)						// Space Group must be in range [1, 230]
		DoAlert 0, "Bad Space Group = "+num2str(SpaceGroup)+", in SetSymOpsForSpaceGroup"
		return 1
	endif
	if (!DataFolderExists("root:Packages:Lattices:SymOps:"))
		DoAlert 0, "Cannot make symmetry matricies, the target data folder does not exist"
		print "Cannot make symmetry matricies, the target data folder does not exist,  'root:Packages:Lattices:SymOps:'\r"
		return 0
	endif

	String symOperations=setSymLine(SpaceGroup)			// a string like "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z"
	Variable i,N=ItemsInList(symOperations)
	String wName = "root:Packages:Lattices:SymOps:equivXYZM"+num2istr(SpaceGroup)
	Make/N=(N,3,3)/O/B $wName								// this only holds 0 or ±1
	Wave equivM = $wName
	wName = "root:Packages:Lattices:SymOps:equivXYZB"+num2istr(SpaceGroup)
	Make/N=(N,3)/O/D $wName
	Wave equivB = $wName

	Make/N=(3,3)/O/D mat_SymItem
	Make/N=3/O/D vec_SymItem
	Wave mat=mat_SymItem, vec=vec_SymItem
	Variable err = 0
	for (i=0;i<N;i+=1)
		err = err || make1MatrixAndVecFromSymLine(StringFromList(i,symOperations))
		equivM[i][][] = mat[q][r]
		equivB[i][] = vec[q]
	endfor
	KillWaves/Z mat_SymItem,vec_SymItem
	if (err)
		Abort "error making symmetry matricies in SetSymOpsForSpaceGroup()"
	endif
	Note/K equivM, ReplaceNumberByKey("numSymOps","",N,"=")
	Note/K equivB, ReplaceNumberByKey("numSymOps","",N,"=")
	return N
End
//
// makes one matrix[3][3] and one vector[3] from the expression like "x+1/3,y+2/3,z+2/3"
Static Function make1MatrixAndVecFromSymLine(symItem)		// returns result in mat_SymItem and vec_SymItem, return value is error flag
	String symItem													// something like "-x+1/2,-y+1/2,z"
	Wave mat=mat_SymItem, vec=vec_SymItem
	if (!WaveExists(mat) || !WaveExists(vec))
		Make/N=(3,3)/O/D mat_SymItem
		Make/N=3/O/D vec_SymItem
		Wave mat=mat_SymItem, vec=vec_SymItem
	endif

	Variable m0,m1,m2, b
	Variable i, err=0
	for (i=0;i<3;i+=1)
		err = err || ParseOneSymEquation(StringFromList(i,symItem,","),m0,m1,m2,b)
		mat[i][0] = m0
		mat[i][1] = m1
		mat[i][2] = m2
		vec[i] = b
	endfor
	return err
End
//
Static Function ParseOneSymEquation(expression,m0,m1,m2,b)		// parse one expression of form "-x+y"  or "-x", or "-x+y, etc.
	String expression
	Variable &m0,&m1,&m2, &b
	m0=0  ;  m1=0  ;  m2=0 ; b=0	// init, some may not be set in the strswitch
	Variable num=NaN, denom=NaN

	Variable i,is, N=strlen(expression), op
	for (i=0, op=1,is=1; i<N && op; i+=1)
		strswitch(expression[i,i])
			case "-":
				is = -1
				break
			case "+":
				is = 1
				break
			case "x":
				m0 = is
				is = 1
				break
			case "y":
				m1 = is
				is = 1
				break
			case "z":
				m2 = is
				is = 1
				break
			default:					//should be a digit
				op=0					// halt loop, and set pointer back
				num=str2num(expression[i,Inf])
		endswitch
	endfor
	if (op)								// ran out of things to do, no b
		return 0
	endif
	if (char2num("/")!=char2num(expression[i]))
		DoAlert 0, "ERROR"
		print "error on expression = ",expression
		return 1
	endif
	b = is * num/str2num(expression[i+1]) // eval the constant
	if (numtype(b))
		DoAlert 0, "ERROR"
		print "error on expression = ",expression
		return 1
	endif
	return 0							// return no-error
End
//Function testParseOne()
//	String expression = "-x+y-2/3"
//	Variable m0,m1,m2, b
//	ParseOneSymEquation(expression,m0,m1,m2,b)
//	print expression,"    ",m0,"  ",m1,"  ",m2,"  ",b
//	expression = "x-y"
//	ParseOneSymEquation(expression,m0,m1,m2,b)
//	print expression,"    ",m0,"  ",m1,"  ",m2,"  ",b
//	expression = "-z-1/4"
//	ParseOneSymEquation(expression,m0,m1,m2,b)
//	print expression,"    ",m0,"  ",m1,"  ",m2,"  ",b
//End
//
//
//
//Window Table_symLines() : Table
//	PauseUpdate; Silent 1		// building window...
//	Edit/W=(5,44,1379,833) numOps.xy,symLines.y
//	ModifyTable format(Point)=1,width(Point)=36,alignment(symLines.y)=0,width(symLines.y)=1248
//	ModifyTable width(numOps.x)=48,alignment(numOps.d)=1,width(numOps.d)=54
//EndMacro
//
Static Function/T setSymLine(SpaceGroup)
	Variable SpaceGroup									// Space Group number [1,230]
	if (!(1<=SpaceGroup && SpaceGroup<=230))		// invalid
		return ""
	endif
	Make/N=230/O/T symLines_temp__
	Wave/T symLines = symLines_temp__
	symLines[0]   = "x,y,z"
	symLines[1]   = "x,y,z;-x,-y,-z"
	symLines[2]   = "x,y,z;-x,y,-z"
	symLines[3]   = "x,y,z;-x,y+1/2,-z"
	symLines[4]   = "x,y,z;-x,y,-z;x+1/2,y+1/2,z;-x+1/2,y+1/2,-z"
	symLines[5]   = "x,y,z;x,-y,z"
	symLines[6]   = "x,y,z;x,-y,z+1/2"
	symLines[7]   = "x,y,z;x,-y,z;x+1/2,y+1/2,z;x+1/2,-y+1/2,z"
	symLines[8]   = "x,y,z;x,-y,z+1/2;x+1/2,y+1/2,z;x+1/2,-y+1/2,z+1/2"
	symLines[9]   = "x,y,z;-x,y,-z;-x,-y,-z;x,-y,z"
	symLines[10]   = "x,y,z;-x,y+1/2,-z;-x,-y,-z;x,-y+1/2,z"
	symLines[11]   = "x,y,z;-x,y,-z;-x,-y,-z;x,-y,z;x+1/2,y+1/2,z;-x+1/2,y+1/2,-z;-x+1/2,-y+1/2,-z;x+1/2,-y+1/2,z"
	symLines[12]   = "x,y,z;-x,y,-z+1/2;-x,-y,-z;x,-y,z+1/2"
	symLines[13]   = "x,y,z;-x,y+1/2,-z+1/2;-x,-y,-z;x,-y+1/2,z+1/2"
	symLines[14]   = "x,y,z;-x,y,-z+1/2;-x,-y,-z;x,-y,z+1/2;x+1/2,y+1/2,z;-x+1/2,y+1/2,-z+1/2;-x+1/2,-y+1/2,-z;x+1/2,-y+1/2,z+1/2"
	symLines[15]   = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z"
	symLines[16]   = "x,y,z;-x,-y,z+1/2;-x,y,-z+1/2;x,-y,-z"
	symLines[17]   = "x,y,z;-x,-y,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z"
	symLines[18]   = "x,y,z;-x+1/2,-y,z+1/2;-x,y+1/2,-z+1/2;x+1/2,-y+1/2,-z"
	symLines[19]   = "x,y,z;-x,-y,z+1/2;-x,y,-z+1/2;x,-y,-z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,-z"
	symLines[20]   = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z"
	symLines[21]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;-x,y+1/2,-z+1/2;"
	symLines[21] += "x,-y+1/2,-z+1/2;x+1/2,y,z+1/2;-x+1/2,-y,z+1/2;-x+1/2,y,-z+1/2;x+1/2,-y,-z+1/2;"
	symLines[21] += "x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z"
	symLines[22]   = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;x+1/2,y+1/2,z+1/2;-x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,-z+1/2"
	symLines[23]   = "x,y,z;-x+1/2,-y,z+1/2;-x,y+1/2,-z+1/2;x+1/2,-y+1/2,-z;x+1/2,y+1/2,z+1/2;-x,-y+1/2,z;-x+1/2,y,-z;x,-y,-z+1/2"
	symLines[24]   = "x,y,z;-x,-y,z;x,-y,z;-x,y,z"
	symLines[25]   = "x,y,z;-x,-y,z+1/2;x,-y,z+1/2;-x,y,z"
	symLines[26]   = "x,y,z;-x,-y,z;x,-y,z+1/2;-x,y,z+1/2"
	symLines[27]   = "x,y,z;-x,-y,z;x+1/2,-y,z;-x+1/2,y,z"
	symLines[28]   = "x,y,z;-x,-y,z+1/2;x+1/2,-y,z;-x+1/2,y,z+1/2"
	symLines[29]   = "x,y,z;-x,-y,z;x,-y+1/2,z+1/2;-x,y+1/2,z+1/2"
	symLines[30]   = "x,y,z;-x+1/2,-y,z+1/2;x+1/2,-y,z+1/2;-x,y,z"
	symLines[31]   = "x,y,z;-x,-y,z;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z"
	symLines[32]   = "x,y,z;-x,-y,z+1/2;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z+1/2"
	symLines[33]   = "x,y,z;-x,-y,z;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2"
	symLines[34]   = "x,y,z;-x,-y,z;x,-y,z;-x,y,z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z"
	symLines[35]   = "x,y,z;-x,-y,z+1/2;x,-y,z+1/2;-x,y,z;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z+1/2;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z"
	symLines[36]   = "x,y,z;-x,-y,z;x,-y,z+1/2;-x,y,z+1/2;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2"
	symLines[37]   = "x,y,z;-x,-y,z;x,-y,z;-x,y,z;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;x,-y+1/2,z+1/2;-x,y+1/2,z+1/2"
	symLines[38]   = "x,y,z;-x,-y,z;x,-y+1/2,z;-x,y+1/2,z;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;x,-y,z+1/2;-x,y,z+1/2"
	symLines[39]   = "x,y,z;-x,-y,z;x+1/2,-y,z;-x+1/2,y,z;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2"
	symLines[40]   = "x,y,z;-x,-y,z;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;x+1/2,-y,z+1/2;-x+1/2,y,z+1/2"
	symLines[41]    = "x,y,z;-x,-y,z;x,-y,z;-x,y,z;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;x,-y+1/2,z+1/2;"
	symLines[41] += "-x,y+1/2,z+1/2;x+1/2,y,z+1/2;-x+1/2,-y,z+1/2;x+1/2,-y,z+1/2;-x+1/2,y,z+1/2;"
	symLines[41] += "x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z"
	symLines[42]    = "x,y,z;-x,-y,z;x+1/4,-y+1/4,z+1/4;-x+1/4,y+1/4,z+1/4;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;"
	symLines[42] += "x+1/4,-y+3/4,z+3/4;-x+1/4,y+3/4,z+3/4;x+1/2,y,z+1/2;-x+1/2,-y,z+1/2;x+3/4,-y+1/4,z+3/4;"
	symLines[42] += "-x+3/4,y+1/4,z+3/4;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;x+3/4,-y+3/4,z+1/4;-x+3/4,y+3/4,z+1/4"
	symLines[43]   = "x,y,z;-x,-y,z;x,-y,z;-x,y,z;x+1/2,y+1/2,z+1/2;-x+1/2,-y+1/2,z+1/2;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2"
	symLines[44]   = "x,y,z;-x,-y,z;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z;x+1/2,y+1/2,z+1/2;-x+1/2,-y+1/2,z+1/2;x,-y,z+1/2;-x,y,z+1/2"
	symLines[45]   = "x,y,z;-x,-y,z;x+1/2,-y,z;-x+1/2,y,z;x+1/2,y+1/2,z+1/2;-x+1/2,-y+1/2,z+1/2;x,-y+1/2,z+1/2;-x,y+1/2,z+1/2"
	symLines[46]   = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;-x,-y,-z;x,y,-z;x,-y,z;-x,y,z"
	symLines[47]   = "x,y,z;-x+1/2,-y+1/2,z;-x+1/2,y,-z+1/2;x,-y+1/2,-z+1/2;-x,-y,-z;x+1/2,y+1/2,-z;x+1/2,-y,z+1/2;-x,y+1/2,z+1/2"
	symLines[48]   = "x,y,z;-x,-y,z;-x,y,-z+1/2;x,-y,-z+1/2;-x,-y,-z;x,y,-z;x,-y,z+1/2;-x,y,z+1/2"
	symLines[49]   = "x,y,z;-x+1/2,-y+1/2,z;-x+1/2,y,-z;x,-y+1/2,-z;-x,-y,-z;x+1/2,y+1/2,-z;x+1/2,-y,z;-x,y+1/2,z"
	symLines[50]   = "x,y,z;-x+1/2,-y,z;-x,y,-z;x+1/2,-y,-z;-x,-y,-z;x+1/2,y,-z;x,-y,z;-x+1/2,y,z"
	symLines[51]   = "x,y,z;-x+1/2,-y,z;-x+1/2,y+1/2,-z+1/2;x,-y+1/2,-z+1/2;-x,-y,-z;x+1/2,y,-z;x+1/2,-y+1/2,z+1/2;-x,y+1/2,z+1/2"
	symLines[52]   = "x,y,z;-x+1/2,-y,z+1/2;-x+1/2,y,-z+1/2;x,-y,-z;-x,-y,-z;x+1/2,y,-z+1/2;x+1/2,-y,z+1/2;-x,y,z"
	symLines[53]   = "x,y,z;-x+1/2,-y,z;-x,y,-z+1/2;x+1/2,-y,-z+1/2;-x,-y,-z;x+1/2,y,-z;x,-y,z+1/2;-x+1/2,y,z+1/2"
	symLines[54]   = "x,y,z;-x,-y,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;-x,-y,-z;x,y,-z;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z"
	symLines[55]   = "x,y,z;-x+1/2,-y+1/2,z;-x,y+1/2,-z+1/2;x+1/2,-y,-z+1/2;-x,-y,-z;x+1/2,y+1/2,-z;x,-y+1/2,z+1/2;-x+1/2,y,z+1/2"
	symLines[56]   = "x,y,z;-x,-y,z+1/2;-x,y+1/2,-z+1/2;x,-y+1/2,-z;-x,-y,-z;x,y,-z+1/2;x,-y+1/2,z+1/2;-x,y+1/2,z"
	symLines[57]   = "x,y,z;-x,-y,z;-x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,-z+1/2;-x,-y,-z;x,y,-z;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2"
	symLines[58]   = "x,y,z;-x+1/2,-y+1/2,z;-x,y+1/2,-z;x+1/2,-y,-z;-x,-y,-z;x+1/2,y+1/2,-z;x,-y+1/2,z;-x+1/2,y,z"
	symLines[59]   = "x,y,z;-x+1/2,-y+1/2,z+1/2;-x,y,-z+1/2;x+1/2,-y+1/2,-z;-x,-y,-z;x+1/2,y+1/2,-z+1/2;x,-y,z+1/2;-x+1/2,y+1/2,z"
	symLines[60]   = "x,y,z;-x+1/2,-y,z+1/2;-x,y+1/2,-z+1/2;x+1/2,-y+1/2,-z;-x,-y,-z;x+1/2,y,-z+1/2;x,-y+1/2,z+1/2;-x+1/2,y+1/2,z"
	symLines[61]   = "x,y,z;-x+1/2,-y,z+1/2;-x,y+1/2,-z;x+1/2,-y+1/2,-z+1/2;-x,-y,-z;x+1/2,y,-z+1/2;x,-y+1/2,z;-x+1/2,y+1/2,z+1/2"
	symLines[62]    = "x,y,z;-x,-y,z+1/2;-x,y,-z+1/2;x,-y,-z;-x,-y,-z;x,y,-z+1/2;x,-y,z+1/2;-x,y,z;"
	symLines[62] += "x+1/2,y+1/2,z;-x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,-z;-x+1/2,-y+1/2,-z;"
	symLines[62] += "x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z"
	symLines[63]    = "x,y,z;-x,-y+1/2,z+1/2;-x,y+1/2,-z+1/2;x,-y,-z;-x,-y,-z;x,y+1/2,-z+1/2;x,-y+1/2,z+1/2;"
	symLines[63] += "-x,y,z;x+1/2,y+1/2,z;-x+1/2,-y,z+1/2;-x+1/2,y,-z+1/2;x+1/2,-y+1/2,-z;-x+1/2,-y+1/2,-z;"
	symLines[63] += "x+1/2,y,-z+1/2;x+1/2,-y,z+1/2;-x+1/2,y+1/2,z"
	symLines[64]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;-x,-y,-z;x,y,-z;x,-y,z;-x,y,z;x+1/2,y+1/2,z;"
	symLines[64] += "-x+1/2,-y+1/2,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;-x+1/2,-y+1/2,-z;x+1/2,y+1/2,-z;"
	symLines[64] += "x+1/2,-y+1/2,z;-x+1/2,y+1/2,z"
	symLines[65]    = "x,y,z;-x,-y,z;-x,y,-z+1/2;x,-y,-z+1/2;-x,-y,-z;x,y,-z;x,-y,z+1/2;-x,y,z+1/2;"
	symLines[65] += "x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,-z+1/2;-x+1/2,-y+1/2,-z;"
	symLines[65] += "x+1/2,y+1/2,-z;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2"
	symLines[66]    = "x,y,z;-x,-y+1/2,z;-x,y+1/2,-z;x,-y,-z;-x,-y,-z;x,y+1/2,-z;x,-y+1/2,z;-x,y,z;"
	symLines[66] += "x+1/2,y+1/2,z;-x+1/2,-y,z;-x+1/2,y,-z;x+1/2,-y+1/2,-z;-x+1/2,-y+1/2,-z;"
	symLines[66] += "x+1/2,y,-z;x+1/2,-y,z;-x+1/2,y+1/2,z"
	symLines[67]    = "x,y,z;-x+1/2,-y,z;-x,y,-z+1/2;x+1/2,-y,-z+1/2;-x,-y,-z;x+1/2,y,-z;x,-y,z+1/2;"
	symLines[67] += "-x+1/2,y,z+1/2;x+1/2,y+1/2,z;-x,-y+1/2,z;-x+1/2,y+1/2,-z+1/2;x,-y+1/2,-z+1/2;"
	symLines[67] += "-x+1/2,-y+1/2,-z;x,y+1/2,-z;x+1/2,-y+1/2,z+1/2;-x,y+1/2,z+1/2"
	symLines[68]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;-x,-y,-z;x,y,-z;x,-y,z;-x,y,z;x,y+1/2,z+1/2;"
	symLines[68] += "-x,-y+1/2,z+1/2;-x,y+1/2,-z+1/2;x,-y+1/2,-z+1/2;-x,-y+1/2,-z+1/2;x,y+1/2,-z+1/2;"
	symLines[68] += "x,-y+1/2,z+1/2;-x,y+1/2,z+1/2;x+1/2,y,z+1/2;-x+1/2,-y,z+1/2;-x+1/2,y,-z+1/2;"
	symLines[68] += "x+1/2,-y,-z+1/2;-x+1/2,-y,-z+1/2;x+1/2,y,-z+1/2;x+1/2,-y,z+1/2;-x+1/2,y,z+1/2;"
	symLines[68] += "x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;-x+1/2,-y+1/2,-z;"
	symLines[68] += "x+1/2,y+1/2,-z;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z"
	symLines[69]    = "x,y,z;-x+3/4,-y+3/4,z;-x+3/4,y,-z+3/4;x,-y+3/4,-z+3/4;-x,-y,-z;x+1/4,y+1/4,-z;"
	symLines[69] += "x+1/4,-y,z+1/4;-x,y+1/4,z+1/4;x,y+1/2,z+1/2;-x+3/4,-y+1/4,z+1/2;-x+3/4,y+1/2,-z+1/4;"
	symLines[69] += "x,-y+1/4,-z+1/4;-x,-y+1/2,-z+1/2;x+1/4,y+3/4,-z+1/2;x+1/4,-y+1/2,z+3/4;"
	symLines[69] += "-x,y+3/4,z+3/4;x+1/2,y,z+1/2;-x+1/4,-y+3/4,z+1/2;-x+1/4,y,-z+1/4;x+1/2,-y+3/4,-z+1/4;"
	symLines[69] += "-x+1/2,-y,-z+1/2;x+3/4,y+1/4,-z+1/2;x+3/4,-y,z+3/4;-x+1/2,y+1/4,z+3/4;x+1/2,y+1/2,z;"
	symLines[69] += "-x+1/4,-y+1/4,z;-x+1/4,y+1/2,-z+3/4;x+1/2,-y+1/4,-z+3/4;-x+1/2,-y+1/2,-z;"
	symLines[69] += "x+3/4,y+3/4,-z;x+3/4,-y+1/2,z+1/4;-x+1/2,y+3/4,z+1/4"
	symLines[70]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;-x,-y,-z;x,y,-z;x,-y,z;-x,y,z;x+1/2,y+1/2,z+1/2;"
	symLines[70] += "-x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,-z+1/2;-x+1/2,-y+1/2,-z+1/2;"
	symLines[70] += "x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2"
	symLines[71]    = "x,y,z;-x,-y,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;-x,-y,-z;x,y,-z;x+1/2,-y+1/2,z;"
	symLines[71] += "-x+1/2,y+1/2,z;x+1/2,y+1/2,z+1/2;-x+1/2,-y+1/2,z+1/2;-x,y,-z+1/2;x,-y,-z+1/2;"
	symLines[71] += "-x+1/2,-y+1/2,-z+1/2;x+1/2,y+1/2,-z+1/2;x,-y,z+1/2;-x,y,z+1/2"
	symLines[72]    = "x,y,z;-x+1/2,-y,z+1/2;-x,y+1/2,-z+1/2;x+1/2,-y+1/2,-z;-x,-y,-z;x+1/2,y,-z+1/2;"
	symLines[72] += "x,-y+1/2,z+1/2;-x+1/2,y+1/2,z;x+1/2,y+1/2,z+1/2;-x,-y+1/2,z;-x+1/2,y,-z;"
	symLines[72] += "x,-y,-z+1/2;-x+1/2,-y+1/2,-z+1/2;x,y+1/2,-z;x+1/2,-y,z;-x,y,z+1/2"
	symLines[73]    = "x,y,z;-x,-y+1/2,z;-x,y+1/2,-z;x,-y,-z;-x,-y,-z;x,y+1/2,-z;x,-y+1/2,z;-x,y,z;"
	symLines[73] += "x+1/2,y+1/2,z+1/2;-x+1/2,-y,z+1/2;-x+1/2,y,-z+1/2;x+1/2,-y+1/2,-z+1/2;-x+1/2,-y+1/2,-z+1/2;"
	symLines[73] += "x+1/2,y,-z+1/2;x+1/2,-y,z+1/2;-x+1/2,y+1/2,z+1/2"
	symLines[74]   = "x,y,z;-x,-y,z;-y,x,z;y,-x,z"
	symLines[75]   = "x,y,z;-x,-y,z+1/2;-y,x,z+1/4;y,-x,z+3/4"
	symLines[76]   = "x,y,z;-x,-y,z;-y,x,z+1/2;y,-x,z+1/2"
	symLines[77]   = "x,y,z;-x,-y,z+1/2;-y,x,z+3/4;y,-x,z+1/4"
	symLines[78]   = "x,y,z;-x,-y,z;-y,x,z;y,-x,z;x+1/2,y+1/2,z+1/2;-x+1/2,-y+1/2,z+1/2;-y+1/2,x+1/2,z+1/2;y+1/2,-x+1/2,z+1/2"
	symLines[79]   = "x,y,z;-x+1/2,-y+1/2,z+1/2;-y,x+1/2,z+1/4;y+1/2,-x,z+3/4;x+1/2,y+1/2,z+1/2;-x,-y,z;-y+1/2,x,z+3/4;y,-x+1/2,z+1/4"
	symLines[80]   = "x,y,z;-x,-y,z;y,-x,-z;-y,x,-z"
	symLines[81]   = "x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;x+1/2,y+1/2,z+1/2;-x+1/2,-y+1/2,z+1/2;y+1/2,-x+1/2,-z+1/2;-y+1/2,x+1/2,-z+1/2"
	symLines[82]   = "x,y,z;-x,-y,z;-y,x,z;y,-x,z;-x,-y,-z;x,y,-z;y,-x,-z;-y,x,-z"
	symLines[83]   = "x,y,z;-x,-y,z;-y,x,z+1/2;y,-x,z+1/2;-x,-y,-z;x,y,-z;y,-x,-z+1/2;-y,x,-z+1/2"
	symLines[84]   = "x,y,z;-x+1/2,-y+1/2,z;-y+1/2,x,z;y,-x+1/2,z;-x,-y,-z;x+1/2,y+1/2,-z;y+1/2,-x,-z;-y,x+1/2,-z"
	symLines[85]   = "x,y,z;-x+1/2,-y+1/2,z;-y,x+1/2,z+1/2;y+1/2,-x,z+1/2;-x,-y,-z;x+1/2,y+1/2,-z;y,-x+1/2,-z+1/2;-y+1/2,x,-z+1/2"
	symLines[86]    = "x,y,z;-x,-y,z;-y,x,z;y,-x,z;-x,-y,-z;x,y,-z;y,-x,-z;-y,x,-z;x+1/2,y+1/2,z+1/2;"
	symLines[86] += "-x+1/2,-y+1/2,z+1/2;-y+1/2,x+1/2,z+1/2;y+1/2,-x+1/2,z+1/2;-x+1/2,-y+1/2,-z+1/2;"
	symLines[86] += "x+1/2,y+1/2,-z+1/2;y+1/2,-x+1/2,-z+1/2;-y+1/2,x+1/2,-z+1/2"
	symLines[87]    = "x,y,z;-x+1/2,-y,z+1/2;-y+3/4,x+1/4,z+1/4;y+3/4,-x+3/4,z+3/4;-x,-y,-z;x+1/2,y,-z+1/2;"
	symLines[87] += "y+1/4,-x+3/4,-z+3/4;-y+1/4,x+1/4,-z+1/4;x+1/2,y+1/2,z+1/2;-x,-y+1/2,z;-y+1/4,x+3/4,z+3/4;"
	symLines[87] += "y+1/4,-x+1/4,z+1/4;-x+1/2,-y+1/2,-z+1/2;x,y+1/2,-z;y+3/4,-x+1/4,-z+1/4;"
	symLines[87] += "-y+3/4,x+3/4,-z+3/4"
	symLines[88]   = "x,y,z;-x,-y,z;-y,x,z;y,-x,z;-x,y,-z;x,-y,-z;y,x,-z;-y,-x,-z"
	symLines[89]   = "x,y,z;-x,-y,z;-y+1/2,x+1/2,z;y+1/2,-x+1/2,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;y,x,-z;-y,-x,-z"
	symLines[90]   = "x,y,z;-x,-y,z+1/2;-y,x,z+1/4;y,-x,z+3/4;-x,y,-z;x,-y,-z+1/2;y,x,-z+3/4;-y,-x,-z+1/4"
	symLines[91]    = "x,y,z;-x,-y,z+1/2;-y+1/2,x+1/2,z+1/4;y+1/2,-x+1/2,z+3/4;-x+1/2,y+1/2,-z+1/4;"
	symLines[91] += "x+1/2,-y+1/2,-z+3/4;y,x,-z;-y,-x,-z+1/2"
	symLines[92]   = "x,y,z;-x,-y,z;-y,x,z+1/2;y,-x,z+1/2;-x,y,-z;x,-y,-z;y,x,-z+1/2;-y,-x,-z+1/2"
	symLines[93]   = "x,y,z;-x,-y,z;-y+1/2,x+1/2,z+1/2;y+1/2,-x+1/2,z+1/2;-x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,-z+1/2;y,x,-z;-y,-x,-z"
	symLines[94]   = "x,y,z;-x,-y,z+1/2;-y,x,z+3/4;y,-x,z+1/4;-x,y,-z;x,-y,-z+1/2;y,x,-z+1/4;-y,-x,-z+3/4"
	symLines[95]    = "x,y,z;-x,-y,z+1/2;-y+1/2,x+1/2,z+3/4;y+1/2,-x+1/2,z+1/4;-x+1/2,y+1/2,-z+3/4;"
	symLines[95] += "x+1/2,-y+1/2,-z+1/4;y,x,-z;-y,-x,-z+1/2"
	symLines[96]    = "x,y,z;-x,-y,z;-y,x,z;y,-x,z;-x,y,-z;x,-y,-z;y,x,-z;-y,-x,-z;x+1/2,y+1/2,z+1/2;"
	symLines[96] += "-x+1/2,-y+1/2,z+1/2;-y+1/2,x+1/2,z+1/2;y+1/2,-x+1/2,z+1/2;-x+1/2,y+1/2,-z+1/2;"
	symLines[96] += "x+1/2,-y+1/2,-z+1/2;y+1/2,x+1/2,-z+1/2;-y+1/2,-x+1/2,-z+1/2"
	symLines[97]    = "x,y,z;-x+1/2,-y+1/2,z+1/2;-y,x+1/2,z+1/4;y+1/2,-x,z+3/4;-x+1/2,y,-z+3/4;"
	symLines[97] += "x,-y+1/2,-z+1/4;y+1/2,x+1/2,-z+1/2;-y,-x,-z;x+1/2,y+1/2,z+1/2;-x,-y,z;-y+1/2,x,z+3/4;"
	symLines[97] += "y,-x+1/2,z+1/4;-x,y+1/2,-z+1/4;x+1/2,-y,-z+3/4;y,x,-z;-y+1/2,-x+1/2,-z+1/2"
	symLines[98]   = "x,y,z;-x,-y,z;-y,x,z;y,-x,z;x,-y,z;-x,y,z;-y,-x,z;y,x,z"
	symLines[99]   = "x,y,z;-x,-y,z;-y,x,z;y,-x,z;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z;-y+1/2,-x+1/2,z;y+1/2,x+1/2,z"
	symLines[100]   = "x,y,z;-x,-y,z;-y,x,z+1/2;y,-x,z+1/2;x,-y,z+1/2;-x,y,z+1/2;-y,-x,z;y,x,z"
	symLines[101]   = "x,y,z;-x,-y,z;-y+1/2,x+1/2,z+1/2;y+1/2,-x+1/2,z+1/2;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2;-y,-x,z;y,x,z"
	symLines[102]   = "x,y,z;-x,-y,z;-y,x,z;y,-x,z;x,-y,z+1/2;-x,y,z+1/2;-y,-x,z+1/2;y,x,z+1/2"
	symLines[103]   = "x,y,z;-x,-y,z;-y,x,z;y,-x,z;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2;-y+1/2,-x+1/2,z+1/2;y+1/2,x+1/2,z+1/2"
	symLines[104]   = "x,y,z;-x,-y,z;-y,x,z+1/2;y,-x,z+1/2;x,-y,z;-x,y,z;-y,-x,z+1/2;y,x,z+1/2"
	symLines[105]   = "x,y,z;-x,-y,z;-y,x,z+1/2;y,-x,z+1/2;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z;-y+1/2,-x+1/2,z+1/2;y+1/2,x+1/2,z+1/2"
	symLines[106]    = "x,y,z;-x,-y,z;-y,x,z;y,-x,z;x,-y,z;-x,y,z;-y,-x,z;y,x,z;x+1/2,y+1/2,z+1/2;"
	symLines[106] += "-x+1/2,-y+1/2,z+1/2;-y+1/2,x+1/2,z+1/2;y+1/2,-x+1/2,z+1/2;x+1/2,-y+1/2,z+1/2;"
	symLines[106] += "-x+1/2,y+1/2,z+1/2;-y+1/2,-x+1/2,z+1/2;y+1/2,x+1/2,z+1/2"
	symLines[107]    = "x,y,z;-x,-y,z;-y,x,z;y,-x,z;x,-y,z+1/2;-x,y,z+1/2;-y,-x,z+1/2;y,x,z+1/2;"
	symLines[107] += "x+1/2,y+1/2,z+1/2;-x+1/2,-y+1/2,z+1/2;-y+1/2,x+1/2,z+1/2;y+1/2,-x+1/2,z+1/2;"
	symLines[107] += "x+1/2,-y+1/2,z;-x+1/2,y+1/2,z;-y+1/2,-x+1/2,z;y+1/2,x+1/2,z"
	symLines[108]    = "x,y,z;-x+1/2,-y+1/2,z+1/2;-y,x+1/2,z+1/4;y+1/2,-x,z+3/4;x,-y,z;-x+1/2,y+1/2,z+1/2;"
	symLines[108] += "-y,-x+1/2,z+1/4;y+1/2,x,z+3/4;x+1/2,y+1/2,z+1/2;-x,-y,z;-y+1/2,x,z+3/4;"
	symLines[108] += "y,-x+1/2,z+1/4;x+1/2,-y+1/2,z+1/2;-x,y,z;-y+1/2,-x,z+3/4;y,x+1/2,z+1/4"
	symLines[109]    = "x,y,z;-x+1/2,-y+1/2,z+1/2;-y,x+1/2,z+1/4;y+1/2,-x,z+3/4;x,-y,z+1/2;-x+1/2,y+1/2,z;"
	symLines[109] += "-y,-x+1/2,z+3/4;y+1/2,x,z+1/4;x+1/2,y+1/2,z+1/2;-x,-y,z;-y+1/2,x,z+3/4;"
	symLines[109] += "y,-x+1/2,z+1/4;x+1/2,-y+1/2,z;-x,y,z+1/2;-y+1/2,-x,z+1/4;y,x+1/2,z+3/4"
	symLines[110]   = "x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;-x,y,-z;x,-y,-z;-y,-x,z;y,x,z"
	symLines[111]   = "x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;-x,y,-z+1/2;x,-y,-z+1/2;-y,-x,z+1/2;y,x,z+1/2"
	symLines[112]   = "x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;-y+1/2,-x+1/2,z;y+1/2,x+1/2,z"
	symLines[113]   = "x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;-x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,-z+1/2;-y+1/2,-x+1/2,z+1/2;y+1/2,x+1/2,z+1/2"
	symLines[114]   = "x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;x,-y,z;-x,y,z;y,x,-z;-y,-x,-z"
	symLines[115]   = "x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;x,-y,z+1/2;-x,y,z+1/2;y,x,-z+1/2;-y,-x,-z+1/2"
	symLines[116]   = "x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z;y+1/2,x+1/2,-z;-y+1/2,-x+1/2,-z"
	symLines[117]   = "x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2;y+1/2,x+1/2,-z+1/2;-y+1/2,-x+1/2,-z+1/2"
	symLines[118]    = "x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;x,-y,z;-x,y,z;y,x,-z;-y,-x,-z;x+1/2,y+1/2,z+1/2;"
	symLines[118] += "-x+1/2,-y+1/2,z+1/2;y+1/2,-x+1/2,-z+1/2;-y+1/2,x+1/2,-z+1/2;x+1/2,-y+1/2,z+1/2;"
	symLines[118] += "-x+1/2,y+1/2,z+1/2;y+1/2,x+1/2,-z+1/2;-y+1/2,-x+1/2,-z+1/2"
	symLines[119]    = "x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;x,-y,z+1/2;-x,y,z+1/2;y,x,-z+1/2;-y,-x,-z+1/2;"
	symLines[119] += "x+1/2,y+1/2,z+1/2;-x+1/2,-y+1/2,z+1/2;y+1/2,-x+1/2,-z+1/2;-y+1/2,x+1/2,-z+1/2;"
	symLines[119] += "x+1/2,-y+1/2,z;-x+1/2,y+1/2,z;y+1/2,x+1/2,-z;-y+1/2,-x+1/2,-z"
	symLines[120]    = "x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;-x,y,-z;x,-y,-z;-y,-x,z;y,x,z;x+1/2,y+1/2,z+1/2;"
	symLines[120] += "-x+1/2,-y+1/2,z+1/2;y+1/2,-x+1/2,-z+1/2;-y+1/2,x+1/2,-z+1/2;-x+1/2,y+1/2,-z+1/2;"
	symLines[120] += "x+1/2,-y+1/2,-z+1/2;-y+1/2,-x+1/2,z+1/2;y+1/2,x+1/2,z+1/2"
	symLines[121]    = "x,y,z;-x,-y,z;y,-x,-z;-y,x,-z;-x+1/2,y,-z+3/4;x+1/2,-y,-z+3/4;-y+1/2,-x,z+3/4;"
	symLines[121] += "y+1/2,x,z+3/4;x+1/2,y+1/2,z+1/2;-x+1/2,-y+1/2,z+1/2;y+1/2,-x+1/2,-z+1/2;"
	symLines[121] += "-y+1/2,x+1/2,-z+1/2;-x,y+1/2,-z+1/4;x,-y+1/2,-z+1/4;-y,-x+1/2,z+1/4;y,x+1/2,z+1/4"
	symLines[122]    = "x,y,z;-x,-y,z;-y,x,z;y,-x,z;-x,y,-z;x,-y,-z;y,x,-z;-y,-x,-z;-x,-y,-z;x,y,-z;"
	symLines[122] += "y,-x,-z;-y,x,-z;x,-y,z;-x,y,z;-y,-x,z;y,x,z"
	symLines[123]    = "x,y,z;-x,-y,z;-y,x,z;y,-x,z;-x,y,-z+1/2;x,-y,-z+1/2;y,x,-z+1/2;-y,-x,-z+1/2;"
	symLines[123] += "-x,-y,-z;x,y,-z;y,-x,-z;-y,x,-z;x,-y,z+1/2;-x,y,z+1/2;-y,-x,z+1/2;y,x,z+1/2"
	symLines[124]    = "x,y,z;-x+1/2,-y+1/2,z;-y+1/2,x,z;y,-x+1/2,z;-x+1/2,y,-z;x,-y+1/2,-z;y,x,-z;"
	symLines[124] += "-y+1/2,-x+1/2,-z;-x,-y,-z;x+1/2,y+1/2,-z;y+1/2,-x,-z;-y,x+1/2,-z;x+1/2,-y,z;"
	symLines[124] += "-x,y+1/2,z;-y,-x,z;y+1/2,x+1/2,z"
	symLines[125]    = "x,y,z;-x+1/2,-y+1/2,z;-y+1/2,x,z;y,-x+1/2,z;-x+1/2,y,-z+1/2;x,-y+1/2,-z+1/2;"
	symLines[125] += "y,x,-z+1/2;-y+1/2,-x+1/2,-z+1/2;-x,-y,-z;x+1/2,y+1/2,-z;y+1/2,-x,-z;-y,x+1/2,-z;"
	symLines[125] += "x+1/2,-y,z+1/2;-x,y+1/2,z+1/2;-y,-x,z+1/2;y+1/2,x+1/2,z+1/2"
	symLines[126]    = "x,y,z;-x,-y,z;-y,x,z;y,-x,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;y+1/2,x+1/2,-z;"
	symLines[126] += "-y+1/2,-x+1/2,-z;-x,-y,-z;x,y,-z;y,-x,-z;-y,x,-z;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z;"
	symLines[126] += "-y+1/2,-x+1/2,z;y+1/2,x+1/2,z"
	symLines[127]    = "x,y,z;-x,-y,z;-y,x,z;y,-x,z;-x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,-z+1/2;y+1/2,x+1/2,-z+1/2;"
	symLines[127] += "-y+1/2,-x+1/2,-z+1/2;-x,-y,-z;x,y,-z;y,-x,-z;-y,x,-z;x+1/2,-y+1/2,z+1/2;"
	symLines[127] += "-x+1/2,y+1/2,z+1/2;-y+1/2,-x+1/2,z+1/2;y+1/2,x+1/2,z+1/2"
	symLines[128]    = "x,y,z;-x+1/2,-y+1/2,z;-y+1/2,x,z;y,-x+1/2,z;-x,y+1/2,-z;x+1/2,-y,-z;y+1/2,x+1/2,-z;"
	symLines[128] += "-y,-x,-z;-x,-y,-z;x+1/2,y+1/2,-z;y+1/2,-x,-z;-y,x+1/2,-z;x,-y+1/2,z;-x+1/2,y,z;"
	symLines[128] += "-y+1/2,-x+1/2,z;y,x,z"
	symLines[129]    = "x,y,z;-x+1/2,-y+1/2,z;-y+1/2,x,z;y,-x+1/2,z;-x,y+1/2,-z+1/2;x+1/2,-y,-z+1/2;"
	symLines[129] += "y+1/2,x+1/2,-z+1/2;-y,-x,-z+1/2;-x,-y,-z;x+1/2,y+1/2,-z;y+1/2,-x,-z;-y,x+1/2,-z;"
	symLines[129] += "x,-y+1/2,z+1/2;-x+1/2,y,z+1/2;-y+1/2,-x+1/2,z+1/2;y,x,z+1/2"
	symLines[130]    = "x,y,z;-x,-y,z;-y,x,z+1/2;y,-x,z+1/2;-x,y,-z;x,-y,-z;y,x,-z+1/2;-y,-x,-z+1/2;"
	symLines[130] += "-x,-y,-z;x,y,-z;y,-x,-z+1/2;-y,x,-z+1/2;x,-y,z;-x,y,z;-y,-x,z+1/2;y,x,z+1/2"
	symLines[131]    = "x,y,z;-x,-y,z;-y,x,z+1/2;y,-x,z+1/2;-x,y,-z+1/2;x,-y,-z+1/2;y,x,-z;-y,-x,-z;"
	symLines[131] += "-x,-y,-z;x,y,-z;y,-x,-z+1/2;-y,x,-z+1/2;x,-y,z+1/2;-x,y,z+1/2;-y,-x,z;y,x,z"
	symLines[132]    = "x,y,z;-x+1/2,-y+1/2,z;-y+1/2,x,z+1/2;y,-x+1/2,z+1/2;-x+1/2,y,-z;x,-y+1/2,-z;"
	symLines[132] += "y,x,-z+1/2;-y+1/2,-x+1/2,-z+1/2;-x,-y,-z;x+1/2,y+1/2,-z;y+1/2,-x,-z+1/2;"
	symLines[132] += "-y,x+1/2,-z+1/2;x+1/2,-y,z;-x,y+1/2,z;-y,-x,z+1/2;y+1/2,x+1/2,z+1/2"
	symLines[133]    = "x,y,z;-x+1/2,-y+1/2,z;-y+1/2,x,z+1/2;y,-x+1/2,z+1/2;-x+1/2,y,-z+1/2;x,-y+1/2,-z+1/2;"
	symLines[133] += "y,x,-z;-y+1/2,-x+1/2,-z;-x,-y,-z;x+1/2,y+1/2,-z;y+1/2,-x,-z+1/2;-y,x+1/2,-z+1/2;"
	symLines[133] += "x+1/2,-y,z+1/2;-x,y+1/2,z+1/2;-y,-x,z;y+1/2,x+1/2,z"
	symLines[134]    = "x,y,z;-x,-y,z;-y,x,z+1/2;y,-x,z+1/2;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;y+1/2,x+1/2,-z+1/2;"
	symLines[134] += "-y+1/2,-x+1/2,-z+1/2;-x,-y,-z;x,y,-z;y,-x,-z+1/2;-y,x,-z+1/2;x+1/2,-y+1/2,z;"
	symLines[134] += "-x+1/2,y+1/2,z;-y+1/2,-x+1/2,z+1/2;y+1/2,x+1/2,z+1/2"
	symLines[135]    = "x,y,z;-x,-y,z;-y+1/2,x+1/2,z+1/2;y+1/2,-x+1/2,z+1/2;-x+1/2,y+1/2,-z+1/2;"
	symLines[135] += "x+1/2,-y+1/2,-z+1/2;y,x,-z;-y,-x,-z;-x,-y,-z;x,y,-z;y+1/2,-x+1/2,-z+1/2;"
	symLines[135] += "-y+1/2,x+1/2,-z+1/2;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2;-y,-x,z;y,x,z"
	symLines[136]    = "x,y,z;-x+1/2,-y+1/2,z;-y+1/2,x,z+1/2;y,-x+1/2,z+1/2;-x,y+1/2,-z;x+1/2,-y,-z;"
	symLines[136] += "y+1/2,x+1/2,-z+1/2;-y,-x,-z+1/2;-x,-y,-z;x+1/2,y+1/2,-z;y+1/2,-x,-z+1/2;"
	symLines[136] += "-y,x+1/2,-z+1/2;x,-y+1/2,z;-x+1/2,y,z;-y+1/2,-x+1/2,z+1/2;y,x,z+1/2"
	symLines[137]    = "x,y,z;-x+1/2,-y+1/2,z;-y+1/2,x,z+1/2;y,-x+1/2,z+1/2;-x,y+1/2,-z+1/2;x+1/2,-y,-z+1/2;"
	symLines[137] += "y+1/2,x+1/2,-z;-y,-x,-z;-x,-y,-z;x+1/2,y+1/2,-z;y+1/2,-x,-z+1/2;-y,x+1/2,-z+1/2;"
	symLines[137] += "x,-y+1/2,z+1/2;-x+1/2,y,z+1/2;-y+1/2,-x+1/2,z;y,x,z"
	symLines[138]    = "x,y,z;-x,-y,z;-y,x,z;y,-x,z;-x,y,-z;x,-y,-z;y,x,-z;-y,-x,-z;-x,-y,-z;x,y,-z;"
	symLines[138] += "y,-x,-z;-y,x,-z;x,-y,z;-x,y,z;-y,-x,z;y,x,z;x+1/2,y+1/2,z+1/2;-x+1/2,-y+1/2,z+1/2;"
	symLines[138] += "-y+1/2,x+1/2,z+1/2;y+1/2,-x+1/2,z+1/2;-x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,-z+1/2;"
	symLines[138] += "y+1/2,x+1/2,-z+1/2;-y+1/2,-x+1/2,-z+1/2;-x+1/2,-y+1/2,-z+1/2;x+1/2,y+1/2,-z+1/2;"
	symLines[138] += "y+1/2,-x+1/2,-z+1/2;-y+1/2,x+1/2,-z+1/2;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2;"
	symLines[138] += "-y+1/2,-x+1/2,z+1/2;y+1/2,x+1/2,z+1/2"
	symLines[139]    = "x,y,z;-x,-y,z;-y,x,z;y,-x,z;-x,y,-z+1/2;x,-y,-z+1/2;y,x,-z+1/2;-y,-x,-z+1/2;"
	symLines[139] += "-x,-y,-z;x,y,-z;y,-x,-z;-y,x,-z;x,-y,z+1/2;-x,y,z+1/2;-y,-x,z+1/2;y,x,z+1/2;"
	symLines[139] += "x+1/2,y+1/2,z+1/2;-x+1/2,-y+1/2,z+1/2;-y+1/2,x+1/2,z+1/2;y+1/2,-x+1/2,z+1/2;"
	symLines[139] += "-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;y+1/2,x+1/2,-z;-y+1/2,-x+1/2,-z;-x+1/2,-y+1/2,-z+1/2;"
	symLines[139] += "x+1/2,y+1/2,-z+1/2;y+1/2,-x+1/2,-z+1/2;-y+1/2,x+1/2,-z+1/2;x+1/2,-y+1/2,z;"
	symLines[139] += "-x+1/2,y+1/2,z;-y+1/2,-x+1/2,z;y+1/2,x+1/2,z"
	symLines[140]    = "x,y,z;-x+1/2,-y,z+1/2;-y+1/4,x+3/4,z+1/4;y+1/4,-x+1/4,z+3/4;-x+1/2,y,-z+1/2;"
	symLines[140] += "x,-y,-z;y+1/4,x+3/4,-z+1/4;-y+1/4,-x+1/4,-z+3/4;-x,-y,-z;x+1/2,y,-z+1/2;"
	symLines[140] += "y+3/4,-x+1/4,-z+3/4;-y+3/4,x+3/4,-z+1/4;x+1/2,-y,z+1/2;-x,y,z;-y+3/4,-x+1/4,z+3/4;"
	symLines[140] += "y+3/4,x+3/4,z+1/4;x+1/2,y+1/2,z+1/2;-x,-y+1/2,z;-y+3/4,x+1/4,z+3/4;y+3/4,-x+3/4,z+1/4;"
	symLines[140] += "-x,y+1/2,-z;x+1/2,-y+1/2,-z+1/2;y+3/4,x+1/4,-z+3/4;-y+3/4,-x+3/4,-z+1/4;"
	symLines[140] += "-x+1/2,-y+1/2,-z+1/2;x,y+1/2,-z;y+1/4,-x+3/4,-z+1/4;-y+1/4,x+1/4,-z+3/4;"
	symLines[140] += "x,-y+1/2,z;-x+1/2,y+1/2,z+1/2;-y+1/4,-x+3/4,z+1/4;y+1/4,x+1/4,z+3/4"
	symLines[141]    = "x,y,z;-x+1/2,-y,z+1/2;-y+1/4,x+3/4,z+1/4;y+1/4,-x+1/4,z+3/4;-x+1/2,y,-z;"
	symLines[141] += "x,-y,-z+1/2;y+1/4,x+3/4,-z+3/4;-y+1/4,-x+1/4,-z+1/4;-x,-y,-z;x+1/2,y,-z+1/2;"
	symLines[141] += "y+3/4,-x+1/4,-z+3/4;-y+3/4,x+3/4,-z+1/4;x+1/2,-y,z;-x,y,z+1/2;-y+3/4,-x+1/4,z+1/4;"
	symLines[141] += "y+3/4,x+3/4,z+3/4;x+1/2,y+1/2,z+1/2;-x,-y+1/2,z;-y+3/4,x+1/4,z+3/4;y+3/4,-x+3/4,z+1/4;"
	symLines[141] += "-x,y+1/2,-z+1/2;x+1/2,-y+1/2,-z;y+3/4,x+1/4,-z+1/4;-y+3/4,-x+3/4,-z+3/4;"
	symLines[141] += "-x+1/2,-y+1/2,-z+1/2;x,y+1/2,-z;y+1/4,-x+3/4,-z+1/4;-y+1/4,x+1/4,-z+3/4;"
	symLines[141] += "x,-y+1/2,z+1/2;-x+1/2,y+1/2,z;-y+1/4,-x+3/4,z+3/4;y+1/4,x+1/4,z+1/4"
	symLines[142]   = "x,y,z;-y,x-y,z;-x+y,-x,z"
	symLines[143]   = "x,y,z;-y,x-y,z+1/3;-x+y,-x,z+2/3"
	symLines[144]   = "x,y,z;-y,x-y,z+2/3;-x+y,-x,z+1/3"
	symLines[145]    = "x,y,z;-y,x-y,z;-x+y,-x,z;x+2/3,y+1/3,z+1/3;-y+2/3,x-y+1/3,z+1/3;-x+y+2/3,-x+1/3,z+1/3;"
	symLines[145] += "x+1/3,y+2/3,z+2/3;-y+1/3,x-y+2/3,z+2/3;-x+y+1/3,-x+2/3,z+2/3"
	symLines[146]   = "x,y,z;-y,x-y,z;-x+y,-x,z;-x,-y,-z;y,-x+y,-z;x-y,x,-z"
	symLines[147]    = "x,y,z;-y,x-y,z;-x+y,-x,z;-x,-y,-z;y,-x+y,-z;x-y,x,-z;x+2/3,y+1/3,z+1/3;"
	symLines[147] += "-y+2/3,x-y+1/3,z+1/3;-x+y+2/3,-x+1/3,z+1/3;-x+2/3,-y+1/3,-z+1/3;y+2/3,-x+y+1/3,-z+1/3;"
	symLines[147] += "x-y+2/3,x+1/3,-z+1/3;x+1/3,y+2/3,z+2/3;-y+1/3,x-y+2/3,z+2/3;-x+y+1/3,-x+2/3,z+2/3;"
	symLines[147] += "-x+1/3,-y+2/3,-z+2/3;y+1/3,-x+y+2/3,-z+2/3;x-y+1/3,x+2/3,-z+2/3"
	symLines[148]   = "x,y,z;-y,x-y,z;-x+y,-x,z;-y,-x,-z;-x+y,y,-z;x,x-y,-z"
	symLines[149]   = "x,y,z;-y,x-y,z;-x+y,-x,z;y,x,-z;x-y,-y,-z;-x,-x+y,-z"
	symLines[150]   = "x,y,z;-y,x-y,z+1/3;-x+y,-x,z+2/3;-y,-x,-z+2/3;-x+y,y,-z+1/3;x,x-y,-z"
	symLines[151]   = "x,y,z;-y,x-y,z+1/3;-x+y,-x,z+2/3;y,x,-z;x-y,-y,-z+2/3;-x,-x+y,-z+1/3"
	symLines[152]   = "x,y,z;-y,x-y,z+2/3;-x+y,-x,z+1/3;-y,-x,-z+1/3;-x+y,y,-z+2/3;x,x-y,-z"
	symLines[153]   = "x,y,z;-y,x-y,z+2/3;-x+y,-x,z+1/3;y,x,-z;x-y,-y,-z+1/3;-x,-x+y,-z+2/3"
	symLines[154]    = "x,y,z;-y,x-y,z;-x+y,-x,z;y,x,-z;x-y,-y,-z;-x,-x+y,-z;x+2/3,y+1/3,z+1/3;"
	symLines[154] += "-y+2/3,x-y+1/3,z+1/3;-x+y+2/3,-x+1/3,z+1/3;y+2/3,x+1/3,-z+1/3;x-y+2/3,-y+1/3,-z+1/3;"
	symLines[154] += "-x+2/3,-x+y+1/3,-z+1/3;x+1/3,y+2/3,z+2/3;-y+1/3,x-y+2/3,z+2/3;-x+y+1/3,-x+2/3,z+2/3;"
	symLines[154] += "y+1/3,x+2/3,-z+2/3;x-y+1/3,-y+2/3,-z+2/3;-x+1/3,-x+y+2/3,-z+2/3"
	symLines[155]   = "x,y,z;-y,x-y,z;-x+y,-x,z;-y,-x,z;-x+y,y,z;x,x-y,z"
	symLines[156]   = "x,y,z;-y,x-y,z;-x+y,-x,z;y,x,z;x-y,-y,z;-x,-x+y,z"
	symLines[157]   = "x,y,z;-y,x-y,z;-x+y,-x,z;-y,-x,z+1/2;-x+y,y,z+1/2;x,x-y,z+1/2"
	symLines[158]   = "x,y,z;-y,x-y,z;-x+y,-x,z;y,x,z+1/2;x-y,-y,z+1/2;-x,-x+y,z+1/2"
	symLines[159]    = "x,y,z;-y,x-y,z;-x+y,-x,z;-y,-x,z;-x+y,y,z;x,x-y,z;x+2/3,y+1/3,z+1/3;-y+2/3,x-y+1/3,z+1/3;"
	symLines[159] += "-x+y+2/3,-x+1/3,z+1/3;-y+2/3,-x+1/3,z+1/3;-x+y+2/3,y+1/3,z+1/3;x+2/3,x-y+1/3,z+1/3;"
	symLines[159] += "x+1/3,y+2/3,z+2/3;-y+1/3,x-y+2/3,z+2/3;-x+y+1/3,-x+2/3,z+2/3;-y+1/3,-x+2/3,z+2/3;"
	symLines[159] += "-x+y+1/3,y+2/3,z+2/3;x+1/3,x-y+2/3,z+2/3"
	symLines[160]    = "x,y,z;-y,x-y,z;-x+y,-x,z;-y,-x,z+1/2;-x+y,y,z+1/2;x,x-y,z+1/2;x+2/3,y+1/3,z+1/3;"
	symLines[160] += "-y+2/3,x-y+1/3,z+1/3;-x+y+2/3,-x+1/3,z+1/3;-y+2/3,-x+1/3,z+5/6;-x+y+2/3,y+1/3,z+5/6;"
	symLines[160] += "x+2/3,x-y+1/3,z+5/6;x+1/3,y+2/3,z+2/3;-y+1/3,x-y+2/3,z+2/3;-x+y+1/3,-x+2/3,z+2/3;"
	symLines[160] += "-y+1/3,-x+2/3,z+1/6;-x+y+1/3,y+2/3,z+1/6;x+1/3,x-y+2/3,z+1/6"
	symLines[161]   = "x,y,z;-y,x-y,z;-x+y,-x,z;-y,-x,-z;-x+y,y,-z;x,x-y,-z;-x,-y,-z;y,-x+y,-z;x-y,x,-z;y,x,z;x-y,-y,z;-x,-x+y,z"
	symLines[162]    = "x,y,z;-y,x-y,z;-x+y,-x,z;-y,-x,-z+1/2;-x+y,y,-z+1/2;x,x-y,-z+1/2;-x,-y,-z;"
	symLines[162] += "y,-x+y,-z;x-y,x,-z;y,x,z+1/2;x-y,-y,z+1/2;-x,-x+y,z+1/2"
	symLines[163]   = "x,y,z;-y,x-y,z;-x+y,-x,z;y,x,-z;x-y,-y,-z;-x,-x+y,-z;-x,-y,-z;y,-x+y,-z;x-y,x,-z;-y,-x,z;-x+y,y,z;x,x-y,z"
	symLines[164]    = "x,y,z;-y,x-y,z;-x+y,-x,z;y,x,-z+1/2;x-y,-y,-z+1/2;-x,-x+y,-z+1/2;-x,-y,-z;"
	symLines[164] += "y,-x+y,-z;x-y,x,-z;-y,-x,z+1/2;-x+y,y,z+1/2;x,x-y,z+1/2"
	symLines[165]    = "x,y,z;-y,x-y,z;-x+y,-x,z;y,x,-z;x-y,-y,-z;-x,-x+y,-z;-x,-y,-z;y,-x+y,-z;"
	symLines[165] += "x-y,x,-z;-y,-x,z;-x+y,y,z;x,x-y,z;x+2/3,y+1/3,z+1/3;-y+2/3,x-y+1/3,z+1/3;"
	symLines[165] += "-x+y+2/3,-x+1/3,z+1/3;y+2/3,x+1/3,-z+1/3;x-y+2/3,-y+1/3,-z+1/3;-x+2/3,-x+y+1/3,-z+1/3;"
	symLines[165] += "-x+2/3,-y+1/3,-z+1/3;y+2/3,-x+y+1/3,-z+1/3;x-y+2/3,x+1/3,-z+1/3;-y+2/3,-x+1/3,z+1/3;"
	symLines[165] += "-x+y+2/3,y+1/3,z+1/3;x+2/3,x-y+1/3,z+1/3;x+1/3,y+2/3,z+2/3;-y+1/3,x-y+2/3,z+2/3;"
	symLines[165] += "-x+y+1/3,-x+2/3,z+2/3;y+1/3,x+2/3,-z+2/3;x-y+1/3,-y+2/3,-z+2/3;-x+1/3,-x+y+2/3,-z+2/3;"
	symLines[165] += "-x+1/3,-y+2/3,-z+2/3;y+1/3,-x+y+2/3,-z+2/3;x-y+1/3,x+2/3,-z+2/3;-y+1/3,-x+2/3,z+2/3;"
	symLines[165] += "-x+y+1/3,y+2/3,z+2/3;x+1/3,x-y+2/3,z+2/3"
	symLines[166]    = "x,y,z;-y,x-y,z;-x+y,-x,z;y,x,-z+1/2;x-y,-y,-z+1/2;-x,-x+y,-z+1/2;-x,-y,-z;"
	symLines[166] += "y,-x+y,-z;x-y,x,-z;-y,-x,z+1/2;-x+y,y,z+1/2;x,x-y,z+1/2;x+2/3,y+1/3,z+1/3;"
	symLines[166] += "-y+2/3,x-y+1/3,z+1/3;-x+y+2/3,-x+1/3,z+1/3;y+2/3,x+1/3,-z+5/6;x-y+2/3,-y+1/3,-z+5/6;"
	symLines[166] += "-x+2/3,-x+y+1/3,-z+5/6;-x+2/3,-y+1/3,-z+1/3;y+2/3,-x+y+1/3,-z+1/3;x-y+2/3,x+1/3,-z+1/3;"
	symLines[166] += "-y+2/3,-x+1/3,z+5/6;-x+y+2/3,y+1/3,z+5/6;x+2/3,x-y+1/3,z+5/6;x+1/3,y+2/3,z+2/3;"
	symLines[166] += "-y+1/3,x-y+2/3,z+2/3;-x+y+1/3,-x+2/3,z+2/3;y+1/3,x+2/3,-z+1/6;x-y+1/3,-y+2/3,-z+1/6;"
	symLines[166] += "-x+1/3,-x+y+2/3,-z+1/6;-x+1/3,-y+2/3,-z+2/3;y+1/3,-x+y+2/3,-z+2/3;x-y+1/3,x+2/3,-z+2/3;"
	symLines[166] += "-y+1/3,-x+2/3,z+1/6;-x+y+1/3,y+2/3,z+1/6;x+1/3,x-y+2/3,z+1/6"
	symLines[167]   = "x,y,z;-y,x-y,z;-x+y,-x,z;-x,-y,z;y,-x+y,z;x-y,x,z"
	symLines[168]   = "x,y,z;-y,x-y,z+1/3;-x+y,-x,z+2/3;-x,-y,z+1/2;y,-x+y,z+5/6;x-y,x,z+1/6"
	symLines[169]   = "x,y,z;-y,x-y,z+2/3;-x+y,-x,z+1/3;-x,-y,z+1/2;y,-x+y,z+1/6;x-y,x,z+5/6"
	symLines[170]   = "x,y,z;-y,x-y,z+2/3;-x+y,-x,z+1/3;-x,-y,z;y,-x+y,z+2/3;x-y,x,z+1/3"
	symLines[171]   = "x,y,z;-y,x-y,z+1/3;-x+y,-x,z+2/3;-x,-y,z;y,-x+y,z+1/3;x-y,x,z+2/3"
	symLines[172]   = "x,y,z;-y,x-y,z;-x+y,-x,z;-x,-y,z+1/2;y,-x+y,z+1/2;x-y,x,z+1/2"
	symLines[173]   = "x,y,z;-y,x-y,z;-x+y,-x,z;x,y,-z;-y,x-y,-z;-x+y,-x,-z"
	symLines[174]   = "x,y,z;-y,x-y,z;-x+y,-x,z;-x,-y,z;y,-x+y,z;x-y,x,z;-x,-y,-z;y,-x+y,-z;x-y,x,-z;x,y,-z;-y,x-y,-z;-x+y,-x,-z"
	symLines[175]    = "x,y,z;-y,x-y,z;-x+y,-x,z;-x,-y,z+1/2;y,-x+y,z+1/2;x-y,x,z+1/2;-x,-y,-z;"
	symLines[175] += "y,-x+y,-z;x-y,x,-z;x,y,-z+1/2;-y,x-y,-z+1/2;-x+y,-x,-z+1/2"
	symLines[176]   = "x,y,z;-y,x-y,z;-x+y,-x,z;-x,-y,z;y,-x+y,z;x-y,x,z;y,x,-z;x-y,-y,-z;-x,-x+y,-z;-y,-x,-z;-x+y,y,-z;x,x-y,-z"
	symLines[177]    = "x,y,z;-y,x-y,z+1/3;-x+y,-x,z+2/3;-x,-y,z+1/2;y,-x+y,z+5/6;x-y,x,z+1/6;y,x,-z+1/3;"
	symLines[177] += "x-y,-y,-z;-x,-x+y,-z+2/3;-y,-x,-z+5/6;-x+y,y,-z+1/2;x,x-y,-z+1/6"
	symLines[178]    = "x,y,z;-y,x-y,z+2/3;-x+y,-x,z+1/3;-x,-y,z+1/2;y,-x+y,z+1/6;x-y,x,z+5/6;y,x,-z+2/3;"
	symLines[178] += "x-y,-y,-z;-x,-x+y,-z+1/3;-y,-x,-z+1/6;-x+y,y,-z+1/2;x,x-y,-z+5/6"
	symLines[179]    = "x,y,z;-y,x-y,z+2/3;-x+y,-x,z+1/3;-x,-y,z;y,-x+y,z+2/3;x-y,x,z+1/3;y,x,-z+2/3;"
	symLines[179] += "x-y,-y,-z;-x,-x+y,-z+1/3;-y,-x,-z+2/3;-x+y,y,-z;x,x-y,-z+1/3"
	symLines[180]    = "x,y,z;-y,x-y,z+1/3;-x+y,-x,z+2/3;-x,-y,z;y,-x+y,z+1/3;x-y,x,z+2/3;y,x,-z+1/3;"
	symLines[180] += "x-y,-y,-z;-x,-x+y,-z+2/3;-y,-x,-z+1/3;-x+y,y,-z;x,x-y,-z+2/3"
	symLines[181]    = "x,y,z;-y,x-y,z;-x+y,-x,z;-x,-y,z+1/2;y,-x+y,z+1/2;x-y,x,z+1/2;y,x,-z;x-y,-y,-z;"
	symLines[181] += "-x,-x+y,-z;-y,-x,-z+1/2;-x+y,y,-z+1/2;x,x-y,-z+1/2"
	symLines[182]   = "x,y,z;-y,x-y,z;-x+y,-x,z;-x,-y,z;y,-x+y,z;x-y,x,z;-y,-x,z;-x+y,y,z;x,x-y,z;y,x,z;x-y,-y,z;-x,-x+y,z"
	symLines[183]    = "x,y,z;-y,x-y,z;-x+y,-x,z;-x,-y,z;y,-x+y,z;x-y,x,z;-y,-x,z+1/2;-x+y,y,z+1/2;"
	symLines[183] += "x,x-y,z+1/2;y,x,z+1/2;x-y,-y,z+1/2;-x,-x+y,z+1/2"
	symLines[184]    = "x,y,z;-y,x-y,z;-x+y,-x,z;-x,-y,z+1/2;y,-x+y,z+1/2;x-y,x,z+1/2;-y,-x,z+1/2;"
	symLines[184] += "-x+y,y,z+1/2;x,x-y,z+1/2;y,x,z;x-y,-y,z;-x,-x+y,z"
	symLines[185]    = "x,y,z;-y,x-y,z;-x+y,-x,z;-x,-y,z+1/2;y,-x+y,z+1/2;x-y,x,z+1/2;-y,-x,z;-x+y,y,z;"
	symLines[185] += "x,x-y,z;y,x,z+1/2;x-y,-y,z+1/2;-x,-x+y,z+1/2"
	symLines[186]   = "x,y,z;-y,x-y,z;-x+y,-x,z;x,y,-z;-y,x-y,-z;-x+y,-x,-z;-y,-x,z;-x+y,y,z;x,x-y,z;-y,-x,-z;-x+y,y,-z;x,x-y,-z"
	symLines[187]    = "x,y,z;-y,x-y,z;-x+y,-x,z;x,y,-z+1/2;-y,x-y,-z+1/2;-x+y,-x,-z+1/2;-y,-x,z+1/2;"
	symLines[187] += "-x+y,y,z+1/2;x,x-y,z+1/2;-y,-x,-z;-x+y,y,-z;x,x-y,-z"
	symLines[188]   = "x,y,z;-y,x-y,z;-x+y,-x,z;x,y,-z;-y,x-y,-z;-x+y,-x,-z;y,x,-z;x-y,-y,-z;-x,-x+y,-z;y,x,z;x-y,-y,z;-x,-x+y,z"
	symLines[189]    = "x,y,z;-y,x-y,z;-x+y,-x,z;x,y,-z+1/2;-y,x-y,-z+1/2;-x+y,-x,-z+1/2;y,x,-z;"
	symLines[189] += "x-y,-y,-z;-x,-x+y,-z;y,x,z+1/2;x-y,-y,z+1/2;-x,-x+y,z+1/2"
	symLines[190]    = "x,y,z;-y,x-y,z;-x+y,-x,z;-x,-y,z;y,-x+y,z;x-y,x,z;y,x,-z;x-y,-y,-z;-x,-x+y,-z;"
	symLines[190] += "-y,-x,-z;-x+y,y,-z;x,x-y,-z;-x,-y,-z;y,-x+y,-z;x-y,x,-z;x,y,-z;-y,x-y,-z;"
	symLines[190] += "-x+y,-x,-z;-y,-x,z;-x+y,y,z;x,x-y,z;y,x,z;x-y,-y,z;-x,-x+y,z"
	symLines[191]    = "x,y,z;-y,x-y,z;-x+y,-x,z;-x,-y,z;y,-x+y,z;x-y,x,z;y,x,-z+1/2;x-y,-y,-z+1/2;"
	symLines[191] += "-x,-x+y,-z+1/2;-y,-x,-z+1/2;-x+y,y,-z+1/2;x,x-y,-z+1/2;-x,-y,-z;y,-x+y,-z;"
	symLines[191] += "x-y,x,-z;x,y,-z;-y,x-y,-z;-x+y,-x,-z;-y,-x,z+1/2;-x+y,y,z+1/2;x,x-y,z+1/2;"
	symLines[191] += "y,x,z+1/2;x-y,-y,z+1/2;-x,-x+y,z+1/2"
	symLines[192]    = "x,y,z;-y,x-y,z;-x+y,-x,z;-x,-y,z+1/2;y,-x+y,z+1/2;x-y,x,z+1/2;y,x,-z+1/2;"
	symLines[192] += "x-y,-y,-z+1/2;-x,-x+y,-z+1/2;-y,-x,-z;-x+y,y,-z;x,x-y,-z;-x,-y,-z;y,-x+y,-z;"
	symLines[192] += "x-y,x,-z;x,y,-z+1/2;-y,x-y,-z+1/2;-x+y,-x,-z+1/2;-y,-x,z+1/2;-x+y,y,z+1/2;"
	symLines[192] += "x,x-y,z+1/2;y,x,z;x-y,-y,z;-x,-x+y,z"
	symLines[193]    = "x,y,z;-y,x-y,z;-x+y,-x,z;-x,-y,z+1/2;y,-x+y,z+1/2;x-y,x,z+1/2;y,x,-z;x-y,-y,-z;"
	symLines[193] += "-x,-x+y,-z;-y,-x,-z+1/2;-x+y,y,-z+1/2;x,x-y,-z+1/2;-x,-y,-z;y,-x+y,-z;x-y,x,-z;"
	symLines[193] += "x,y,-z+1/2;-y,x-y,-z+1/2;-x+y,-x,-z+1/2;-y,-x,z;-x+y,y,z;x,x-y,z;y,x,z+1/2;"
	symLines[193] += "x-y,-y,z+1/2;-x,-x+y,z+1/2"
	symLines[194]   = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;y,-z,-x;-y,-z,x"
	symLines[195]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[195] += "y,-z,-x;-y,-z,x;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;-x,y+1/2,-z+1/2;x,-y+1/2,-z+1/2;"
	symLines[195] += "z,x+1/2,y+1/2;z,-x+1/2,-y+1/2;-z,-x+1/2,y+1/2;-z,x+1/2,-y+1/2;y,z+1/2,x+1/2;"
	symLines[195] += "-y,z+1/2,-x+1/2;y,-z+1/2,-x+1/2;-y,-z+1/2,x+1/2;x+1/2,y,z+1/2;-x+1/2,-y,z+1/2;"
	symLines[195] += "-x+1/2,y,-z+1/2;x+1/2,-y,-z+1/2;z+1/2,x,y+1/2;z+1/2,-x,-y+1/2;-z+1/2,-x,y+1/2;"
	symLines[195] += "-z+1/2,x,-y+1/2;y+1/2,z,x+1/2;-y+1/2,z,-x+1/2;y+1/2,-z,-x+1/2;-y+1/2,-z,x+1/2;"
	symLines[195] += "x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;z+1/2,x+1/2,y;"
	symLines[195] += "z+1/2,-x+1/2,-y;-z+1/2,-x+1/2,y;-z+1/2,x+1/2,-y;y+1/2,z+1/2,x;-y+1/2,z+1/2,-x;"
	symLines[195] += "y+1/2,-z+1/2,-x;-y+1/2,-z+1/2,x"
	symLines[196]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[196] += "y,-z,-x;-y,-z,x;x+1/2,y+1/2,z+1/2;-x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,-z+1/2;"
	symLines[196] += "x+1/2,-y+1/2,-z+1/2;z+1/2,x+1/2,y+1/2;z+1/2,-x+1/2,-y+1/2;-z+1/2,-x+1/2,y+1/2;"
	symLines[196] += "-z+1/2,x+1/2,-y+1/2;y+1/2,z+1/2,x+1/2;-y+1/2,z+1/2,-x+1/2;y+1/2,-z+1/2,-x+1/2;"
	symLines[196] += "-y+1/2,-z+1/2,x+1/2"
	symLines[197]    = "x,y,z;-x+1/2,-y,z+1/2;-x,y+1/2,-z+1/2;x+1/2,-y+1/2,-z;z,x,y;z+1/2,-x+1/2,-y;"
	symLines[197] += "-z+1/2,-x,y+1/2;-z,x+1/2,-y+1/2;y,z,x;-y,z+1/2,-x+1/2;y+1/2,-z+1/2,-x;-y+1/2,-z,x+1/2"
	symLines[198]    = "x,y,z;-x+1/2,-y,z+1/2;-x,y+1/2,-z+1/2;x+1/2,-y+1/2,-z;z,x,y;z+1/2,-x+1/2,-y;"
	symLines[198] += "-z+1/2,-x,y+1/2;-z,x+1/2,-y+1/2;y,z,x;-y,z+1/2,-x+1/2;y+1/2,-z+1/2,-x;-y+1/2,-z,x+1/2;"
	symLines[198] += "x+1/2,y+1/2,z+1/2;-x,-y+1/2,z;-x+1/2,y,-z;x,-y,-z+1/2;z+1/2,x+1/2,y+1/2;"
	symLines[198] += "z,-x,-y+1/2;-z,-x+1/2,y;-z+1/2,x,-y;y+1/2,z+1/2,x+1/2;-y+1/2,z,-x;y,-z,-x+1/2;"
	symLines[198] += "-y,-z+1/2,x"
	symLines[199]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[199] += "y,-z,-x;-y,-z,x;-x,-y,-z;x,y,-z;x,-y,z;-x,y,z;-z,-x,-y;-z,x,y;z,x,-y;z,-x,y;"
	symLines[199] += "-y,-z,-x;y,-z,x;-y,z,x;y,z,-x"
	symLines[200]    = "x,y,z;-x+1/2,-y+1/2,z;-x+1/2,y,-z+1/2;x,-y+1/2,-z+1/2;z,x,y;z,-x+1/2,-y+1/2;"
	symLines[200] += "-z+1/2,-x+1/2,y;-z+1/2,x,-y+1/2;y,z,x;-y+1/2,z,-x+1/2;y,-z+1/2,-x+1/2;-y+1/2,-z+1/2,x;"
	symLines[200] += "-x,-y,-z;x+1/2,y+1/2,-z;x+1/2,-y,z+1/2;-x,y+1/2,z+1/2;-z,-x,-y;-z,x+1/2,y+1/2;"
	symLines[200] += "z+1/2,x+1/2,-y;z+1/2,-x,y+1/2;-y,-z,-x;y+1/2,-z,x+1/2;-y,z+1/2,x+1/2;y+1/2,z+1/2,-x"
	symLines[201]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[201] += "y,-z,-x;-y,-z,x;-x,-y,-z;x,y,-z;x,-y,z;-x,y,z;-z,-x,-y;-z,x,y;z,x,-y;z,-x,y;"
	symLines[201] += "-y,-z,-x;y,-z,x;-y,z,x;y,z,-x;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;-x,y+1/2,-z+1/2;"
	symLines[201] += "x,-y+1/2,-z+1/2;z,x+1/2,y+1/2;z,-x+1/2,-y+1/2;-z,-x+1/2,y+1/2;-z,x+1/2,-y+1/2;"
	symLines[201] += "y,z+1/2,x+1/2;-y,z+1/2,-x+1/2;y,-z+1/2,-x+1/2;-y,-z+1/2,x+1/2;-x,-y+1/2,-z+1/2;"
	symLines[201] += "x,y+1/2,-z+1/2;x,-y+1/2,z+1/2;-x,y+1/2,z+1/2;-z,-x+1/2,-y+1/2;-z,x+1/2,y+1/2;"
	symLines[201] += "z,x+1/2,-y+1/2;z,-x+1/2,y+1/2;-y,-z+1/2,-x+1/2;y,-z+1/2,x+1/2;-y,z+1/2,x+1/2;"
	symLines[201] += "y,z+1/2,-x+1/2;x+1/2,y,z+1/2;-x+1/2,-y,z+1/2;-x+1/2,y,-z+1/2;x+1/2,-y,-z+1/2;"
	symLines[201] += "z+1/2,x,y+1/2;z+1/2,-x,-y+1/2;-z+1/2,-x,y+1/2;-z+1/2,x,-y+1/2;y+1/2,z,x+1/2;"
	symLines[201] += "-y+1/2,z,-x+1/2;y+1/2,-z,-x+1/2;-y+1/2,-z,x+1/2;-x+1/2,-y,-z+1/2;x+1/2,y,-z+1/2;"
	symLines[201] += "x+1/2,-y,z+1/2;-x+1/2,y,z+1/2;-z+1/2,-x,-y+1/2;-z+1/2,x,y+1/2;z+1/2,x,-y+1/2;"
	symLines[201] += "z+1/2,-x,y+1/2;-y+1/2,-z,-x+1/2;y+1/2,-z,x+1/2;-y+1/2,z,x+1/2;y+1/2,z,-x+1/2;"
	symLines[201] += "x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;z+1/2,x+1/2,y;"
	symLines[201] += "z+1/2,-x+1/2,-y;-z+1/2,-x+1/2,y;-z+1/2,x+1/2,-y;y+1/2,z+1/2,x;-y+1/2,z+1/2,-x;"
	symLines[201] += "y+1/2,-z+1/2,-x;-y+1/2,-z+1/2,x;-x+1/2,-y+1/2,-z;x+1/2,y+1/2,-z;x+1/2,-y+1/2,z;"
	symLines[201] += "-x+1/2,y+1/2,z;-z+1/2,-x+1/2,-y;-z+1/2,x+1/2,y;z+1/2,x+1/2,-y;z+1/2,-x+1/2,y;"
	symLines[201] += "-y+1/2,-z+1/2,-x;y+1/2,-z+1/2,x;-y+1/2,z+1/2,x;y+1/2,z+1/2,-x"
	symLines[202]    = "x,y,z;-x+1/4,-y+1/4,z;-x+1/4,y,-z+1/4;x,-y+1/4,-z+1/4;z,x,y;z,-x+1/4,-y+1/4;"
	symLines[202] += "-z+1/4,-x+1/4,y;-z+1/4,x,-y+1/4;y,z,x;-y+1/4,z,-x+1/4;y,-z+1/4,-x+1/4;-y+1/4,-z+1/4,x;"
	symLines[202] += "-x,-y,-z;x+3/4,y+3/4,-z;x+3/4,-y,z+3/4;-x,y+3/4,z+3/4;-z,-x,-y;-z,x+3/4,y+3/4;"
	symLines[202] += "z+3/4,x+3/4,-y;z+3/4,-x,y+3/4;-y,-z,-x;y+3/4,-z,x+3/4;-y,z+3/4,x+3/4;y+3/4,z+3/4,-x;"
	symLines[202] += "x,y+1/2,z+1/2;-x+1/4,-y+3/4,z+1/2;-x+1/4,y+1/2,-z+3/4;x,-y+3/4,-z+3/4;z,x+1/2,y+1/2;"
	symLines[202] += "z,-x+3/4,-y+3/4;-z+1/4,-x+3/4,y+1/2;-z+1/4,x+1/2,-y+3/4;y,z+1/2,x+1/2;-y+1/4,z+1/2,-x+3/4;"
	symLines[202] += "y,-z+3/4,-x+3/4;-y+1/4,-z+3/4,x+1/2;-x,-y+1/2,-z+1/2;x+3/4,y+1/4,-z+1/2;"
	symLines[202] += "x+3/4,-y+1/2,z+1/4;-x,y+1/4,z+1/4;-z,-x+1/2,-y+1/2;-z,x+1/4,y+1/4;z+3/4,x+1/4,-y+1/2;"
	symLines[202] += "z+3/4,-x+1/2,y+1/4;-y,-z+1/2,-x+1/2;y+3/4,-z+1/2,x+1/4;-y,z+1/4,x+1/4;y+3/4,z+1/4,-x+1/2;"
	symLines[202] += "x+1/2,y,z+1/2;-x+3/4,-y+1/4,z+1/2;-x+3/4,y,-z+3/4;x+1/2,-y+1/4,-z+3/4;z+1/2,x,y+1/2;"
	symLines[202] += "z+1/2,-x+1/4,-y+3/4;-z+3/4,-x+1/4,y+1/2;-z+3/4,x,-y+3/4;y+1/2,z,x+1/2;-y+3/4,z,-x+3/4;"
	symLines[202] += "y+1/2,-z+1/4,-x+3/4;-y+3/4,-z+1/4,x+1/2;-x+1/2,-y,-z+1/2;x+1/4,y+3/4,-z+1/2;"
	symLines[202] += "x+1/4,-y,z+1/4;-x+1/2,y+3/4,z+1/4;-z+1/2,-x,-y+1/2;-z+1/2,x+3/4,y+1/4;z+1/4,x+3/4,-y+1/2;"
	symLines[202] += "z+1/4,-x,y+1/4;-y+1/2,-z,-x+1/2;y+1/4,-z,x+1/4;-y+1/2,z+3/4,x+1/4;y+1/4,z+3/4,-x+1/2;"
	symLines[202] += "x+1/2,y+1/2,z;-x+3/4,-y+3/4,z;-x+3/4,y+1/2,-z+1/4;x+1/2,-y+3/4,-z+1/4;z+1/2,x+1/2,y;"
	symLines[202] += "z+1/2,-x+3/4,-y+1/4;-z+3/4,-x+3/4,y;-z+3/4,x+1/2,-y+1/4;y+1/2,z+1/2,x;-y+3/4,z+1/2,-x+1/4;"
	symLines[202] += "y+1/2,-z+3/4,-x+1/4;-y+3/4,-z+3/4,x;-x+1/2,-y+1/2,-z;x+1/4,y+1/4,-z;x+1/4,-y+1/2,z+3/4;"
	symLines[202] += "-x+1/2,y+1/4,z+3/4;-z+1/2,-x+1/2,-y;-z+1/2,x+1/4,y+3/4;z+1/4,x+1/4,-y;z+1/4,-x+1/2,y+3/4;"
	symLines[202] += "-y+1/2,-z+1/2,-x;y+1/4,-z+1/2,x+3/4;-y+1/2,z+1/4,x+3/4;y+1/4,z+1/4,-x"
	symLines[203]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[203] += "y,-z,-x;-y,-z,x;-x,-y,-z;x,y,-z;x,-y,z;-x,y,z;-z,-x,-y;-z,x,y;z,x,-y;z,-x,y;"
	symLines[203] += "-y,-z,-x;y,-z,x;-y,z,x;y,z,-x;x+1/2,y+1/2,z+1/2;-x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,-z+1/2;"
	symLines[203] += "x+1/2,-y+1/2,-z+1/2;z+1/2,x+1/2,y+1/2;z+1/2,-x+1/2,-y+1/2;-z+1/2,-x+1/2,y+1/2;"
	symLines[203] += "-z+1/2,x+1/2,-y+1/2;y+1/2,z+1/2,x+1/2;-y+1/2,z+1/2,-x+1/2;y+1/2,-z+1/2,-x+1/2;"
	symLines[203] += "-y+1/2,-z+1/2,x+1/2;-x+1/2,-y+1/2,-z+1/2;x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,z+1/2;"
	symLines[203] += "-x+1/2,y+1/2,z+1/2;-z+1/2,-x+1/2,-y+1/2;-z+1/2,x+1/2,y+1/2;z+1/2,x+1/2,-y+1/2;"
	symLines[203] += "z+1/2,-x+1/2,y+1/2;-y+1/2,-z+1/2,-x+1/2;y+1/2,-z+1/2,x+1/2;-y+1/2,z+1/2,x+1/2;"
	symLines[203] += "y+1/2,z+1/2,-x+1/2"
	symLines[204]    = "x,y,z;-x+1/2,-y,z+1/2;-x,y+1/2,-z+1/2;x+1/2,-y+1/2,-z;z,x,y;z+1/2,-x+1/2,-y;"
	symLines[204] += "-z+1/2,-x,y+1/2;-z,x+1/2,-y+1/2;y,z,x;-y,z+1/2,-x+1/2;y+1/2,-z+1/2,-x;-y+1/2,-z,x+1/2;"
	symLines[204] += "-x,-y,-z;x+1/2,y,-z+1/2;x,-y+1/2,z+1/2;-x+1/2,y+1/2,z;-z,-x,-y;-z+1/2,x+1/2,y;"
	symLines[204] += "z+1/2,x,-y+1/2;z,-x+1/2,y+1/2;-y,-z,-x;y,-z+1/2,x+1/2;-y+1/2,z+1/2,x;y+1/2,z,-x+1/2"
	symLines[205]    = "x,y,z;-x+1/2,-y,z+1/2;-x,y+1/2,-z+1/2;x+1/2,-y+1/2,-z;z,x,y;z+1/2,-x+1/2,-y;"
	symLines[205] += "-z+1/2,-x,y+1/2;-z,x+1/2,-y+1/2;y,z,x;-y,z+1/2,-x+1/2;y+1/2,-z+1/2,-x;-y+1/2,-z,x+1/2;"
	symLines[205] += "-x,-y,-z;x+1/2,y,-z+1/2;x,-y+1/2,z+1/2;-x+1/2,y+1/2,z;-z,-x,-y;-z+1/2,x+1/2,y;"
	symLines[205] += "z+1/2,x,-y+1/2;z,-x+1/2,y+1/2;-y,-z,-x;y,-z+1/2,x+1/2;-y+1/2,z+1/2,x;y+1/2,z,-x+1/2;"
	symLines[205] += "x+1/2,y+1/2,z+1/2;-x,-y+1/2,z;-x+1/2,y,-z;x,-y,-z+1/2;z+1/2,x+1/2,y+1/2;"
	symLines[205] += "z,-x,-y+1/2;-z,-x+1/2,y;-z+1/2,x,-y;y+1/2,z+1/2,x+1/2;-y+1/2,z,-x;y,-z,-x+1/2;"
	symLines[205] += "-y,-z+1/2,x;-x+1/2,-y+1/2,-z+1/2;x,y+1/2,-z;x+1/2,-y,z;-x,y,z+1/2;-z+1/2,-x+1/2,-y+1/2;"
	symLines[205] += "-z,x,y+1/2;z,x+1/2,-y;z+1/2,-x,y;-y+1/2,-z+1/2,-x+1/2;y+1/2,-z,x;-y,z,x+1/2;"
	symLines[205] += "y,z+1/2,-x"
	symLines[206]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[206] += "y,-z,-x;-y,-z,x;y,x,-z;-y,-x,-z;y,-x,z;-y,x,z;x,z,-y;-x,z,y;-x,-z,-y;x,-z,y;"
	symLines[206] += "z,y,-x;z,-y,x;-z,y,x;-z,-y,-x"
	symLines[207]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[207] += "y,-z,-x;-y,-z,x;y+1/2,x+1/2,-z+1/2;-y+1/2,-x+1/2,-z+1/2;y+1/2,-x+1/2,z+1/2;"
	symLines[207] += "-y+1/2,x+1/2,z+1/2;x+1/2,z+1/2,-y+1/2;-x+1/2,z+1/2,y+1/2;-x+1/2,-z+1/2,-y+1/2;"
	symLines[207] += "x+1/2,-z+1/2,y+1/2;z+1/2,y+1/2,-x+1/2;z+1/2,-y+1/2,x+1/2;-z+1/2,y+1/2,x+1/2;"
	symLines[207] += "-z+1/2,-y+1/2,-x+1/2"
	symLines[208]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[208] += "y,-z,-x;-y,-z,x;y,x,-z;-y,-x,-z;y,-x,z;-y,x,z;x,z,-y;-x,z,y;-x,-z,-y;x,-z,y;"
	symLines[208] += "z,y,-x;z,-y,x;-z,y,x;-z,-y,-x;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;-x,y+1/2,-z+1/2;"
	symLines[208] += "x,-y+1/2,-z+1/2;z,x+1/2,y+1/2;z,-x+1/2,-y+1/2;-z,-x+1/2,y+1/2;-z,x+1/2,-y+1/2;"
	symLines[208] += "y,z+1/2,x+1/2;-y,z+1/2,-x+1/2;y,-z+1/2,-x+1/2;-y,-z+1/2,x+1/2;y,x+1/2,-z+1/2;"
	symLines[208] += "-y,-x+1/2,-z+1/2;y,-x+1/2,z+1/2;-y,x+1/2,z+1/2;x,z+1/2,-y+1/2;-x,z+1/2,y+1/2;"
	symLines[208] += "-x,-z+1/2,-y+1/2;x,-z+1/2,y+1/2;z,y+1/2,-x+1/2;z,-y+1/2,x+1/2;-z,y+1/2,x+1/2;"
	symLines[208] += "-z,-y+1/2,-x+1/2;x+1/2,y,z+1/2;-x+1/2,-y,z+1/2;-x+1/2,y,-z+1/2;x+1/2,-y,-z+1/2;"
	symLines[208] += "z+1/2,x,y+1/2;z+1/2,-x,-y+1/2;-z+1/2,-x,y+1/2;-z+1/2,x,-y+1/2;y+1/2,z,x+1/2;"
	symLines[208] += "-y+1/2,z,-x+1/2;y+1/2,-z,-x+1/2;-y+1/2,-z,x+1/2;y+1/2,x,-z+1/2;-y+1/2,-x,-z+1/2;"
	symLines[208] += "y+1/2,-x,z+1/2;-y+1/2,x,z+1/2;x+1/2,z,-y+1/2;-x+1/2,z,y+1/2;-x+1/2,-z,-y+1/2;"
	symLines[208] += "x+1/2,-z,y+1/2;z+1/2,y,-x+1/2;z+1/2,-y,x+1/2;-z+1/2,y,x+1/2;-z+1/2,-y,-x+1/2;"
	symLines[208] += "x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;z+1/2,x+1/2,y;"
	symLines[208] += "z+1/2,-x+1/2,-y;-z+1/2,-x+1/2,y;-z+1/2,x+1/2,-y;y+1/2,z+1/2,x;-y+1/2,z+1/2,-x;"
	symLines[208] += "y+1/2,-z+1/2,-x;-y+1/2,-z+1/2,x;y+1/2,x+1/2,-z;-y+1/2,-x+1/2,-z;y+1/2,-x+1/2,z;"
	symLines[208] += "-y+1/2,x+1/2,z;x+1/2,z+1/2,-y;-x+1/2,z+1/2,y;-x+1/2,-z+1/2,-y;x+1/2,-z+1/2,y;"
	symLines[208] += "z+1/2,y+1/2,-x;z+1/2,-y+1/2,x;-z+1/2,y+1/2,x;-z+1/2,-y+1/2,-x"
	symLines[209]    = "x,y,z;-x,-y+1/2,z+1/2;-x+1/2,y+1/2,-z;x+1/2,-y,-z+1/2;z,x,y;z+1/2,-x,-y+1/2;"
	symLines[209] += "-z,-x+1/2,y+1/2;-z+1/2,x+1/2,-y;y,z,x;-y+1/2,z+1/2,-x;y+1/2,-z,-x+1/2;-y,-z+1/2,x+1/2;"
	symLines[209] += "y+3/4,x+1/4,-z+3/4;-y+1/4,-x+1/4,-z+1/4;y+1/4,-x+3/4,z+3/4;-y+3/4,x+3/4,z+1/4;"
	symLines[209] += "x+3/4,z+1/4,-y+3/4;-x+3/4,z+3/4,y+1/4;-x+1/4,-z+1/4,-y+1/4;x+1/4,-z+3/4,y+3/4;"
	symLines[209] += "z+3/4,y+1/4,-x+3/4;z+1/4,-y+3/4,x+3/4;-z+3/4,y+3/4,x+1/4;-z+1/4,-y+1/4,-x+1/4;"
	symLines[209] += "x,y+1/2,z+1/2;-x,-y,z;-x+1/2,y,-z+1/2;x+1/2,-y+1/2,-z;z,x+1/2,y+1/2;z+1/2,-x+1/2,-y;"
	symLines[209] += "-z,-x,y;-z+1/2,x,-y+1/2;y,z+1/2,x+1/2;-y+1/2,z,-x+1/2;y+1/2,-z+1/2,-x;-y,-z,x;"
	symLines[209] += "y+3/4,x+3/4,-z+1/4;-y+1/4,-x+3/4,-z+3/4;y+1/4,-x+1/4,z+1/4;-y+3/4,x+1/4,z+3/4;"
	symLines[209] += "x+3/4,z+3/4,-y+1/4;-x+3/4,z+1/4,y+3/4;-x+1/4,-z+3/4,-y+3/4;x+1/4,-z+1/4,y+1/4;"
	symLines[209] += "z+3/4,y+3/4,-x+1/4;z+1/4,-y+1/4,x+1/4;-z+3/4,y+1/4,x+3/4;-z+1/4,-y+3/4,-x+3/4;"
	symLines[209] += "x+1/2,y,z+1/2;-x+1/2,-y+1/2,z;-x,y+1/2,-z+1/2;x,-y,-z;z+1/2,x,y+1/2;z,-x,-y;"
	symLines[209] += "-z+1/2,-x+1/2,y;-z,x+1/2,-y+1/2;y+1/2,z,x+1/2;-y,z+1/2,-x+1/2;y,-z,-x;-y+1/2,-z+1/2,x;"
	symLines[209] += "y+1/4,x+1/4,-z+1/4;-y+3/4,-x+1/4,-z+3/4;y+3/4,-x+3/4,z+1/4;-y+1/4,x+3/4,z+3/4;"
	symLines[209] += "x+1/4,z+1/4,-y+1/4;-x+1/4,z+3/4,y+3/4;-x+3/4,-z+1/4,-y+3/4;x+3/4,-z+3/4,y+1/4;"
	symLines[209] += "z+1/4,y+1/4,-x+1/4;z+3/4,-y+3/4,x+1/4;-z+1/4,y+3/4,x+3/4;-z+3/4,-y+1/4,-x+3/4;"
	symLines[209] += "x+1/2,y+1/2,z;-x+1/2,-y,z+1/2;-x,y,-z;x,-y+1/2,-z+1/2;z+1/2,x+1/2,y;z,-x+1/2,-y+1/2;"
	symLines[209] += "-z+1/2,-x,y+1/2;-z,x,-y;y+1/2,z+1/2,x;-y,z,-x;y,-z+1/2,-x+1/2;-y+1/2,-z,x+1/2;"
	symLines[209] += "y+1/4,x+3/4,-z+3/4;-y+3/4,-x+3/4,-z+1/4;y+3/4,-x+1/4,z+3/4;-y+1/4,x+1/4,z+1/4;"
	symLines[209] += "x+1/4,z+3/4,-y+3/4;-x+1/4,z+1/4,y+1/4;-x+3/4,-z+3/4,-y+1/4;x+3/4,-z+1/4,y+3/4;"
	symLines[209] += "z+1/4,y+3/4,-x+3/4;z+3/4,-y+1/4,x+3/4;-z+1/4,y+1/4,x+1/4;-z+3/4,-y+3/4,-x+1/4"
	symLines[210]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[210] += "y,-z,-x;-y,-z,x;y,x,-z;-y,-x,-z;y,-x,z;-y,x,z;x,z,-y;-x,z,y;-x,-z,-y;x,-z,y;"
	symLines[210] += "z,y,-x;z,-y,x;-z,y,x;-z,-y,-x;x+1/2,y+1/2,z+1/2;-x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,-z+1/2;"
	symLines[210] += "x+1/2,-y+1/2,-z+1/2;z+1/2,x+1/2,y+1/2;z+1/2,-x+1/2,-y+1/2;-z+1/2,-x+1/2,y+1/2;"
	symLines[210] += "-z+1/2,x+1/2,-y+1/2;y+1/2,z+1/2,x+1/2;-y+1/2,z+1/2,-x+1/2;y+1/2,-z+1/2,-x+1/2;"
	symLines[210] += "-y+1/2,-z+1/2,x+1/2;y+1/2,x+1/2,-z+1/2;-y+1/2,-x+1/2,-z+1/2;y+1/2,-x+1/2,z+1/2;"
	symLines[210] += "-y+1/2,x+1/2,z+1/2;x+1/2,z+1/2,-y+1/2;-x+1/2,z+1/2,y+1/2;-x+1/2,-z+1/2,-y+1/2;"
	symLines[210] += "x+1/2,-z+1/2,y+1/2;z+1/2,y+1/2,-x+1/2;z+1/2,-y+1/2,x+1/2;-z+1/2,y+1/2,x+1/2;"
	symLines[210] += "-z+1/2,-y+1/2,-x+1/2"
	symLines[211]    = "x,y,z;-x+1/2,-y,z+1/2;-x,y+1/2,-z+1/2;x+1/2,-y+1/2,-z;z,x,y;z+1/2,-x+1/2,-y;"
	symLines[211] += "-z+1/2,-x,y+1/2;-z,x+1/2,-y+1/2;y,z,x;-y,z+1/2,-x+1/2;y+1/2,-z+1/2,-x;-y+1/2,-z,x+1/2;"
	symLines[211] += "y+1/4,x+3/4,-z+3/4;-y+1/4,-x+1/4,-z+1/4;y+3/4,-x+3/4,z+1/4;-y+3/4,x+1/4,z+3/4;"
	symLines[211] += "x+1/4,z+3/4,-y+3/4;-x+3/4,z+1/4,y+3/4;-x+1/4,-z+1/4,-y+1/4;x+3/4,-z+3/4,y+1/4;"
	symLines[211] += "z+1/4,y+3/4,-x+3/4;z+3/4,-y+3/4,x+1/4;-z+3/4,y+1/4,x+3/4;-z+1/4,-y+1/4,-x+1/4"
	symLines[212]    = "x,y,z;-x+1/2,-y,z+1/2;-x,y+1/2,-z+1/2;x+1/2,-y+1/2,-z;z,x,y;z+1/2,-x+1/2,-y;"
	symLines[212] += "-z+1/2,-x,y+1/2;-z,x+1/2,-y+1/2;y,z,x;-y,z+1/2,-x+1/2;y+1/2,-z+1/2,-x;-y+1/2,-z,x+1/2;"
	symLines[212] += "y+3/4,x+1/4,-z+1/4;-y+3/4,-x+3/4,-z+3/4;y+1/4,-x+1/4,z+3/4;-y+1/4,x+3/4,z+1/4;"
	symLines[212] += "x+3/4,z+1/4,-y+1/4;-x+1/4,z+3/4,y+1/4;-x+3/4,-z+3/4,-y+3/4;x+1/4,-z+1/4,y+3/4;"
	symLines[212] += "z+3/4,y+1/4,-x+1/4;z+1/4,-y+1/4,x+3/4;-z+1/4,y+3/4,x+1/4;-z+3/4,-y+3/4,-x+3/4"
	symLines[213]    = "x,y,z;-x+1/2,-y,z+1/2;-x,y+1/2,-z+1/2;x+1/2,-y+1/2,-z;z,x,y;z+1/2,-x+1/2,-y;"
	symLines[213] += "-z+1/2,-x,y+1/2;-z,x+1/2,-y+1/2;y,z,x;-y,z+1/2,-x+1/2;y+1/2,-z+1/2,-x;-y+1/2,-z,x+1/2;"
	symLines[213] += "y+3/4,x+1/4,-z+1/4;-y+3/4,-x+3/4,-z+3/4;y+1/4,-x+1/4,z+3/4;-y+1/4,x+3/4,z+1/4;"
	symLines[213] += "x+3/4,z+1/4,-y+1/4;-x+1/4,z+3/4,y+1/4;-x+3/4,-z+3/4,-y+3/4;x+1/4,-z+1/4,y+3/4;"
	symLines[213] += "z+3/4,y+1/4,-x+1/4;z+1/4,-y+1/4,x+3/4;-z+1/4,y+3/4,x+1/4;-z+3/4,-y+3/4,-x+3/4;"
	symLines[213] += "x+1/2,y+1/2,z+1/2;-x,-y+1/2,z;-x+1/2,y,-z;x,-y,-z+1/2;z+1/2,x+1/2,y+1/2;"
	symLines[213] += "z,-x,-y+1/2;-z,-x+1/2,y;-z+1/2,x,-y;y+1/2,z+1/2,x+1/2;-y+1/2,z,-x;y,-z,-x+1/2;"
	symLines[213] += "-y,-z+1/2,x;y+1/4,x+3/4,-z+3/4;-y+1/4,-x+1/4,-z+1/4;y+3/4,-x+3/4,z+1/4;"
	symLines[213] += "-y+3/4,x+1/4,z+3/4;x+1/4,z+3/4,-y+3/4;-x+3/4,z+1/4,y+3/4;-x+1/4,-z+1/4,-y+1/4;"
	symLines[213] += "x+3/4,-z+3/4,y+1/4;z+1/4,y+3/4,-x+3/4;z+3/4,-y+3/4,x+1/4;-z+3/4,y+1/4,x+3/4;"
	symLines[213] += "-z+1/4,-y+1/4,-x+1/4"
	symLines[214]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[214] += "y,-z,-x;-y,-z,x;y,x,z;-y,-x,z;y,-x,-z;-y,x,-z;x,z,y;-x,z,-y;-x,-z,y;x,-z,-y;"
	symLines[214] += "z,y,x;z,-y,-x;-z,y,-x;-z,-y,x"
	symLines[215]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[215] += "y,-z,-x;-y,-z,x;y,x,z;-y,-x,z;y,-x,-z;-y,x,-z;x,z,y;-x,z,-y;-x,-z,y;x,-z,-y;"
	symLines[215] += "z,y,x;z,-y,-x;-z,y,-x;-z,-y,x;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;-x,y+1/2,-z+1/2;"
	symLines[215] += "x,-y+1/2,-z+1/2;z,x+1/2,y+1/2;z,-x+1/2,-y+1/2;-z,-x+1/2,y+1/2;-z,x+1/2,-y+1/2;"
	symLines[215] += "y,z+1/2,x+1/2;-y,z+1/2,-x+1/2;y,-z+1/2,-x+1/2;-y,-z+1/2,x+1/2;y,x+1/2,z+1/2;"
	symLines[215] += "-y,-x+1/2,z+1/2;y,-x+1/2,-z+1/2;-y,x+1/2,-z+1/2;x,z+1/2,y+1/2;-x,z+1/2,-y+1/2;"
	symLines[215] += "-x,-z+1/2,y+1/2;x,-z+1/2,-y+1/2;z,y+1/2,x+1/2;z,-y+1/2,-x+1/2;-z,y+1/2,-x+1/2;"
	symLines[215] += "-z,-y+1/2,x+1/2;x+1/2,y,z+1/2;-x+1/2,-y,z+1/2;-x+1/2,y,-z+1/2;x+1/2,-y,-z+1/2;"
	symLines[215] += "z+1/2,x,y+1/2;z+1/2,-x,-y+1/2;-z+1/2,-x,y+1/2;-z+1/2,x,-y+1/2;y+1/2,z,x+1/2;"
	symLines[215] += "-y+1/2,z,-x+1/2;y+1/2,-z,-x+1/2;-y+1/2,-z,x+1/2;y+1/2,x,z+1/2;-y+1/2,-x,z+1/2;"
	symLines[215] += "y+1/2,-x,-z+1/2;-y+1/2,x,-z+1/2;x+1/2,z,y+1/2;-x+1/2,z,-y+1/2;-x+1/2,-z,y+1/2;"
	symLines[215] += "x+1/2,-z,-y+1/2;z+1/2,y,x+1/2;z+1/2,-y,-x+1/2;-z+1/2,y,-x+1/2;-z+1/2,-y,x+1/2;"
	symLines[215] += "x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;z+1/2,x+1/2,y;"
	symLines[215] += "z+1/2,-x+1/2,-y;-z+1/2,-x+1/2,y;-z+1/2,x+1/2,-y;y+1/2,z+1/2,x;-y+1/2,z+1/2,-x;"
	symLines[215] += "y+1/2,-z+1/2,-x;-y+1/2,-z+1/2,x;y+1/2,x+1/2,z;-y+1/2,-x+1/2,z;y+1/2,-x+1/2,-z;"
	symLines[215] += "-y+1/2,x+1/2,-z;x+1/2,z+1/2,y;-x+1/2,z+1/2,-y;-x+1/2,-z+1/2,y;x+1/2,-z+1/2,-y;"
	symLines[215] += "z+1/2,y+1/2,x;z+1/2,-y+1/2,-x;-z+1/2,y+1/2,-x;-z+1/2,-y+1/2,x"
	symLines[216]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[216] += "y,-z,-x;-y,-z,x;y,x,z;-y,-x,z;y,-x,-z;-y,x,-z;x,z,y;-x,z,-y;-x,-z,y;x,-z,-y;"
	symLines[216] += "z,y,x;z,-y,-x;-z,y,-x;-z,-y,x;x+1/2,y+1/2,z+1/2;-x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,-z+1/2;"
	symLines[216] += "x+1/2,-y+1/2,-z+1/2;z+1/2,x+1/2,y+1/2;z+1/2,-x+1/2,-y+1/2;-z+1/2,-x+1/2,y+1/2;"
	symLines[216] += "-z+1/2,x+1/2,-y+1/2;y+1/2,z+1/2,x+1/2;-y+1/2,z+1/2,-x+1/2;y+1/2,-z+1/2,-x+1/2;"
	symLines[216] += "-y+1/2,-z+1/2,x+1/2;y+1/2,x+1/2,z+1/2;-y+1/2,-x+1/2,z+1/2;y+1/2,-x+1/2,-z+1/2;"
	symLines[216] += "-y+1/2,x+1/2,-z+1/2;x+1/2,z+1/2,y+1/2;-x+1/2,z+1/2,-y+1/2;-x+1/2,-z+1/2,y+1/2;"
	symLines[216] += "x+1/2,-z+1/2,-y+1/2;z+1/2,y+1/2,x+1/2;z+1/2,-y+1/2,-x+1/2;-z+1/2,y+1/2,-x+1/2;"
	symLines[216] += "-z+1/2,-y+1/2,x+1/2"
	symLines[217]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[217] += "y,-z,-x;-y,-z,x;y+1/2,x+1/2,z+1/2;-y+1/2,-x+1/2,z+1/2;y+1/2,-x+1/2,-z+1/2;"
	symLines[217] += "-y+1/2,x+1/2,-z+1/2;x+1/2,z+1/2,y+1/2;-x+1/2,z+1/2,-y+1/2;-x+1/2,-z+1/2,y+1/2;"
	symLines[217] += "x+1/2,-z+1/2,-y+1/2;z+1/2,y+1/2,x+1/2;z+1/2,-y+1/2,-x+1/2;-z+1/2,y+1/2,-x+1/2;"
	symLines[217] += "-z+1/2,-y+1/2,x+1/2"
	symLines[218]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[218] += "y,-z,-x;-y,-z,x;y+1/2,x+1/2,z+1/2;-y+1/2,-x+1/2,z+1/2;y+1/2,-x+1/2,-z+1/2;"
	symLines[218] += "-y+1/2,x+1/2,-z+1/2;x+1/2,z+1/2,y+1/2;-x+1/2,z+1/2,-y+1/2;-x+1/2,-z+1/2,y+1/2;"
	symLines[218] += "x+1/2,-z+1/2,-y+1/2;z+1/2,y+1/2,x+1/2;z+1/2,-y+1/2,-x+1/2;-z+1/2,y+1/2,-x+1/2;"
	symLines[218] += "-z+1/2,-y+1/2,x+1/2;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;-x,y+1/2,-z+1/2;x,-y+1/2,-z+1/2;"
	symLines[218] += "z,x+1/2,y+1/2;z,-x+1/2,-y+1/2;-z,-x+1/2,y+1/2;-z,x+1/2,-y+1/2;y,z+1/2,x+1/2;"
	symLines[218] += "-y,z+1/2,-x+1/2;y,-z+1/2,-x+1/2;-y,-z+1/2,x+1/2;y+1/2,x,z;-y+1/2,-x,z;y+1/2,-x,-z;"
	symLines[218] += "-y+1/2,x,-z;x+1/2,z,y;-x+1/2,z,-y;-x+1/2,-z,y;x+1/2,-z,-y;z+1/2,y,x;z+1/2,-y,-x;"
	symLines[218] += "-z+1/2,y,-x;-z+1/2,-y,x;x+1/2,y,z+1/2;-x+1/2,-y,z+1/2;-x+1/2,y,-z+1/2;x+1/2,-y,-z+1/2;"
	symLines[218] += "z+1/2,x,y+1/2;z+1/2,-x,-y+1/2;-z+1/2,-x,y+1/2;-z+1/2,x,-y+1/2;y+1/2,z,x+1/2;"
	symLines[218] += "-y+1/2,z,-x+1/2;y+1/2,-z,-x+1/2;-y+1/2,-z,x+1/2;y,x+1/2,z;-y,-x+1/2,z;y,-x+1/2,-z;"
	symLines[218] += "-y,x+1/2,-z;x,z+1/2,y;-x,z+1/2,-y;-x,-z+1/2,y;x,-z+1/2,-y;z,y+1/2,x;z,-y+1/2,-x;"
	symLines[218] += "-z,y+1/2,-x;-z,-y+1/2,x;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;"
	symLines[218] += "z+1/2,x+1/2,y;z+1/2,-x+1/2,-y;-z+1/2,-x+1/2,y;-z+1/2,x+1/2,-y;y+1/2,z+1/2,x;"
	symLines[218] += "-y+1/2,z+1/2,-x;y+1/2,-z+1/2,-x;-y+1/2,-z+1/2,x;y,x,z+1/2;-y,-x,z+1/2;y,-x,-z+1/2;"
	symLines[218] += "-y,x,-z+1/2;x,z,y+1/2;-x,z,-y+1/2;-x,-z,y+1/2;x,-z,-y+1/2;z,y,x+1/2;z,-y,-x+1/2;"
	symLines[218] += "-z,y,-x+1/2;-z,-y,x+1/2"
	symLines[219]    = "x,y,z;-x+1/2,-y,z+1/2;-x,y+1/2,-z+1/2;x+1/2,-y+1/2,-z;z,x,y;z+1/2,-x+1/2,-y;"
	symLines[219] += "-z+1/2,-x,y+1/2;-z,x+1/2,-y+1/2;y,z,x;-y,z+1/2,-x+1/2;y+1/2,-z+1/2,-x;-y+1/2,-z,x+1/2;"
	symLines[219] += "y+1/4,x+1/4,z+1/4;-y+1/4,-x+3/4,z+3/4;y+3/4,-x+1/4,-z+3/4;-y+3/4,x+3/4,-z+1/4;"
	symLines[219] += "x+1/4,z+1/4,y+1/4;-x+3/4,z+3/4,-y+1/4;-x+1/4,-z+3/4,y+3/4;x+3/4,-z+1/4,-y+3/4;"
	symLines[219] += "z+1/4,y+1/4,x+1/4;z+3/4,-y+1/4,-x+3/4;-z+3/4,y+3/4,-x+1/4;-z+1/4,-y+3/4,x+3/4;"
	symLines[219] += "x+1/2,y+1/2,z+1/2;-x,-y+1/2,z;-x+1/2,y,-z;x,-y,-z+1/2;z+1/2,x+1/2,y+1/2;"
	symLines[219] += "z,-x,-y+1/2;-z,-x+1/2,y;-z+1/2,x,-y;y+1/2,z+1/2,x+1/2;-y+1/2,z,-x;y,-z,-x+1/2;"
	symLines[219] += "-y,-z+1/2,x;y+3/4,x+3/4,z+3/4;-y+3/4,-x+1/4,z+1/4;y+1/4,-x+3/4,-z+1/4;-y+1/4,x+1/4,-z+3/4;"
	symLines[219] += "x+3/4,z+3/4,y+3/4;-x+1/4,z+1/4,-y+3/4;-x+3/4,-z+1/4,y+1/4;x+1/4,-z+3/4,-y+1/4;"
	symLines[219] += "z+3/4,y+3/4,x+3/4;z+1/4,-y+3/4,-x+1/4;-z+1/4,y+1/4,-x+3/4;-z+3/4,-y+1/4,x+1/4"
	symLines[220]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[220] += "y,-z,-x;-y,-z,x;y,x,-z;-y,-x,-z;y,-x,z;-y,x,z;x,z,-y;-x,z,y;-x,-z,-y;x,-z,y;"
	symLines[220] += "z,y,-x;z,-y,x;-z,y,x;-z,-y,-x;-x,-y,-z;x,y,-z;x,-y,z;-x,y,z;-z,-x,-y;-z,x,y;"
	symLines[220] += "z,x,-y;z,-x,y;-y,-z,-x;y,-z,x;-y,z,x;y,z,-x;-y,-x,z;y,x,z;-y,x,-z;y,-x,-z;"
	symLines[220] += "-x,-z,y;x,-z,-y;x,z,y;-x,z,-y;-z,-y,x;-z,y,-x;z,-y,-x;z,y,x"
	symLines[221]    = "x,y,z;-x+1/2,-y+1/2,z;-x+1/2,y,-z+1/2;x,-y+1/2,-z+1/2;z,x,y;z,-x+1/2,-y+1/2;"
	symLines[221] += "-z+1/2,-x+1/2,y;-z+1/2,x,-y+1/2;y,z,x;-y+1/2,z,-x+1/2;y,-z+1/2,-x+1/2;-y+1/2,-z+1/2,x;"
	symLines[221] += "y,x,-z+1/2;-y+1/2,-x+1/2,-z+1/2;y,-x+1/2,z;-y+1/2,x,z;x,z,-y+1/2;-x+1/2,z,y;"
	symLines[221] += "-x+1/2,-z+1/2,-y+1/2;x,-z+1/2,y;z,y,-x+1/2;z,-y+1/2,x;-z+1/2,y,x;-z+1/2,-y+1/2,-x+1/2;"
	symLines[221] += "-x,-y,-z;x+1/2,y+1/2,-z;x+1/2,-y,z+1/2;-x,y+1/2,z+1/2;-z,-x,-y;-z,x+1/2,y+1/2;"
	symLines[221] += "z+1/2,x+1/2,-y;z+1/2,-x,y+1/2;-y,-z,-x;y+1/2,-z,x+1/2;-y,z+1/2,x+1/2;y+1/2,z+1/2,-x;"
	symLines[221] += "-y,-x,z+1/2;y+1/2,x+1/2,z+1/2;-y,x+1/2,-z;y+1/2,-x,-z;-x,-z,y+1/2;x+1/2,-z,-y;"
	symLines[221] += "x+1/2,z+1/2,y+1/2;-x,z+1/2,-y;-z,-y,x+1/2;-z,y+1/2,-x;z+1/2,-y,-x;z+1/2,y+1/2,x+1/2"
	symLines[222]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[222] += "y,-z,-x;-y,-z,x;y+1/2,x+1/2,-z+1/2;-y+1/2,-x+1/2,-z+1/2;y+1/2,-x+1/2,z+1/2;"
	symLines[222] += "-y+1/2,x+1/2,z+1/2;x+1/2,z+1/2,-y+1/2;-x+1/2,z+1/2,y+1/2;-x+1/2,-z+1/2,-y+1/2;"
	symLines[222] += "x+1/2,-z+1/2,y+1/2;z+1/2,y+1/2,-x+1/2;z+1/2,-y+1/2,x+1/2;-z+1/2,y+1/2,x+1/2;"
	symLines[222] += "-z+1/2,-y+1/2,-x+1/2;-x,-y,-z;x,y,-z;x,-y,z;-x,y,z;-z,-x,-y;-z,x,y;z,x,-y;"
	symLines[222] += "z,-x,y;-y,-z,-x;y,-z,x;-y,z,x;y,z,-x;-y+1/2,-x+1/2,z+1/2;y+1/2,x+1/2,z+1/2;"
	symLines[222] += "-y+1/2,x+1/2,-z+1/2;y+1/2,-x+1/2,-z+1/2;-x+1/2,-z+1/2,y+1/2;x+1/2,-z+1/2,-y+1/2;"
	symLines[222] += "x+1/2,z+1/2,y+1/2;-x+1/2,z+1/2,-y+1/2;-z+1/2,-y+1/2,x+1/2;-z+1/2,y+1/2,-x+1/2;"
	symLines[222] += "z+1/2,-y+1/2,-x+1/2;z+1/2,y+1/2,x+1/2"
	symLines[223]    = "x,y,z;-x+1/2,-y+1/2,z;-x+1/2,y,-z+1/2;x,-y+1/2,-z+1/2;z,x,y;z,-x+1/2,-y+1/2;"
	symLines[223] += "-z+1/2,-x+1/2,y;-z+1/2,x,-y+1/2;y,z,x;-y+1/2,z,-x+1/2;y,-z+1/2,-x+1/2;-y+1/2,-z+1/2,x;"
	symLines[223] += "y+1/2,x+1/2,-z;-y,-x,-z;y+1/2,-x,z+1/2;-y,x+1/2,z+1/2;x+1/2,z+1/2,-y;-x,z+1/2,y+1/2;"
	symLines[223] += "-x,-z,-y;x+1/2,-z,y+1/2;z+1/2,y+1/2,-x;z+1/2,-y,x+1/2;-z,y+1/2,x+1/2;-z,-y,-x;"
	symLines[223] += "-x,-y,-z;x+1/2,y+1/2,-z;x+1/2,-y,z+1/2;-x,y+1/2,z+1/2;-z,-x,-y;-z,x+1/2,y+1/2;"
	symLines[223] += "z+1/2,x+1/2,-y;z+1/2,-x,y+1/2;-y,-z,-x;y+1/2,-z,x+1/2;-y,z+1/2,x+1/2;y+1/2,z+1/2,-x;"
	symLines[223] += "-y+1/2,-x+1/2,z;y,x,z;-y+1/2,x,-z+1/2;y,-x+1/2,-z+1/2;-x+1/2,-z+1/2,y;x,-z+1/2,-y+1/2;"
	symLines[223] += "x,z,y;-x+1/2,z,-y+1/2;-z+1/2,-y+1/2,x;-z+1/2,y,-x+1/2;z,-y+1/2,-x+1/2;z,y,x"
	symLines[224]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[224] += "y,-z,-x;-y,-z,x;y,x,-z;-y,-x,-z;y,-x,z;-y,x,z;x,z,-y;-x,z,y;-x,-z,-y;x,-z,y;"
	symLines[224] += "z,y,-x;z,-y,x;-z,y,x;-z,-y,-x;-x,-y,-z;x,y,-z;x,-y,z;-x,y,z;-z,-x,-y;-z,x,y;"
	symLines[224] += "z,x,-y;z,-x,y;-y,-z,-x;y,-z,x;-y,z,x;y,z,-x;-y,-x,z;y,x,z;-y,x,-z;y,-x,-z;"
	symLines[224] += "-x,-z,y;x,-z,-y;x,z,y;-x,z,-y;-z,-y,x;-z,y,-x;z,-y,-x;z,y,x;x,y+1/2,z+1/2;"
	symLines[224] += "-x,-y+1/2,z+1/2;-x,y+1/2,-z+1/2;x,-y+1/2,-z+1/2;z,x+1/2,y+1/2;z,-x+1/2,-y+1/2;"
	symLines[224] += "-z,-x+1/2,y+1/2;-z,x+1/2,-y+1/2;y,z+1/2,x+1/2;-y,z+1/2,-x+1/2;y,-z+1/2,-x+1/2;"
	symLines[224] += "-y,-z+1/2,x+1/2;y,x+1/2,-z+1/2;-y,-x+1/2,-z+1/2;y,-x+1/2,z+1/2;-y,x+1/2,z+1/2;"
	symLines[224] += "x,z+1/2,-y+1/2;-x,z+1/2,y+1/2;-x,-z+1/2,-y+1/2;x,-z+1/2,y+1/2;z,y+1/2,-x+1/2;"
	symLines[224] += "z,-y+1/2,x+1/2;-z,y+1/2,x+1/2;-z,-y+1/2,-x+1/2;-x,-y+1/2,-z+1/2;x,y+1/2,-z+1/2;"
	symLines[224] += "x,-y+1/2,z+1/2;-x,y+1/2,z+1/2;-z,-x+1/2,-y+1/2;-z,x+1/2,y+1/2;z,x+1/2,-y+1/2;"
	symLines[224] += "z,-x+1/2,y+1/2;-y,-z+1/2,-x+1/2;y,-z+1/2,x+1/2;-y,z+1/2,x+1/2;y,z+1/2,-x+1/2;"
	symLines[224] += "-y,-x+1/2,z+1/2;y,x+1/2,z+1/2;-y,x+1/2,-z+1/2;y,-x+1/2,-z+1/2;-x,-z+1/2,y+1/2;"
	symLines[224] += "x,-z+1/2,-y+1/2;x,z+1/2,y+1/2;-x,z+1/2,-y+1/2;-z,-y+1/2,x+1/2;-z,y+1/2,-x+1/2;"
	symLines[224] += "z,-y+1/2,-x+1/2;z,y+1/2,x+1/2;x+1/2,y,z+1/2;-x+1/2,-y,z+1/2;-x+1/2,y,-z+1/2;"
	symLines[224] += "x+1/2,-y,-z+1/2;z+1/2,x,y+1/2;z+1/2,-x,-y+1/2;-z+1/2,-x,y+1/2;-z+1/2,x,-y+1/2;"
	symLines[224] += "y+1/2,z,x+1/2;-y+1/2,z,-x+1/2;y+1/2,-z,-x+1/2;-y+1/2,-z,x+1/2;y+1/2,x,-z+1/2;"
	symLines[224] += "-y+1/2,-x,-z+1/2;y+1/2,-x,z+1/2;-y+1/2,x,z+1/2;x+1/2,z,-y+1/2;-x+1/2,z,y+1/2;"
	symLines[224] += "-x+1/2,-z,-y+1/2;x+1/2,-z,y+1/2;z+1/2,y,-x+1/2;z+1/2,-y,x+1/2;-z+1/2,y,x+1/2;"
	symLines[224] += "-z+1/2,-y,-x+1/2;-x+1/2,-y,-z+1/2;x+1/2,y,-z+1/2;x+1/2,-y,z+1/2;-x+1/2,y,z+1/2;"
	symLines[224] += "-z+1/2,-x,-y+1/2;-z+1/2,x,y+1/2;z+1/2,x,-y+1/2;z+1/2,-x,y+1/2;-y+1/2,-z,-x+1/2;"
	symLines[224] += "y+1/2,-z,x+1/2;-y+1/2,z,x+1/2;y+1/2,z,-x+1/2;-y+1/2,-x,z+1/2;y+1/2,x,z+1/2;"
	symLines[224] += "-y+1/2,x,-z+1/2;y+1/2,-x,-z+1/2;-x+1/2,-z,y+1/2;x+1/2,-z,-y+1/2;x+1/2,z,y+1/2;"
	symLines[224] += "-x+1/2,z,-y+1/2;-z+1/2,-y,x+1/2;-z+1/2,y,-x+1/2;z+1/2,-y,-x+1/2;z+1/2,y,x+1/2;"
	symLines[224] += "x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;z+1/2,x+1/2,y;"
	symLines[224] += "z+1/2,-x+1/2,-y;-z+1/2,-x+1/2,y;-z+1/2,x+1/2,-y;y+1/2,z+1/2,x;-y+1/2,z+1/2,-x;"
	symLines[224] += "y+1/2,-z+1/2,-x;-y+1/2,-z+1/2,x;y+1/2,x+1/2,-z;-y+1/2,-x+1/2,-z;y+1/2,-x+1/2,z;"
	symLines[224] += "-y+1/2,x+1/2,z;x+1/2,z+1/2,-y;-x+1/2,z+1/2,y;-x+1/2,-z+1/2,-y;x+1/2,-z+1/2,y;"
	symLines[224] += "z+1/2,y+1/2,-x;z+1/2,-y+1/2,x;-z+1/2,y+1/2,x;-z+1/2,-y+1/2,-x;-x+1/2,-y+1/2,-z;"
	symLines[224] += "x+1/2,y+1/2,-z;x+1/2,-y+1/2,z;-x+1/2,y+1/2,z;-z+1/2,-x+1/2,-y;-z+1/2,x+1/2,y;"
	symLines[224] += "z+1/2,x+1/2,-y;z+1/2,-x+1/2,y;-y+1/2,-z+1/2,-x;y+1/2,-z+1/2,x;-y+1/2,z+1/2,x;"
	symLines[224] += "y+1/2,z+1/2,-x;-y+1/2,-x+1/2,z;y+1/2,x+1/2,z;-y+1/2,x+1/2,-z;y+1/2,-x+1/2,-z;"
	symLines[224] += "-x+1/2,-z+1/2,y;x+1/2,-z+1/2,-y;x+1/2,z+1/2,y;-x+1/2,z+1/2,-y;-z+1/2,-y+1/2,x;"
	symLines[224] += "-z+1/2,y+1/2,-x;z+1/2,-y+1/2,-x;z+1/2,y+1/2,x"
	symLines[225]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[225] += "y,-z,-x;-y,-z,x;y+1/2,x+1/2,-z+1/2;-y+1/2,-x+1/2,-z+1/2;y+1/2,-x+1/2,z+1/2;"
	symLines[225] += "-y+1/2,x+1/2,z+1/2;x+1/2,z+1/2,-y+1/2;-x+1/2,z+1/2,y+1/2;-x+1/2,-z+1/2,-y+1/2;"
	symLines[225] += "x+1/2,-z+1/2,y+1/2;z+1/2,y+1/2,-x+1/2;z+1/2,-y+1/2,x+1/2;-z+1/2,y+1/2,x+1/2;"
	symLines[225] += "-z+1/2,-y+1/2,-x+1/2;-x,-y,-z;x,y,-z;x,-y,z;-x,y,z;-z,-x,-y;-z,x,y;z,x,-y;"
	symLines[225] += "z,-x,y;-y,-z,-x;y,-z,x;-y,z,x;y,z,-x;-y+1/2,-x+1/2,z+1/2;y+1/2,x+1/2,z+1/2;"
	symLines[225] += "-y+1/2,x+1/2,-z+1/2;y+1/2,-x+1/2,-z+1/2;-x+1/2,-z+1/2,y+1/2;x+1/2,-z+1/2,-y+1/2;"
	symLines[225] += "x+1/2,z+1/2,y+1/2;-x+1/2,z+1/2,-y+1/2;-z+1/2,-y+1/2,x+1/2;-z+1/2,y+1/2,-x+1/2;"
	symLines[225] += "z+1/2,-y+1/2,-x+1/2;z+1/2,y+1/2,x+1/2;x,y+1/2,z+1/2;-x,-y+1/2,z+1/2;-x,y+1/2,-z+1/2;"
	symLines[225] += "x,-y+1/2,-z+1/2;z,x+1/2,y+1/2;z,-x+1/2,-y+1/2;-z,-x+1/2,y+1/2;-z,x+1/2,-y+1/2;"
	symLines[225] += "y,z+1/2,x+1/2;-y,z+1/2,-x+1/2;y,-z+1/2,-x+1/2;-y,-z+1/2,x+1/2;y+1/2,x,-z;"
	symLines[225] += "-y+1/2,-x,-z;y+1/2,-x,z;-y+1/2,x,z;x+1/2,z,-y;-x+1/2,z,y;-x+1/2,-z,-y;x+1/2,-z,y;"
	symLines[225] += "z+1/2,y,-x;z+1/2,-y,x;-z+1/2,y,x;-z+1/2,-y,-x;-x,-y+1/2,-z+1/2;x,y+1/2,-z+1/2;"
	symLines[225] += "x,-y+1/2,z+1/2;-x,y+1/2,z+1/2;-z,-x+1/2,-y+1/2;-z,x+1/2,y+1/2;z,x+1/2,-y+1/2;"
	symLines[225] += "z,-x+1/2,y+1/2;-y,-z+1/2,-x+1/2;y,-z+1/2,x+1/2;-y,z+1/2,x+1/2;y,z+1/2,-x+1/2;"
	symLines[225] += "-y+1/2,-x,z;y+1/2,x,z;-y+1/2,x,-z;y+1/2,-x,-z;-x+1/2,-z,y;x+1/2,-z,-y;x+1/2,z,y;"
	symLines[225] += "-x+1/2,z,-y;-z+1/2,-y,x;-z+1/2,y,-x;z+1/2,-y,-x;z+1/2,y,x;x+1/2,y,z+1/2;"
	symLines[225] += "-x+1/2,-y,z+1/2;-x+1/2,y,-z+1/2;x+1/2,-y,-z+1/2;z+1/2,x,y+1/2;z+1/2,-x,-y+1/2;"
	symLines[225] += "-z+1/2,-x,y+1/2;-z+1/2,x,-y+1/2;y+1/2,z,x+1/2;-y+1/2,z,-x+1/2;y+1/2,-z,-x+1/2;"
	symLines[225] += "-y+1/2,-z,x+1/2;y,x+1/2,-z;-y,-x+1/2,-z;y,-x+1/2,z;-y,x+1/2,z;x,z+1/2,-y;"
	symLines[225] += "-x,z+1/2,y;-x,-z+1/2,-y;x,-z+1/2,y;z,y+1/2,-x;z,-y+1/2,x;-z,y+1/2,x;-z,-y+1/2,-x;"
	symLines[225] += "-x+1/2,-y,-z+1/2;x+1/2,y,-z+1/2;x+1/2,-y,z+1/2;-x+1/2,y,z+1/2;-z+1/2,-x,-y+1/2;"
	symLines[225] += "-z+1/2,x,y+1/2;z+1/2,x,-y+1/2;z+1/2,-x,y+1/2;-y+1/2,-z,-x+1/2;y+1/2,-z,x+1/2;"
	symLines[225] += "-y+1/2,z,x+1/2;y+1/2,z,-x+1/2;-y,-x+1/2,z;y,x+1/2,z;-y,x+1/2,-z;y,-x+1/2,-z;"
	symLines[225] += "-x,-z+1/2,y;x,-z+1/2,-y;x,z+1/2,y;-x,z+1/2,-y;-z,-y+1/2,x;-z,y+1/2,-x;z,-y+1/2,-x;"
	symLines[225] += "z,y+1/2,x;x+1/2,y+1/2,z;-x+1/2,-y+1/2,z;-x+1/2,y+1/2,-z;x+1/2,-y+1/2,-z;"
	symLines[225] += "z+1/2,x+1/2,y;z+1/2,-x+1/2,-y;-z+1/2,-x+1/2,y;-z+1/2,x+1/2,-y;y+1/2,z+1/2,x;"
	symLines[225] += "-y+1/2,z+1/2,-x;y+1/2,-z+1/2,-x;-y+1/2,-z+1/2,x;y,x,-z+1/2;-y,-x,-z+1/2;"
	symLines[225] += "y,-x,z+1/2;-y,x,z+1/2;x,z,-y+1/2;-x,z,y+1/2;-x,-z,-y+1/2;x,-z,y+1/2;z,y,-x+1/2;"
	symLines[225] += "z,-y,x+1/2;-z,y,x+1/2;-z,-y,-x+1/2;-x+1/2,-y+1/2,-z;x+1/2,y+1/2,-z;x+1/2,-y+1/2,z;"
	symLines[225] += "-x+1/2,y+1/2,z;-z+1/2,-x+1/2,-y;-z+1/2,x+1/2,y;z+1/2,x+1/2,-y;z+1/2,-x+1/2,y;"
	symLines[225] += "-y+1/2,-z+1/2,-x;y+1/2,-z+1/2,x;-y+1/2,z+1/2,x;y+1/2,z+1/2,-x;-y,-x,z+1/2;"
	symLines[225] += "y,x,z+1/2;-y,x,-z+1/2;y,-x,-z+1/2;-x,-z,y+1/2;x,-z,-y+1/2;x,z,y+1/2;-x,z,-y+1/2;"
	symLines[225] += "-z,-y,x+1/2;-z,y,-x+1/2;z,-y,-x+1/2;z,y,x+1/2"
	symLines[226]    = "x,y,z;-x+3/4,-y+1/4,z+1/2;-x+1/4,y+1/2,-z+3/4;x+1/2,-y+3/4,-z+1/4;z,x,y;"
	symLines[226] += "z+1/2,-x+3/4,-y+1/4;-z+3/4,-x+1/4,y+1/2;-z+1/4,x+1/2,-y+3/4;y,z,x;-y+1/4,z+1/2,-x+3/4;"
	symLines[226] += "y+1/2,-z+3/4,-x+1/4;-y+3/4,-z+1/4,x+1/2;y+3/4,x+1/4,-z+1/2;-y,-x,-z;y+1/4,-x+1/2,z+3/4;"
	symLines[226] += "-y+1/2,x+3/4,z+1/4;x+3/4,z+1/4,-y+1/2;-x+1/2,z+3/4,y+1/4;-x,-z,-y;x+1/4,-z+1/2,y+3/4;"
	symLines[226] += "z+3/4,y+1/4,-x+1/2;z+1/4,-y+1/2,x+3/4;-z+1/2,y+3/4,x+1/4;-z,-y,-x;-x,-y,-z;"
	symLines[226] += "x+1/4,y+3/4,-z+1/2;x+3/4,-y+1/2,z+1/4;-x+1/2,y+1/4,z+3/4;-z,-x,-y;-z+1/2,x+1/4,y+3/4;"
	symLines[226] += "z+1/4,x+3/4,-y+1/2;z+3/4,-x+1/2,y+1/4;-y,-z,-x;y+3/4,-z+1/2,x+1/4;-y+1/2,z+1/4,x+3/4;"
	symLines[226] += "y+1/4,z+3/4,-x+1/2;-y+1/4,-x+3/4,z+1/2;y,x,z;-y+3/4,x+1/2,-z+1/4;y+1/2,-x+1/4,-z+3/4;"
	symLines[226] += "-x+1/4,-z+3/4,y+1/2;x+1/2,-z+1/4,-y+3/4;x,z,y;-x+3/4,z+1/2,-y+1/4;-z+1/4,-y+3/4,x+1/2;"
	symLines[226] += "-z+3/4,y+1/2,-x+1/4;z+1/2,-y+1/4,-x+3/4;z,y,x;x,y+1/2,z+1/2;-x+3/4,-y+3/4,z;"
	symLines[226] += "-x+1/4,y,-z+1/4;x+1/2,-y+1/4,-z+3/4;z,x+1/2,y+1/2;z+1/2,-x+1/4,-y+3/4;-z+3/4,-x+3/4,y;"
	symLines[226] += "-z+1/4,x,-y+1/4;y,z+1/2,x+1/2;-y+1/4,z,-x+1/4;y+1/2,-z+1/4,-x+3/4;-y+3/4,-z+3/4,x;"
	symLines[226] += "y+3/4,x+3/4,-z;-y,-x+1/2,-z+1/2;y+1/4,-x,z+1/4;-y+1/2,x+1/4,z+3/4;x+3/4,z+3/4,-y;"
	symLines[226] += "-x+1/2,z+1/4,y+3/4;-x,-z+1/2,-y+1/2;x+1/4,-z,y+1/4;z+3/4,y+3/4,-x;z+1/4,-y,x+1/4;"
	symLines[226] += "-z+1/2,y+1/4,x+3/4;-z,-y+1/2,-x+1/2;-x,-y+1/2,-z+1/2;x+1/4,y+1/4,-z;x+3/4,-y,z+3/4;"
	symLines[226] += "-x+1/2,y+3/4,z+1/4;-z,-x+1/2,-y+1/2;-z+1/2,x+3/4,y+1/4;z+1/4,x+1/4,-y;z+3/4,-x,y+3/4;"
	symLines[226] += "-y,-z+1/2,-x+1/2;y+3/4,-z,x+3/4;-y+1/2,z+3/4,x+1/4;y+1/4,z+1/4,-x;-y+1/4,-x+1/4,z;"
	symLines[226] += "y,x+1/2,z+1/2;-y+3/4,x,-z+3/4;y+1/2,-x+3/4,-z+1/4;-x+1/4,-z+1/4,y;x+1/2,-z+3/4,-y+1/4;"
	symLines[226] += "x,z+1/2,y+1/2;-x+3/4,z,-y+3/4;-z+1/4,-y+1/4,x;-z+3/4,y,-x+3/4;z+1/2,-y+3/4,-x+1/4;"
	symLines[226] += "z,y+1/2,x+1/2;x+1/2,y,z+1/2;-x+1/4,-y+1/4,z;-x+3/4,y+1/2,-z+1/4;x,-y+3/4,-z+3/4;"
	symLines[226] += "z+1/2,x,y+1/2;z,-x+3/4,-y+3/4;-z+1/4,-x+1/4,y;-z+3/4,x+1/2,-y+1/4;y+1/2,z,x+1/2;"
	symLines[226] += "-y+3/4,z+1/2,-x+1/4;y,-z+3/4,-x+3/4;-y+1/4,-z+1/4,x;y+1/4,x+1/4,-z;-y+1/2,-x,-z+1/2;"
	symLines[226] += "y+3/4,-x+1/2,z+1/4;-y,x+3/4,z+3/4;x+1/4,z+1/4,-y;-x,z+3/4,y+3/4;-x+1/2,-z,-y+1/2;"
	symLines[226] += "x+3/4,-z+1/2,y+1/4;z+1/4,y+1/4,-x;z+3/4,-y+1/2,x+1/4;-z,y+3/4,x+3/4;-z+1/2,-y,-x+1/2;"
	symLines[226] += "-x+1/2,-y,-z+1/2;x+3/4,y+3/4,-z;x+1/4,-y+1/2,z+3/4;-x,y+1/4,z+1/4;-z+1/2,-x,-y+1/2;"
	symLines[226] += "-z,x+1/4,y+1/4;z+3/4,x+3/4,-y;z+1/4,-x+1/2,y+3/4;-y+1/2,-z,-x+1/2;y+1/4,-z+1/2,x+3/4;"
	symLines[226] += "-y,z+1/4,x+1/4;y+3/4,z+3/4,-x;-y+3/4,-x+3/4,z;y+1/2,x,z+1/2;-y+1/4,x+1/2,-z+3/4;"
	symLines[226] += "y,-x+1/4,-z+1/4;-x+3/4,-z+3/4,y;x,-z+1/4,-y+1/4;x+1/2,z,y+1/2;-x+1/4,z+1/2,-y+3/4;"
	symLines[226] += "-z+3/4,-y+3/4,x;-z+1/4,y+1/2,-x+3/4;z,-y+1/4,-x+1/4;z+1/2,y,x+1/2;x+1/2,y+1/2,z;"
	symLines[226] += "-x+1/4,-y+3/4,z+1/2;-x+3/4,y,-z+3/4;x,-y+1/4,-z+1/4;z+1/2,x+1/2,y;z,-x+1/4,-y+1/4;"
	symLines[226] += "-z+1/4,-x+3/4,y+1/2;-z+3/4,x,-y+3/4;y+1/2,z+1/2,x;-y+3/4,z,-x+3/4;y,-z+1/4,-x+1/4;"
	symLines[226] += "-y+1/4,-z+3/4,x+1/2;y+1/4,x+3/4,-z+1/2;-y+1/2,-x+1/2,-z;y+3/4,-x,z+3/4;"
	symLines[226] += "-y,x+1/4,z+1/4;x+1/4,z+3/4,-y+1/2;-x,z+1/4,y+1/4;-x+1/2,-z+1/2,-y;x+3/4,-z,y+3/4;"
	symLines[226] += "z+1/4,y+3/4,-x+1/2;z+3/4,-y,x+3/4;-z,y+1/4,x+1/4;-z+1/2,-y+1/2,-x;-x+1/2,-y+1/2,-z;"
	symLines[226] += "x+3/4,y+1/4,-z+1/2;x+1/4,-y,z+1/4;-x,y+3/4,z+3/4;-z+1/2,-x+1/2,-y;-z,x+3/4,y+3/4;"
	symLines[226] += "z+3/4,x+1/4,-y+1/2;z+1/4,-x,y+1/4;-y+1/2,-z+1/2,-x;y+1/4,-z,x+1/4;-y,z+3/4,x+3/4;"
	symLines[226] += "y+3/4,z+1/4,-x+1/2;-y+3/4,-x+1/4,z+1/2;y+1/2,x+1/2,z;-y+1/4,x,-z+1/4;y,-x+3/4,-z+3/4;"
	symLines[226] += "-x+3/4,-z+1/4,y+1/2;x,-z+3/4,-y+3/4;x+1/2,z+1/2,y;-x+1/4,z,-y+1/4;-z+3/4,-y+1/4,x+1/2;"
	symLines[226] += "-z+1/4,y,-x+1/4;z,-y+3/4,-x+3/4;z+1/2,y+1/2,x"
	symLines[227]    = "x,y,z;-x+1/4,-y+3/4,z+1/2;-x+3/4,y+1/2,-z+1/4;x+1/2,-y+1/4,-z+3/4;z,x,y;"
	symLines[227] += "z+1/2,-x+1/4,-y+3/4;-z+1/4,-x+3/4,y+1/2;-z+3/4,x+1/2,-y+1/4;y,z,x;-y+3/4,z+1/2,-x+1/4;"
	symLines[227] += "y+1/2,-z+1/4,-x+3/4;-y+1/4,-z+3/4,x+1/2;y+3/4,x+1/4,-z;-y+1/2,-x+1/2,-z+1/2;"
	symLines[227] += "y+1/4,-x,z+3/4;-y,x+3/4,z+1/4;x+3/4,z+1/4,-y;-x,z+3/4,y+1/4;-x+1/2,-z+1/2,-y+1/2;"
	symLines[227] += "x+1/4,-z,y+3/4;z+3/4,y+1/4,-x;z+1/4,-y,x+3/4;-z,y+3/4,x+1/4;-z+1/2,-y+1/2,-x+1/2;"
	symLines[227] += "-x,-y,-z;x+3/4,y+1/4,-z+1/2;x+1/4,-y+1/2,z+3/4;-x+1/2,y+3/4,z+1/4;-z,-x,-y;"
	symLines[227] += "-z+1/2,x+3/4,y+1/4;z+3/4,x+1/4,-y+1/2;z+1/4,-x+1/2,y+3/4;-y,-z,-x;y+1/4,-z+1/2,x+3/4;"
	symLines[227] += "-y+1/2,z+3/4,x+1/4;y+3/4,z+1/4,-x+1/2;-y+1/4,-x+3/4,z;y+1/2,x+1/2,z+1/2;"
	symLines[227] += "-y+3/4,x,-z+1/4;y,-x+1/4,-z+3/4;-x+1/4,-z+3/4,y;x,-z+1/4,-y+3/4;x+1/2,z+1/2,y+1/2;"
	symLines[227] += "-x+3/4,z,-y+1/4;-z+1/4,-y+3/4,x;-z+3/4,y,-x+1/4;z,-y+1/4,-x+3/4;z+1/2,y+1/2,x+1/2;"
	symLines[227] += "x,y+1/2,z+1/2;-x+1/4,-y+1/4,z;-x+3/4,y,-z+3/4;x+1/2,-y+3/4,-z+1/4;z,x+1/2,y+1/2;"
	symLines[227] += "z+1/2,-x+3/4,-y+1/4;-z+1/4,-x+1/4,y;-z+3/4,x,-y+3/4;y,z+1/2,x+1/2;-y+3/4,z,-x+3/4;"
	symLines[227] += "y+1/2,-z+3/4,-x+1/4;-y+1/4,-z+1/4,x;y+3/4,x+3/4,-z+1/2;-y+1/2,-x,-z;y+1/4,-x+1/2,z+1/4;"
	symLines[227] += "-y,x+1/4,z+3/4;x+3/4,z+3/4,-y+1/2;-x,z+1/4,y+3/4;-x+1/2,-z,-y;x+1/4,-z+1/2,y+1/4;"
	symLines[227] += "z+3/4,y+3/4,-x+1/2;z+1/4,-y+1/2,x+1/4;-z,y+1/4,x+3/4;-z+1/2,-y,-x;-x,-y+1/2,-z+1/2;"
	symLines[227] += "x+3/4,y+3/4,-z;x+1/4,-y,z+1/4;-x+1/2,y+1/4,z+3/4;-z,-x+1/2,-y+1/2;-z+1/2,x+1/4,y+3/4;"
	symLines[227] += "z+3/4,x+3/4,-y;z+1/4,-x,y+1/4;-y,-z+1/2,-x+1/2;y+1/4,-z,x+1/4;-y+1/2,z+1/4,x+3/4;"
	symLines[227] += "y+3/4,z+3/4,-x;-y+1/4,-x+1/4,z+1/2;y+1/2,x,z;-y+3/4,x+1/2,-z+3/4;y,-x+3/4,-z+1/4;"
	symLines[227] += "-x+1/4,-z+1/4,y+1/2;x,-z+3/4,-y+1/4;x+1/2,z,y;-x+3/4,z+1/2,-y+3/4;-z+1/4,-y+1/4,x+1/2;"
	symLines[227] += "-z+3/4,y+1/2,-x+3/4;z,-y+3/4,-x+1/4;z+1/2,y,x;x+1/2,y,z+1/2;-x+3/4,-y+3/4,z;"
	symLines[227] += "-x+1/4,y+1/2,-z+3/4;x,-y+1/4,-z+1/4;z+1/2,x,y+1/2;z,-x+1/4,-y+1/4;-z+3/4,-x+3/4,y;"
	symLines[227] += "-z+1/4,x+1/2,-y+3/4;y+1/2,z,x+1/2;-y+1/4,z+1/2,-x+3/4;y,-z+1/4,-x+1/4;-y+3/4,-z+3/4,x;"
	symLines[227] += "y+1/4,x+1/4,-z+1/2;-y,-x+1/2,-z;y+3/4,-x,z+1/4;-y+1/2,x+3/4,z+3/4;x+1/4,z+1/4,-y+1/2;"
	symLines[227] += "-x+1/2,z+3/4,y+3/4;-x,-z+1/2,-y;x+3/4,-z,y+1/4;z+1/4,y+1/4,-x+1/2;z+3/4,-y,x+1/4;"
	symLines[227] += "-z+1/2,y+3/4,x+3/4;-z,-y+1/2,-x;-x+1/2,-y,-z+1/2;x+1/4,y+1/4,-z;x+3/4,-y+1/2,z+1/4;"
	symLines[227] += "-x,y+3/4,z+3/4;-z+1/2,-x,-y+1/2;-z,x+3/4,y+3/4;z+1/4,x+1/4,-y;z+3/4,-x+1/2,y+1/4;"
	symLines[227] += "-y+1/2,-z,-x+1/2;y+3/4,-z+1/2,x+1/4;-y,z+3/4,x+3/4;y+1/4,z+1/4,-x;-y+3/4,-x+3/4,z+1/2;"
	symLines[227] += "y,x+1/2,z;-y+1/4,x,-z+3/4;y+1/2,-x+1/4,-z+1/4;-x+3/4,-z+3/4,y+1/2;x+1/2,-z+1/4,-y+1/4;"
	symLines[227] += "x,z+1/2,y;-x+1/4,z,-y+3/4;-z+3/4,-y+3/4,x+1/2;-z+1/4,y,-x+3/4;z+1/2,-y+1/4,-x+1/4;"
	symLines[227] += "z,y+1/2,x;x+1/2,y+1/2,z;-x+3/4,-y+1/4,z+1/2;-x+1/4,y,-z+1/4;x,-y+3/4,-z+3/4;"
	symLines[227] += "z+1/2,x+1/2,y;z,-x+3/4,-y+3/4;-z+3/4,-x+1/4,y+1/2;-z+1/4,x,-y+1/4;y+1/2,z+1/2,x;"
	symLines[227] += "-y+1/4,z,-x+1/4;y,-z+3/4,-x+3/4;-y+3/4,-z+1/4,x+1/2;y+1/4,x+3/4,-z;-y,-x,-z+1/2;"
	symLines[227] += "y+3/4,-x+1/2,z+3/4;-y+1/2,x+1/4,z+1/4;x+1/4,z+3/4,-y;-x+1/2,z+1/4,y+1/4;"
	symLines[227] += "-x,-z,-y+1/2;x+3/4,-z+1/2,y+3/4;z+1/4,y+3/4,-x;z+3/4,-y+1/2,x+3/4;-z+1/2,y+1/4,x+1/4;"
	symLines[227] += "-z,-y,-x+1/2;-x+1/2,-y+1/2,-z;x+1/4,y+3/4,-z+1/2;x+3/4,-y,z+3/4;-x,y+1/4,z+1/4;"
	symLines[227] += "-z+1/2,-x+1/2,-y;-z,x+1/4,y+1/4;z+1/4,x+3/4,-y+1/2;z+3/4,-x,y+3/4;-y+1/2,-z+1/2,-x;"
	symLines[227] += "y+3/4,-z,x+3/4;-y,z+1/4,x+1/4;y+1/4,z+3/4,-x+1/2;-y+3/4,-x+1/4,z;y,x,z+1/2;"
	symLines[227] += "-y+1/4,x+1/2,-z+1/4;y+1/2,-x+3/4,-z+3/4;-x+3/4,-z+1/4,y;x+1/2,-z+3/4,-y+3/4;"
	symLines[227] += "x,z,y+1/2;-x+1/4,z+1/2,-y+1/4;-z+3/4,-y+1/4,x;-z+1/4,y+1/2,-x+1/4;z+1/2,-y+3/4,-x+3/4;"
	symLines[227] += "z,y,x+1/2"
	symLines[228]    = "x,y,z;-x,-y,z;-x,y,-z;x,-y,-z;z,x,y;z,-x,-y;-z,-x,y;-z,x,-y;y,z,x;-y,z,-x;"
	symLines[228] += "y,-z,-x;-y,-z,x;y,x,-z;-y,-x,-z;y,-x,z;-y,x,z;x,z,-y;-x,z,y;-x,-z,-y;x,-z,y;"
	symLines[228] += "z,y,-x;z,-y,x;-z,y,x;-z,-y,-x;-x,-y,-z;x,y,-z;x,-y,z;-x,y,z;-z,-x,-y;-z,x,y;"
	symLines[228] += "z,x,-y;z,-x,y;-y,-z,-x;y,-z,x;-y,z,x;y,z,-x;-y,-x,z;y,x,z;-y,x,-z;y,-x,-z;"
	symLines[228] += "-x,-z,y;x,-z,-y;x,z,y;-x,z,-y;-z,-y,x;-z,y,-x;z,-y,-x;z,y,x;x+1/2,y+1/2,z+1/2;"
	symLines[228] += "-x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,-z+1/2;z+1/2,x+1/2,y+1/2;"
	symLines[228] += "z+1/2,-x+1/2,-y+1/2;-z+1/2,-x+1/2,y+1/2;-z+1/2,x+1/2,-y+1/2;y+1/2,z+1/2,x+1/2;"
	symLines[228] += "-y+1/2,z+1/2,-x+1/2;y+1/2,-z+1/2,-x+1/2;-y+1/2,-z+1/2,x+1/2;y+1/2,x+1/2,-z+1/2;"
	symLines[228] += "-y+1/2,-x+1/2,-z+1/2;y+1/2,-x+1/2,z+1/2;-y+1/2,x+1/2,z+1/2;x+1/2,z+1/2,-y+1/2;"
	symLines[228] += "-x+1/2,z+1/2,y+1/2;-x+1/2,-z+1/2,-y+1/2;x+1/2,-z+1/2,y+1/2;z+1/2,y+1/2,-x+1/2;"
	symLines[228] += "z+1/2,-y+1/2,x+1/2;-z+1/2,y+1/2,x+1/2;-z+1/2,-y+1/2,-x+1/2;-x+1/2,-y+1/2,-z+1/2;"
	symLines[228] += "x+1/2,y+1/2,-z+1/2;x+1/2,-y+1/2,z+1/2;-x+1/2,y+1/2,z+1/2;-z+1/2,-x+1/2,-y+1/2;"
	symLines[228] += "-z+1/2,x+1/2,y+1/2;z+1/2,x+1/2,-y+1/2;z+1/2,-x+1/2,y+1/2;-y+1/2,-z+1/2,-x+1/2;"
	symLines[228] += "y+1/2,-z+1/2,x+1/2;-y+1/2,z+1/2,x+1/2;y+1/2,z+1/2,-x+1/2;-y+1/2,-x+1/2,z+1/2;"
	symLines[228] += "y+1/2,x+1/2,z+1/2;-y+1/2,x+1/2,-z+1/2;y+1/2,-x+1/2,-z+1/2;-x+1/2,-z+1/2,y+1/2;"
	symLines[228] += "x+1/2,-z+1/2,-y+1/2;x+1/2,z+1/2,y+1/2;-x+1/2,z+1/2,-y+1/2;-z+1/2,-y+1/2,x+1/2;"
	symLines[228] += "-z+1/2,y+1/2,-x+1/2;z+1/2,-y+1/2,-x+1/2;z+1/2,y+1/2,x+1/2"
	symLines[229]    = "x,y,z;-x+1/2,-y,z+1/2;-x,y+1/2,-z+1/2;x+1/2,-y+1/2,-z;z,x,y;z+1/2,-x+1/2,-y;"
	symLines[229] += "-z+1/2,-x,y+1/2;-z,x+1/2,-y+1/2;y,z,x;-y,z+1/2,-x+1/2;y+1/2,-z+1/2,-x;-y+1/2,-z,x+1/2;"
	symLines[229] += "y+3/4,x+1/4,-z+1/4;-y+3/4,-x+3/4,-z+3/4;y+1/4,-x+1/4,z+3/4;-y+1/4,x+3/4,z+1/4;"
	symLines[229] += "x+3/4,z+1/4,-y+1/4;-x+1/4,z+3/4,y+1/4;-x+3/4,-z+3/4,-y+3/4;x+1/4,-z+1/4,y+3/4;"
	symLines[229] += "z+3/4,y+1/4,-x+1/4;z+1/4,-y+1/4,x+3/4;-z+1/4,y+3/4,x+1/4;-z+3/4,-y+3/4,-x+3/4;"
	symLines[229] += "-x,-y,-z;x+1/2,y,-z+1/2;x,-y+1/2,z+1/2;-x+1/2,y+1/2,z;-z,-x,-y;-z+1/2,x+1/2,y;"
	symLines[229] += "z+1/2,x,-y+1/2;z,-x+1/2,y+1/2;-y,-z,-x;y,-z+1/2,x+1/2;-y+1/2,z+1/2,x;y+1/2,z,-x+1/2;"
	symLines[229] += "-y+1/4,-x+3/4,z+3/4;y+1/4,x+1/4,z+1/4;-y+3/4,x+3/4,-z+1/4;y+3/4,-x+1/4,-z+3/4;"
	symLines[229] += "-x+1/4,-z+3/4,y+3/4;x+3/4,-z+1/4,-y+3/4;x+1/4,z+1/4,y+1/4;-x+3/4,z+3/4,-y+1/4;"
	symLines[229] += "-z+1/4,-y+3/4,x+3/4;-z+3/4,y+3/4,-x+1/4;z+3/4,-y+1/4,-x+3/4;z+1/4,y+1/4,x+1/4;"
	symLines[229] += "x+1/2,y+1/2,z+1/2;-x,-y+1/2,z;-x+1/2,y,-z;x,-y,-z+1/2;z+1/2,x+1/2,y+1/2;"
	symLines[229] += "z,-x,-y+1/2;-z,-x+1/2,y;-z+1/2,x,-y;y+1/2,z+1/2,x+1/2;-y+1/2,z,-x;y,-z,-x+1/2;"
	symLines[229] += "-y,-z+1/2,x;y+1/4,x+3/4,-z+3/4;-y+1/4,-x+1/4,-z+1/4;y+3/4,-x+3/4,z+1/4;"
	symLines[229] += "-y+3/4,x+1/4,z+3/4;x+1/4,z+3/4,-y+3/4;-x+3/4,z+1/4,y+3/4;-x+1/4,-z+1/4,-y+1/4;"
	symLines[229] += "x+3/4,-z+3/4,y+1/4;z+1/4,y+3/4,-x+3/4;z+3/4,-y+3/4,x+1/4;-z+3/4,y+1/4,x+3/4;"
	symLines[229] += "-z+1/4,-y+1/4,-x+1/4;-x+1/2,-y+1/2,-z+1/2;x,y+1/2,-z;x+1/2,-y,z;-x,y,z+1/2;"
	symLines[229] += "-z+1/2,-x+1/2,-y+1/2;-z,x,y+1/2;z,x+1/2,-y;z+1/2,-x,y;-y+1/2,-z+1/2,-x+1/2;"
	symLines[229] += "y+1/2,-z,x;-y,z,x+1/2;y,z+1/2,-x;-y+3/4,-x+1/4,z+1/4;y+3/4,x+3/4,z+3/4;"
	symLines[229] += "-y+1/4,x+1/4,-z+3/4;y+1/4,-x+3/4,-z+1/4;-x+3/4,-z+1/4,y+1/4;x+1/4,-z+3/4,-y+1/4;"
	symLines[229] += "x+3/4,z+3/4,y+3/4;-x+1/4,z+1/4,-y+3/4;-z+3/4,-y+1/4,x+1/4;-z+1/4,y+1/4,-x+3/4;"
	symLines[229] += "z+1/4,-y+3/4,-x+1/4;z+3/4,y+3/4,x+3/4"
	String str = symLines[SpaceGroup-1]
	KillWaves/Z symLines_temp__
	return str
End