OpenWrite::noopen: Cannot open /stmp/mathematica/tmp_529450.txt. Content-type: text/html MGROUPS
Bilbao Crystallographic Server arrow SUBGROUPS Help

The magnetic space groups derived from the Fedorov space group: 212 > 096 (id = 8195)HHHHRead tr. matrix for the supergroup from /tmp/wp-supertrm8195.trnHHHH1.000000 0.000000 0.000000 0.000000 HHHH0.000000 1.000000 0.000000 0.000000 HHHH0.000000 0.000000 1.000000 0.000000 HHHHinverted:HHHH1.000000 0.000000 0.000000 0.000000 HHHH0.000000 1.000000 0.000000 0.000000 HHHH0.000000 0.000000 1.000000 0.000000 HHHHRead tr. matrix for the subgroup from /tmp/wp-subtrm8195.trnHHHH1.000000 0.000000 0.000000 0.000000 HHHH0.000000 1.000000 0.000000 0.000000 HHHH0.000000 0.000000 1.000000 0.000000 HHHHinverted:HHHH1.000000 0.000000 0.000000 0.000000 HHHH0.000000 1.000000 0.000000 0.000000 HHHH0.000000 0.000000 1.000000 0.000000 HHHHRead tr. matrix from /tmp/wp-trm8195.trnHHHH1.000000 0.000000 0.000000 0.250000 HHHH0.000000 1.000000 0.000000 0.000000 HHHH0.000000 0.000000 1.000000 0.375000 HHHHTransformation matrix:HHHH1.000000 0.000000 0.000000 0.250000 HHHH0.000000 1.000000 0.000000 0.000000 HHHH0.000000 0.000000 1.000000 0.375000 HHHHdeterminant: 1.000000(det-ONE=0.000000)HHHHInverted of the transformation matrix:HHHH1.000000 0.000000 0.000000 -0.250000 HHHH0.000000 1.000000 0.000000 0.000000 HHHH0.000000 0.000000 1.000000 -0.375000 HHHHSubgroup generators: 2, general positions: 8HHHH(x,y,z)HHHH(0.500000 - y, 0.500000 +x, 0.750000 +z)HHHH(0.500000 +y, 0.500000 - x, 0.250000 +z)HHHH(0.500000 +x, 0.500000 - y, 0.250000 - z)HHHH(0.500000 - x, 0.500000 +y, 0.750000 - z)HHHH(-x, -y, 0.500000 +z)HHHH(y,x, -z)HHHH(-y, -x, 0.500000 - z)HHHHSubgroup Wyckoff positions:HHHHList of Wyckoff positions:HHHHOrbit No:0HHHHMultiplicity:8HHHHLetter:bHHHH(x,y,z)HHHH(0.500000 - y, 0.500000 +x, 0.750000 +z)HHHH(0.500000 +y, 0.500000 - x, 0.250000 +z)HHHH(0.500000 +x, 0.500000 - y, 0.250000 - z)HHHH(0.500000 - x, 0.500000 +y, 0.750000 - z)HHHH(-x, -y, 0.500000 +z)HHHH(y,x, -z)HHHH(-y, -x, 0.500000 - z)HHHHOrbit No:1HHHHMultiplicity:4HHHHLetter:aHHHH(x,x, 0.000000)HHHH(0.500000 - x, 0.500000 +x, 0.750000)HHHH(0.500000 +x, 0.500000 - x, 0.250000)HHHH(-x, -x, 0.500000)HHHHtr. matrix:(0.250000 +x,y, 0.375000 +z)HHHHdet = 1.000000HHHHSupergroup is transformed to unconventional setting.HHHHtake memory for 9 cells.HHHHtr. matrix:(0.250000 +x,y, 0.375000 +z)HHHHNumber of gen. pos. = 24, det = 1.000000. New number of general positions: 24HHHHchange the basis with the matrix (0.250000 +x,y, 0.375000 +z)HHHHAfter checking group we obtain 24 elementsHHHH000HHHHBefore expanding:HHHH(x,y,z)HHHH(-x, -y, 0.500000 +z)HHHH(0.500000 - x, 0.500000 +y, 0.750000 - z)HHHH(0.500000 +x, 0.500000 - y, 0.250000 - z)HHHH(0.125000 +z, 0.250000 +x, 0.625000 +y)HHHH(0.625000 +z, 0.250000 - x, 0.625000 - y)HHHH(0.875000 - z, 0.750000 - x, 0.125000 +y)HHHH(0.375000 - z, 0.750000 +x, 0.125000 - y)HHHH(0.750000 +y, 0.375000 +z, 0.875000 +x)HHHH(0.750000 - y, 0.875000 +z, 0.875000 - x)HHHH(0.250000 +y, 0.125000 - z, 0.375000 - x)HHHH(0.250000 - y, 0.625000 - z, 0.375000 +x)HHHH(y,x, -z)HHHH(-y, -x, 0.500000 - z)HHHH(0.500000 +y, 0.500000 - x, 0.250000 +z)HHHH(0.500000 - y, 0.500000 +x, 0.750000 +z)HHHH(0.250000 +x, 0.125000 +z, 0.375000 - y)HHHH(0.250000 - x, 0.625000 +z, 0.375000 +y)HHHH(0.750000 - x, 0.875000 - z, 0.875000 - y)HHHH(0.750000 +x, 0.375000 - z, 0.875000 +y)HHHH(0.375000 +z, 0.750000 +y, 0.125000 - x)HHHH(0.875000 +z, 0.750000 - y, 0.125000 +x)HHHH(0.125000 - z, 0.250000 +y, 0.625000 +x)HHHH(0.625000 - z, 0.250000 - y, 0.625000 - x)HHHHAfter expanding general positions: number of cells: 1HHHHNumber of gen. pos. = 0, det = 1.000000. New number of general positions: 0HHHH(x,y,z)HHHH(-x, -y, 0.500000 +z)HHHH(0.500000 - x, 0.500000 +y, 0.750000 - z)HHHH(0.500000 +x, 0.500000 - y, 0.250000 - z)HHHH(0.125000 +z, 0.250000 +x, 0.625000 +y)HHHH(0.625000 +z, 0.250000 - x, 0.625000 - y)HHHH(0.875000 - z, 0.750000 - x, 0.125000 +y)HHHH(0.375000 - z, 0.750000 +x, 0.125000 - y)HHHH(0.750000 +y, 0.375000 +z, 0.875000 +x)HHHH(0.750000 - y, 0.875000 +z, 0.875000 - x)HHHH(0.250000 +y, 0.125000 - z, 0.375000 - x)HHHH(0.250000 - y, 0.625000 - z, 0.375000 +x)HHHH(y,x, -z)HHHH(-y, -x, 0.500000 - z)HHHH(0.500000 +y, 0.500000 - x, 0.250000 +z)HHHH(0.500000 - y, 0.500000 +x, 0.750000 +z)HHHH(0.250000 +x, 0.125000 +z, 0.375000 - y)HHHH(0.250000 - x, 0.625000 +z, 0.375000 +y)HHHH(0.750000 - x, 0.875000 - z, 0.875000 - y)HHHH(0.750000 +x, 0.375000 - z, 0.875000 +y)HHHH(0.375000 +z, 0.750000 +y, 0.125000 - x)HHHH(0.875000 +z, 0.750000 - y, 0.125000 +x)HHHH(0.125000 - z, 0.250000 +y, 0.625000 +x)HHHH(0.625000 - z, 0.250000 - y, 0.625000 - x)HHHH000HHHHSupergroup is transformed (24 gen.pos.)->return the new group.HHHH(x,y,z)HHHH(-x, -y, 0.500000 +z)HHHH(0.500000 - x, 0.500000 +y, 0.750000 - z)HHHH(0.500000 +x, 0.500000 - y, 0.250000 - z)HHHH(0.125000 +z, 0.250000 +x, 0.625000 +y)HHHH(0.625000 +z, 0.250000 - x, 0.625000 - y)HHHH(0.875000 - z, 0.750000 - x, 0.125000 +y)HHHH(0.375000 - z, 0.750000 +x, 0.125000 - y)HHHH(0.750000 +y, 0.375000 +z, 0.875000 +x)HHHH(0.750000 - y, 0.875000 +z, 0.875000 - x)HHHH(0.250000 +y, 0.125000 - z, 0.375000 - x)HHHH(0.250000 - y, 0.625000 - z, 0.375000 +x)HHHH(y,x, -z)HHHH(-y, -x, 0.500000 - z)HHHH(0.500000 +y, 0.500000 - x, 0.250000 +z)HHHH(0.500000 - y, 0.500000 +x, 0.750000 +z)HHHH(0.250000 +x, 0.125000 +z, 0.375000 - y)HHHH(0.250000 - x, 0.625000 +z, 0.375000 +y)HHHH(0.750000 - x, 0.875000 - z, 0.875000 - y)HHHH(0.750000 +x, 0.375000 - z, 0.875000 +y)HHHH(0.375000 +z, 0.750000 +y, 0.125000 - x)HHHH(0.875000 +z, 0.750000 - y, 0.125000 +x)HHHH(0.125000 - z, 0.250000 +y, 0.625000 +x)HHHH(0.625000 - z, 0.250000 - y, 0.625000 - x)HHHHSupergroup is transformed to the subgroup basis. there are 24 general positionsHHHHSupergroup generators: xxx, general positions:24HHHHSubgroup basis:HHHH(x,y,z)HHHH(-x, -y, 0.500000 +z)HHHH(0.500000 - x, 0.500000 +y, 0.750000 - z)HHHH(0.500000 +x, 0.500000 - y, 0.250000 - z)HHHH(0.125000 +z, 0.250000 +x, 0.625000 +y)HHHH(0.625000 +z, 0.250000 - x, 0.625000 - y)HHHH(0.875000 - z, 0.750000 - x, 0.125000 +y)HHHH(0.375000 - z, 0.750000 +x, 0.125000 - y)HHHH(0.750000 +y, 0.375000 +z, 0.875000 +x)HHHH(0.750000 - y, 0.875000 +z, 0.875000 - x)HHHH(0.250000 +y, 0.125000 - z, 0.375000 - x)HHHH(0.250000 - y, 0.625000 - z, 0.375000 +x)HHHH(y,x, -z)HHHH(-y, -x, 0.500000 - z)HHHH(0.500000 +y, 0.500000 - x, 0.250000 +z)HHHH(0.500000 - y, 0.500000 +x, 0.750000 +z)HHHH(0.250000 +x, 0.125000 +z, 0.375000 - y)HHHH(0.250000 - x, 0.625000 +z, 0.375000 +y)HHHH(0.750000 - x, 0.875000 - z, 0.875000 - y)HHHH(0.750000 +x, 0.375000 - z, 0.875000 +y)HHHH(0.375000 +z, 0.750000 +y, 0.125000 - x)HHHH(0.875000 +z, 0.750000 - y, 0.125000 +x)HHHH(0.125000 - z, 0.250000 +y, 0.625000 +x)HHHH(0.625000 - z, 0.250000 - y, 0.625000 - x)HHHHnumber of cells: 1HHHH000HHHHSupergroup Wyckoff positions:HHHHOwn basis.HHHHList of Wyckoff positions:HHHHOrbit No:0HHHHMultiplicity:24HHHHLetter:eHHHH(x,y,z)HHHHOrbit No:1HHHHMultiplicity:12HHHHLetter:dHHHH(0.125000,y, 0.250000 - y)HHHHOrbit No:2HHHHMultiplicity:8HHHHLetter:cHHHH(x,x,x)HHHHOrbit No:3HHHHMultiplicity:4HHHHLetter:bHHHH(0.625000, 0.625000, 0.625000)HHHHOrbit No:4HHHHMultiplicity:4HHHHLetter:aHHHH(0.125000, 0.125000, 0.125000)HHHHSubgroup basis.HHHHList of Wyckoff positions:HHHHOrbit No:0HHHHMultiplicity:24HHHHLetter:eHHHH(0.750000 +x,y, 0.625000 +z)HHHHOrbit No:1HHHHMultiplicity:12HHHHLetter:dHHHH(0.875000,y, 0.875000 - y)HHHHOrbit No:2HHHHMultiplicity:8HHHHLetter:cHHHH(0.750000 +x,x, 0.625000 +x)HHHHOrbit No:3HHHHMultiplicity:4HHHHLetter:bHHHH(0.375000, 0.625000, 0.250000)HHHHOrbit No:4HHHHMultiplicity:4HHHHLetter:aHHHH(0.875000, 0.125000, 0.750000)HHHHindex : 3HHHHSplitting of the general position of the supergroup...HHHHThe general position splits into 3 suborbits.HHHH&Splitting of all positions:HHHHGGGG24e: 8b 8b 8bHHHH12d: 8b 4aHHHH8c: 8bHHHH4b: 4aHHHH4a: 4aHHHH&Splitting of Wyckoff position 24e: 8b 8b 8bHHHHOrbit 0:HHHH[0]TTTT(x,y,z)TTTT(-0.250000 +x,y, -0.375000 +z)TTTT8bTTTT(x,y,z)HHHH[1]TTTT(-0.500000 - x, -y, -0.500000 +z)TTTT(-0.750000 - x, -y, -0.875000 +z)TTTT8bTTTT(-x, -y, 0.500000 +z)HHHH[2]TTTT(-0.250000 - y, 0.250000 +x, -0.250000 +z)TTTT(-0.500000 - y, 0.250000 +x, -0.625000 +z)TTTT8bTTTT(0.500000 - y, 0.500000 +x, 0.750000 +z)HHHH[3]TTTT(-0.250000 +y, 0.750000 - x, 0.250000 +z)TTTT(-0.500000 +y, 0.750000 - x, -0.125000 +z)TTTT8bTTTT(0.500000 +y, 0.500000 - x, 0.250000 +z)HHHH[4]TTTT(-x, 0.500000 +y, -0.500000 - z)TTTT(-0.250000 - x, 0.500000 +y, -0.875000 - z)TTTT8bTTTT(0.500000 - x, 0.500000 +y, 0.750000 - z)HHHH[5]TTTT(-0.500000 +x, 0.500000 - y, -z)TTTT(-0.750000 +x, 0.500000 - y, -0.375000 - z)TTTT8bTTTT(0.500000 +x, 0.500000 - y, 0.250000 - z)HHHH[6]TTTT(-0.750000 +y, 0.750000 +x, -0.250000 - z)TTTT(-1.000000 +y, 0.750000 +x, -0.625000 - z)TTTT8bTTTT(y,x, -z)HHHH[7]TTTT(-0.750000 - y, 0.250000 - x, 0.250000 - z)TTTT(-1.000000 - y, 0.250000 - x, -0.125000 - z)TTTT8bTTTT(-y, -x, 0.500000 - z)HHHHOrbit 1:HHHH[0]TTTT(-0.750000 - x, 0.250000 - z, 0.250000 - y)TTTT(-1.000000 - x, 0.250000 - z, -0.125000 - y)TTTT8bTTTT(x,y,z)HHHH[1]TTTT(-0.750000 +x, 0.750000 +z, -0.250000 - y)TTTT(-1.000000 +x, 0.750000 +z, -0.625000 - y)TTTT8bTTTT(-x, -y, 0.500000 +z)HHHH[2]TTTT(-0.500000 +z, 0.500000 - x, -y)TTTT(-0.750000 +z, 0.500000 - x, -0.375000 - y)TTTT8bTTTT(0.500000 - y, 0.500000 +x, 0.750000 +z)HHHH[3]TTTT(-z, 0.500000 +x, -0.500000 - y)TTTT(-0.250000 - z, 0.500000 +x, -0.875000 - y)TTTT8bTTTT(0.500000 +y, 0.500000 - x, 0.250000 +z)HHHH[4]TTTT(-0.250000 +x, 0.750000 - z, 0.250000 +y)TTTT(-0.500000 +x, 0.750000 - z, -0.125000 +y)TTTT8bTTTT(0.500000 - x, 0.500000 +y, 0.750000 - z)HHHH[5]TTTT(-0.250000 - x, 0.250000 +z, -0.250000 +y)TTTT(-0.500000 - x, 0.250000 +z, -0.625000 +y)TTTT8bTTTT(0.500000 +x, 0.500000 - y, 0.250000 - z)HHHH[6]TTTT(-0.500000 - z, -x, -0.500000 +y)TTTT(-0.750000 - z, -x, -0.875000 +y)TTTT8bTTTT(y,x, -z)HHHH[7]TTTT(z,x,y)TTTT(-0.250000 +z,x, -0.375000 +y)TTTT8bTTTT(-y, -x, 0.500000 - z)HHHHOrbit 2:HHHH[0]TTTT(-0.500000 - y, -z, -0.500000 +x)TTTT(-0.750000 - y, -z, -0.875000 +x)TTTT8bTTTT(x,y,z)HHHH[1]TTTT(y,z,x)TTTT(-0.250000 +y,z, -0.375000 +x)TTTT8bTTTT(-x, -y, 0.500000 +z)HHHH[2]TTTT(-0.250000 +z, 0.750000 - y, 0.250000 +x)TTTT(-0.500000 +z, 0.750000 - y, -0.125000 +x)TTTT8bTTTT(0.500000 - y, 0.500000 +x, 0.750000 +z)HHHH[3]TTTT(-0.250000 - z, 0.250000 +y, -0.250000 +x)TTTT(-0.500000 - z, 0.250000 +y, -0.625000 +x)TTTT8bTTTT(0.500000 +y, 0.500000 - x, 0.250000 +z)HHHH[4]TTTT(-0.500000 +y, 0.500000 - z, -x)TTTT(-0.750000 +y, 0.500000 - z, -0.375000 - x)TTTT8bTTTT(0.500000 - x, 0.500000 +y, 0.750000 - z)HHHH[5]TTTT(-y, 0.500000 +z, -0.500000 - x)TTTT(-0.250000 - y, 0.500000 +z, -0.875000 - x)TTTT8bTTTT(0.500000 +x, 0.500000 - y, 0.250000 - z)HHHH[6]TTTT(-0.750000 - z, 0.250000 - y, 0.250000 - x)TTTT(-1.000000 - z, 0.250000 - y, -0.125000 - x)TTTT8bTTTT(y,x, -z)HHHH[7]TTTT(-0.750000 +z, 0.750000 +y, -0.250000 - x)TTTT(-1.000000 +z, 0.750000 +y, -0.625000 - x)TTTT8bTTTT(-y, -x, 0.500000 - z)HHHHGGGG$Splitting of Wyckoff position 12d: 8b 4aHHHHOrbit 0:HHHH[0]TTTT(0.125000,y, 0.250000 - y)TTTT(-0.125000,y, -0.125000 - y)TTTT8bTTTT(x,y,z)HHHH[1]TTTT(-0.625000, -y, -0.250000 - y)TTTT(-0.875000, -y, -0.625000 - y)TTTT8bTTTT(-x, -y, 0.500000 +z)HHHH[2]TTTT(-0.250000 - y, 0.375000, -y)TTTT(-0.500000 - y, 0.375000, -0.375000 - y)TTTT8bTTTT(0.500000 - y, 0.500000 +x, 0.750000 +z)HHHH[3]TTTT(-0.250000 +y, 0.625000, -0.500000 - y)TTTT(-0.500000 +y, 0.625000, -0.875000 - y)TTTT8bTTTT(0.500000 +y, 0.500000 - x, 0.250000 +z)HHHH[4]TTTT(-0.125000, 0.500000 +y, 0.250000 +y)TTTT(-0.375000, 0.500000 +y, -0.125000 +y)TTTT8bTTTT(0.500000 - x, 0.500000 +y, 0.750000 - z)HHHH[5]TTTT(-0.375000, 0.500000 - y, -0.250000 +y)TTTT(-0.625000, 0.500000 - y, -0.625000 +y)TTTT8bTTTT(0.500000 +x, 0.500000 - y, 0.250000 - z)HHHH[6]TTTT(-0.750000 +y, 0.875000, -0.500000 +y)TTTT(-1.000000 +y, 0.875000, -0.875000 +y)TTTT8bTTTT(y,x, -z)HHHH[7]TTTT(-0.750000 - y, 0.125000,y)TTTT(-1.000000 - y, 0.125000, -0.375000 +y)TTTT8bTTTT(-y, -x, 0.500000 - z)HHHHOrbit 1:HHHH[0]TTTT(-0.500000 - y, 0.750000 +y, -0.375000)TTTT(-0.750000 - y, 0.750000 +y, -0.750000)TTTT4aTTTT(0.500000 +x, 0.500000 - x, 0.250000)HHHH[1]TTTT(y, 0.250000 - y, 0.125000)TTTT(-0.250000 +y, 0.250000 - y, -0.250000)TTTT4aTTTT(0.500000 - x, 0.500000 +x, 0.750000)HHHH[2]TTTT(-y, 0.750000 - y, -0.625000)TTTT(-0.250000 - y, 0.750000 - y, -1.000000)TTTT4aTTTT(x,x, 0.000000)HHHH[3]TTTT(-0.500000 +y, 0.250000 +y, -0.125000)TTTT(-0.750000 +y, 0.250000 +y, -0.500000)TTTT4aTTTT(-x, -x, 0.500000)HHHHGGGG$Splitting of Wyckoff position 8c: 8bHHHHOrbit 0:HHHH[0]TTTT(x,x,x)TTTT(-0.250000 +x,x, -0.375000 +x)TTTT8bTTTT(x,y,z)HHHH[1]TTTT(-0.500000 - x, -x, -0.500000 +x)TTTT(-0.750000 - x, -x, -0.875000 +x)TTTT8bTTTT(-x, -y, 0.500000 +z)HHHH[2]TTTT(-0.250000 - x, 0.250000 +x, -0.250000 +x)TTTT(-0.500000 - x, 0.250000 +x, -0.625000 +x)TTTT8bTTTT(0.500000 - y, 0.500000 +x, 0.750000 +z)HHHH[3]TTTT(-0.250000 +x, 0.750000 - x, 0.250000 +x)TTTT(-0.500000 +x, 0.750000 - x, -0.125000 +x)TTTT8bTTTT(0.500000 +y, 0.500000 - x, 0.250000 +z)HHHH[4]TTTT(-x, 0.500000 +x, -0.500000 - x)TTTT(-0.250000 - x, 0.500000 +x, -0.875000 - x)TTTT8bTTTT(0.500000 - x, 0.500000 +y, 0.750000 - z)HHHH[5]TTTT(-0.500000 +x, 0.500000 - x, -x)TTTT(-0.750000 +x, 0.500000 - x, -0.375000 - x)TTTT8bTTTT(0.500000 +x, 0.500000 - y, 0.250000 - z)HHHH[6]TTTT(-0.750000 +x, 0.750000 +x, -0.250000 - x)TTTT(-1.000000 +x, 0.750000 +x, -0.625000 - x)TTTT8bTTTT(y,x, -z)HHHH[7]TTTT(-0.750000 - x, 0.250000 - x, 0.250000 - x)TTTT(-1.000000 - x, 0.250000 - x, -0.125000 - x)TTTT8bTTTT(-y, -x, 0.500000 - z)HHHHGGGG$Splitting of Wyckoff position 4b: 4aHHHHOrbit 0:HHHH[0]TTTT(-0.375000, 0.625000, -0.375000)TTTT(-0.625000, 0.625000, -0.750000)TTTT4aTTTT(0.500000 +x, 0.500000 - x, 0.250000)HHHH[1]TTTT(-0.125000, 0.375000, 0.125000)TTTT(-0.375000, 0.375000, -0.250000)TTTT4aTTTT(0.500000 - x, 0.500000 +x, 0.750000)HHHH[2]TTTT(0.125000, 0.875000, -0.625000)TTTT(-0.125000, 0.875000, -1.000000)TTTT4aTTTT(x,x, 0.000000)HHHH[3]TTTT(-0.625000, 0.125000, -0.125000)TTTT(-0.875000, 0.125000, -0.500000)TTTT4aTTTT(-x, -x, 0.500000)HHHHGGGG$Splitting of Wyckoff position 4a: 4aHHHHOrbit 0:HHHH[0]TTTT(0.125000, 0.125000, 0.125000)TTTT(-0.125000, 0.125000, -0.250000)TTTT4aTTTT(0.500000 - x, 0.500000 +x, 0.750000)HHHH[1]TTTT(-0.625000, 0.875000, -0.375000)TTTT(-0.875000, 0.875000, -0.750000)TTTT4aTTTT(0.500000 +x, 0.500000 - x, 0.250000)HHHH[2]TTTT(-0.375000, 0.375000, -0.125000)TTTT(-0.625000, 0.375000, -0.500000)TTTT4aTTTT(-x, -x, 0.500000)HHHH[3]TTTT(-0.125000, 0.625000, -0.625000)TTTT(-0.375000, 0.625000, -1.000000)TTTT4aTTTT(x,x, 0.000000)HHHHGGGG&{{24, e}, {12, d}, {8, c}, {4, b}, {4, a}}${{{8, b}, {8, b}, {8, b}}, {{8, b}, {4, a}}, {{8, b}}, {{4, a}}, {{4, a}}}${{{{x, y, z}, {-1/2 - x, -y, -1/2 + z}, {-1/4 - y, 1/4 + x, -1/4 + z}, {-1/4 + y, 3/4 - x, 1/4 + z}, {-x, 1/2 + y, -1/2 - z}, {-1/2 + x, 1/2 - y, -z}, {-3/4 + y, 3/4 + x, -1/4 - z}, {-3/4 - y, 1/4 - x, 1/4 - z}}, {{-3/4 - x, 1/4 - z, 1/4 - y}, {-3/4 + x, 3/4 + z, -1/4 - y}, {-1/2 + z, 1/2 - x, -y}, {-z, 1/2 + x, -1/2 - y}, {-1/4 + x, 3/4 - z, 1/4 + y}, {-1/4 - x, 1/4 + z, -1/4 + y}, {-1/2 - z, -x, -1/2 + y}, {z, x, y}}, {{-1/2 - y, -z, -1/2 + x}, {y, z, x}, {-1/4 + z, 3/4 - y, 1/4 + x}, {-1/4 - z, 1/4 + y, -1/4 + x}, {-1/2 + y, 1/2 - z, -x}, {-y, 1/2 + z, -1/2 - x}, {-3/4 - z, 1/4 - y, 1/4 - x}, {-3/4 + z, 3/4 + y, -1/4 - x}}}, {{{1/8, y, 1/4 - y}, {-5/8, -y, -1/4 - y}, {-1/4 - y, 3/8, -y}, {-1/4 + y, 5/8, -1/2 - y}, {-1/8, 1/2 + y, 1/4 + y}, {-3/8, 1/2 - y, -1/4 + y}, {-3/4 + y, 7/8, -1/2 + y}, {-3/4 - y, 1/8, y}}, {{-1/2 - y, 3/4 + y, -3/8}, {y, 1/4 - y, 1/8}, {-y, 3/4 - y, -5/8}, {-1/2 + y, 1/4 + y, -1/8}}}, {{{x, x, x}, {-1/2 - x, -x, -1/2 + x}, {-1/4 - x, 1/4 + x, -1/4 + x}, {-1/4 + x, 3/4 - x, 1/4 + x}, {-x, 1/2 + x, -1/2 - x}, {-1/2 + x, 1/2 - x, -x}, {-3/4 + x, 3/4 + x, -1/4 - x}, {-3/4 - x, 1/4 - x, 1/4 - x}}}, {{{-3/8, 5/8, -3/8}, {-1/8, 3/8, 1/8}, {1/8, 7/8, -5/8}, {-5/8, 1/8, -1/8}}}, {{{1/8, 1/8, 1/8}, {-5/8, 7/8, -3/8}, {-3/8, 3/8, -1/8}, {-1/8, 5/8, -5/8}}}}${{{{-1/4 + x, y, -3/8 + z}, {-3/4 - x, -y, -7/8 + z}, {-1/2 - y, 1/4 + x, -5/8 + z}, {-1/2 + y, 3/4 - x, -1/8 + z}, {-1/4 - x, 1/2 + y, -7/8 - z}, {-3/4 + x, 1/2 - y, -3/8 - z}, {-1 + y, 3/4 + x, -5/8 - z}, {-1 - y, 1/4 - x, -1/8 - z}}, {{-1 - x, 1/4 - z, -1/8 - y}, {-1 + x, 3/4 + z, -5/8 - y}, {-3/4 + z, 1/2 - x, -3/8 - y}, {-1/4 - z, 1/2 + x, -7/8 - y}, {-1/2 + x, 3/4 - z, -1/8 + y}, {-1/2 - x, 1/4 + z, -5/8 + y}, {-3/4 - z, -x, -7/8 + y}, {-1/4 + z, x, -3/8 + y}}, {{-3/4 - y, -z, -7/8 + x}, {-1/4 + y, z, -3/8 + x}, {-1/2 + z, 3/4 - y, -1/8 + x}, {-1/2 - z, 1/4 + y, -5/8 + x}, {-3/4 + y, 1/2 - z, -3/8 - x}, {-1/4 - y, 1/2 + z, -7/8 - x}, {-1 - z, 1/4 - y, -1/8 - x}, {-1 + z, 3/4 + y, -5/8 - x}}}, {{{-1/8, y, -1/8 - y}, {-7/8, -y, -5/8 - y}, {-1/2 - y, 3/8, -3/8 - y}, {-1/2 + y, 5/8, -7/8 - y}, {-3/8, 1/2 + y, -1/8 + y}, {-5/8, 1/2 - y, -5/8 + y}, {-1 + y, 7/8, -7/8 + y}, {-1 - y, 1/8, -3/8 + y}}, {{-3/4 - y, 3/4 + y, -3/4}, {-1/4 + y, 1/4 - y, -1/4}, {-1/4 - y, 3/4 - y, -1}, {-3/4 + y, 1/4 + y, -1/2}}}, {{{-1/4 + x, x, -3/8 + x}, {-3/4 - x, -x, -7/8 + x}, {-1/2 - x, 1/4 + x, -5/8 + x}, {-1/2 + x, 3/4 - x, -1/8 + x}, {-1/4 - x, 1/2 + x, -7/8 - x}, {-3/4 + x, 1/2 - x, -3/8 - x}, {-1 + x, 3/4 + x, -5/8 - x}, {-1 - x, 1/4 - x, -1/8 - x}}}, {{{-5/8, 5/8, -3/4}, {-3/8, 3/8, -1/4}, {-1/8, 7/8, -1}, {-7/8, 1/8, -1/2}}}, {{{-1/8, 1/8, -1/4}, {-7/8, 7/8, -3/4}, {-5/8, 3/8, -1/2}, {-3/8, 5/8, -1}}}}${{{{x, y, z}, {-x, -y, 1/2 + z}, {1/2 - y, 1/2 + x, 3/4 + z}, {1/2 + y, 1/2 - x, 1/4 + z}, {1/2 - x, 1/2 + y, 3/4 - z}, {1/2 + x, 1/2 - y, 1/4 - z}, {y, x, -z}, {-y, -x, 1/2 - z}}, {{x, y, z}, {-x, -y, 1/2 + z}, {1/2 - y, 1/2 + x, 3/4 + z}, {1/2 + y, 1/2 - x, 1/4 + z}, {1/2 - x, 1/2 + y, 3/4 - z}, {1/2 + x, 1/2 - y, 1/4 - z}, {y, x, -z}, {-y, -x, 1/2 - z}}, {{x, y, z}, {-x, -y, 1/2 + z}, {1/2 - y, 1/2 + x, 3/4 + z}, {1/2 + y, 1/2 - x, 1/4 + z}, {1/2 - x, 1/2 + y, 3/4 - z}, {1/2 + x, 1/2 - y, 1/4 - z}, {y, x, -z}, {-y, -x, 1/2 - z}}}, {{{x, y, z}, {-x, -y, 1/2 + z}, {1/2 - y, 1/2 + x, 3/4 + z}, {1/2 + y, 1/2 - x, 1/4 + z}, {1/2 - x, 1/2 + y, 3/4 - z}, {1/2 + x, 1/2 - y, 1/4 - z}, {y, x, -z}, {-y, -x, 1/2 - z}}, {{1/2 + x, 1/2 - x, 1/4}, {1/2 - x, 1/2 + x, 3/4}, {x, x, 0}, {-x, -x, 1/2}}}, {{{x, y, z}, {-x, -y, 1/2 + z}, {1/2 - y, 1/2 + x, 3/4 + z}, {1/2 + y, 1/2 - x, 1/4 + z}, {1/2 - x, 1/2 + y, 3/4 - z}, {1/2 + x, 1/2 - y, 1/4 - z}, {y, x, -z}, {-y, -x, 1/2 - z}}}, {{{1/2 + x, 1/2 - x, 1/4}, {1/2 - x, 1/2 + x, 3/4}, {x, x, 0}, {-x, -x, 1/2}}}, {{{1/2 - x, 1/2 + x, 3/4}, {1/2 + x, 1/2 - x, 1/4}, {-x, -x, 1/2}, {x, x, 0}}}}&OK! (#)

Listed with respect to the BNS setting:


Listed with respect to the OG setting:



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