[Triclinic] 1 P1 x,y,z 2 P-1 x,y,z -x,-y,-z [Monoclinic] 3 P2 x,y,z -x,y,-z 4 P2(1) x,y,z -x,1/2+y,-z 5 C2 x,y,z -x,y,-z +(1/2,1/2,0) 6 Pm x,y,z x,-y,z 7 Pc x,y,z x,-y,1/2+z 7 Pa x,y,z 1/2+x,-y,z 7 Pn x,y,z 1/2+x,-y,1/2+z 8 Cm x,y,z x,-y,z +(1/2,1/2,0) 9 Cc x,y,z x,-y,1/2+z +(1/2,1/2,0) 10 P2/m x,y,z -x,y,-z -x,-y,-z x,-y,z 11 P2(1)/m x,y,z -x,1/2+y,-z -x,-y,-z x,1/2-y,z 12 C2/m x,y,z -x,y,-z -x,-y,-z x,-y,z +(1/2,1/2,0) 13 P2/c x,y,z -x,y,1/2-z -x,-y,-z x,-y,1/2+z 13 P2/a x,y,z 1/2-x,y,-z -x,-y,-z 1/2+x,-y,z 13 P2/n x,y,z 1/2-x,y,1/2-z -x,-y,-z 1/2+x,-y,1/2+z 14 P2(1)/c x,y,z -x,1/2+y,1/2-z -x,-y,-z x,1/2-y,1/2+z 14 P2(1)/a x,y,z 1/2-x,1/2+y,-z -x,-y,-z 1/2+x,1/2-y,z 14 P2(1)/n x,y,z 1/2-x,1/2+y,1/2-z -x,-y,-z 1/2+x,1/2-y,1/2+z 15 C2/c (c-glide) x,y,z -x,y,1/2-z -x,-y,-z x,-y,1/2+z +(1/2,1/2,0) 15 C2/c (n-glide) x,y,z 1/2-x,y,1/2-z -x,-y,-z 1/2+x,-y,1/2+z +(1/2,1/2,0) [Orthorhombic] 16 P222 x,y,z x,-y,-z -x,y,-z -x,-y,z 17 P222(1) (x 2-axis) x,y,z x,-y,-z -x,y,1/2-z -x,-y,1/2+z 17 P222(1) (y 2-axis) x,y,z x,-y,1/2-z -x,y,-z -x,-y,1/2+z 17 P22(1)2 (z 2-axis) x,y,z x,1/2-y,-z -x,1/2+y,-z -x,-y,z 17 P22(1)2 (x 2-axis) x,y,z x,-y,-z -x,1/2+y,-z -x,1/2-y,z 17 P2(1)22 (y 2-axis) x,y,z 1/2+x,-y,-z -x,y,-z 1/2-x,-y,z 17 P2(1)22 (z 2-axis) x,y,z 1/2+x,-y,-z 1/2-x,y,-z -x,-y,z 18 P2(1)2(1)2 x,y,z 1/2+x,1/2-y,-z 1/2-x,1/2+y,-z -x,-y,z 18 P2(1)22(1) x,y,z 1/2+x,-y,1/2-z -x,y,-z 1/2-x,-y,1/2+z 18 P22(1)2(1) x,y,z x,-y,-z -x,1/2+y,1/2-z -x,1/2-y,1/2+z 19 P2(1)2(1)2(1) x,y,z 1/2+x,1/2-y,-z -x,1/2+y,1/2-z 1/2-x,-y,1/2+z 19 P2(1)2(1)2(1) (alt.) x,y,z 1/2+x,-y,1/2-z 1/2-x,1/2+y,-z -x,1/2-y,1/2+z 20 C222(1) x,y,z x,-y,-z -x,y,1/2-z -x,-y,1/2+z +(1/2,1/2,0) 20 C222(1) (alt.) x,y,z x,-y,1/2-z -x,y,-z -x,-y,1/2+z +(1/2,1/2,0) 21 C222 x,y,z x,-y,-z -x,y,-z -x,-y,z +(1/2,1/2,0) 22 F222 x,y,z x,-y,-z -x,y,-z -x,-y,z +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 23 I222 x,y,z x,-y,-z -x,y,-z -x,-y,z +(1/2,1/2,1/2) 24 I2(1)2(1)2(1) x,y,z x,-y,1/2-z 1/2-x,y,-z -x,1/2-y,z +(1/2,1/2,1/2) 25 Pmm2 x,y,z -x,y,z x,-y,z -x,-y,z 25 Pm2m x,y,z -x,y,z -x,y,-z x,y,-z 25 P2mm x,y,z x,-y,-z x,-y,z x,y,-z 26 Pmc2(1) x,y,z -x,y,z x,-y,1/2+z -x,-y,1/2+z 26 Pcm2(1) x,y,z -x,y,1/2+z x,-y,z -x,-y,1/2+z 26 Pb2(1)m x,y,z -x,1/2+y,z -x,1/2+y,-z x,y,-z 26 Pm2(1)b x,y,z -x,y,z -x,1/2+y,-z x,1/2+y,-z 26 P2(1)ma x,y,z 1/2+x,-y,-z x,-y,z 1/2+x,y,-z 26 P2(1)am x,y,z 1/2+x,-y,-z 1/2+x,-y,z x,y,-z 27 Pcc2 x,y,z -x,y,1/2+z x,-y,1/2+z -x,-y,z 27 Pb2b x,y,z -x,1/2+y,z -x,y,-z x,1/2+y,-z 27 P2aa x,y,z x,-y,-z 1/2+x,-y,z 1/2+x,y,-z 28 Pma2 x,y,z 1/2-x,y,z 1/2+x,-y,z -x,-y,z 28 Pbm2 x,y,z -x,1/2+y,z x,1/2-y,z -x,-y,z 28 Pc2m x,y,z -x,y,1/2+z -x,y,-z x,y,1/2-z 28 Pm2a x,y,z 1/2-x,y,z -x,y,-z 1/2+x,y,-z 28 P2mb x,y,z x,-y,-z x,1/2-y,z x,1/2+y,-z 28 P2cm x,y,z x,-y,-z x,-y,1/2+z x,y,1/2-z 29 Pca2(1) x,y,z 1/2-x,y,1/2+z 1/2+x,-y,z -x,-y,1/2+z 29 Pbc2(1) x,y,z -x,1/2+y,z x,1/2-y,1/2+z -x,-y,1/2+z 29 Pc2(1)b x,y,z -x,y,1/2+z -x,1/2+y,-z x,1/2+y,1/2-z 29 Pb2(1)a x,y,z -x,1/2+y,z 1/2-x,1/2+y,-z 1/2+x,y,-z 29 P2(1)ab x,y,z 1/2+x,-y,-z 1/2+x,1/2-y,z x,1/2+y,-z 29 P2(1)ca x,y,z 1/2+x,-y,-z x,-y,1/2+z 1/2+x,y,1/2-z 30 Pnc2 x,y,z -x,1/2+y,1/2+z x,1/2-y,1/2+z -x,-y,z 30 Pcn2 x,y,z 1/2-x,y,1/2+z 1/2+x,-y,1/2+z -x,-y,z 30 Pb2n x,y,z 1/2-x,1/2+y,z -x,y,-z 1/2+x,1/2+y,-z 30 Pn2b x,y,z -x,1/2+y,1/2+z -x,y,-z x,1/2+y,1/2-z 30 P2na x,y,z x,-y,-z 1/2+x,-y,1/2+z 1/2+x,y,1/2-z 30 P2an x,y,z x,-y,-z 1/2+x,1/2-y,z 1/2+x,1/2+y,-z 31 Pmn2(1) x,y,z -x,y,z 1/2+x,-y,1/2+z 1/2-x,-y,1/2+z 31 Pnm2(1) x,y,z -x,1/2+y,1/2+z x,-y,z -x,1/2-y,1/2+z 31 Pn2(1)m x,y,z -x,1/2+y,1/2+z -x,1/2+y,1/2-z x,y,-z 31 Pm2(1)n x,y,z -x,y,z 1/2-x,1/2+y,-z 1/2+x,1/2+y,-z 31 P2(1)mn x,y,z 1/2+x,1/2-y,-z x,-y,z 1/2+x,1/2+y,-z 31 P2(1)nm x,y,z 1/2+x,-y,1/2-z 1/2+x,-y,1/2+z x,y,-z 32 Pba2 x,y,z 1/2-x,1/2+y,z 1/2+x,1/2-y,z -x,-y,z 32 Pc2a x,y,z 1/2-x,y,1/2+z -x,y,-z 1/2+x,y,1/2-z 32 P2cb x,y,z x,-y,-z x,1/2-y,1/2+z x,1/2+y,1/2-z 33 Pna2(1) x,y,z 1/2-x,1/2+y,1/2+z 1/2+x,1/2-y,z -x,-y,1/2+z 33 Pbn2(1) x,y,z 1/2-x,1/2+y,z 1/2+x,1/2-y,1/2+z -x,-y,1/2+z 33 Pc2(1)n x,y,z 1/2-x,y,1/2+z -x,1/2+y,-z 1/2+x,1/2+y,1/2-z 33 Pn2(1)a x,y,z 1/2-x,1/2+y,1/2+z -x,1/2+y,-z 1/2+x,y,1/2-z 33 P2(1)nb x,y,z 1/2+x,-y,-z 1/2+x,1/2-y,1/2+z x,1/2+y,1/2-z 33 P2(1)cn x,y,z 1/2+x,-y,-z x,1/2-y,1/2+z 1/2+x,1/2+y,1/2-z 34 Pnn2 x,y,z 1/2-x,1/2+y,1/2+z 1/2+x,1/2-y,1/2+z -x,-y,z 34 Pn2n x,y,z 1/2-x,1/2+y,1/2+z -x,y,-z 1/2+x,1/2+y,1/2-z 34 P2nn x,y,z x,-y,-z 1/2+x,1/2-y,1/2+z 1/2+x,1/2+y,1/2-z 35 Cmm2 x,y,z -x,y,z x,-y,z -x,-y,z +(1/2,1/2,0) 36 Cmc2(1) x,y,z -x,y,z x,-y,1/2+z -x,-y,1/2+z +(1/2,1/2,0) 36 Ccm2(1) x,y,z -x,y,1/2+z x,-y,z -x,-y,1/2+z +(1/2,1/2,0) 37 Ccc2 x,y,z -x,y,1/2+z x,-y,1/2+z -x,-y,z +(1/2,1/2,0) 38 Amm2 x,y,z -x,y,z x,-y,z -x,-y,z +(0,1/2,1/2) 38 Cm2m x,y,z -x,y,z -x,y,-z x,y,-z +(1/2,1/2,0) 38 C2mm x,y,z x,-y,-z x,-y,z x,y,-z +(1/2,1/2,0) 39 Abm2 x,y,z -x,1/2+y,z x,1/2-y,z -x,-y,z +(0,1/2,1/2) 39 Cm2a x,y,z -x,1/2+y,z -x,y,-z x,1/2+y,-z +(1/2,1/2,0) 39 C2ma x,y,z x,-y,-z x,1/2-y,z x,1/2+y,-z +(1/2,1/2,0) 40 Ama2 x,y,z 1/2-x,y,z 1/2+x,-y,z -x,-y,z +(0,1/2,1/2) 40 Cc2m x,y,z -x,y,1/2+z -x,y,-z x,y,1/2-z +(1/2,1/2,0) 40 C2cm x,y,z x,-y,-z x,-y,1/2+z x,y,1/2-z +(1/2,1/2,0) 41 Aba2 x,y,z 1/2-x,1/2+y,z 1/2+x,1/2-y,z -x,-y,z +(0,1/2,1/2) 41 Cc2a x,y,z -x,1/2+y,1/2+z -x,y,-z x,1/2+y,1/2-z +(1/2,1/2,0) 41 C2ca x,y,z x,-y,-z x,1/2-y,1/2+z x,1/2+y,1/2-z +(1/2,1/2,0) 42 Fmm2 x,y,z -x,y,z x,-y,z -x,-y,z +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 43 Fdd2 x,y,z 1/4-x,1/4+y,1/4+z 1/4+x,1/4-y,1/4+z -x,-y,z +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 43 Fd2d x,y,z 1/4-x,1/4+y,1/4+z -x,y,-z 1/4+x,1/4+y,1/4-z +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 43 F2dd x,y,z x,-y,-z 1/4+x,1/4-y,1/4+z 1/4+x,1/4+y,1/4-z +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 44 Imm2 x,y,z -x,y,z x,-y,z -x,-y,z +(1/2,1/2,1/2) 45 Iba2 x,y,z -x,y,1/2+z x,-y,1/2+z -x,-y,z +(1/2,1/2,1/2) 45 Ib2a x,y,z -x,1/2+y,z -x,y,-z x,1/2+y,-z +(1/2,1/2,1/2) 45 I2aa x,y,z x,-y,-z 1/2+x,-y,z 1/2+x,y,-z +(1/2,1/2,1/2) 46 Ima2 x,y,z 1/2-x,y,z 1/2+x,-y,z -x,-y,z +(1/2,1/2,1/2) 46 Ibm2 x,y,z -x,1/2+y,z x,1/2-y,z -x,-y,z +(1/2,1/2,1/2) 46 Ib2m x,y,z -x,y,1/2+z -x,y,-z x,y,1/2-z +(1/2,1/2,1/2) 46 Im2a x,y,z 1/2-x,y,z -x,y,-z 1/2+x,y,-z +(1/2,1/2,1/2) 46 I2ma x,y,z x,-y,-z x,1/2-y,z x,1/2+y,-z +(1/2,1/2,1/2) 46 I2am x,y,z x,-y,-z x,-y,1/2+z x,y,1/2-z +(1/2,1/2,1/2) 47 Pmmm x,y,z -x,y,z x,-y,z x,y,-z -x,-y,-z x,-y,-z -x,y,-z -x,-y,z 48 Pnnn (222 origin) x,y,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-x,1/2-y,1/2-z x,-y,-z -x,y,-z -x,-y,z 48 Pnnn (-1 origin) x,y,z -x,1/2+y,1/2+z 1/2+x,-y,1/2+z 1/2+x,1/2+y,-z -x,-y,-z x,1/2-y,1/2-z 1/2-x,y,1/2-z 1/2-x,1/2-y,z 49 Pccm 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 49 Pbmb 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 49 Pmaa 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 50 Pban x,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 x,-y,-z -x,y,-z -x,-y,z 50 Pban (alt.) x,y,z -x,1/2+y,z 1/2+x,-y,z 1/2+x,1/2+y,-z -x,-y,-z x,1/2-y,-z 1/2-x,y,-z 1/2-x,1/2-y,z 50 Pcna x,y,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 x,-y,-z -x,y,-z -x,-y,z 50 Pcna (alt.) 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-x,-y,z 50 Pncb 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 x,-y,-z -x,y,-z -x,-y,z 50 Pncb (alt.) 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 51 Pmma x,y,z 1/2-x,y,z x,-y,z 1/2+x,y,-z -x,-y,-z 1/2+x,-y,-z -x,y,-z 1/2-x,-y,z 51 Pmmb x,y,z -x,y,z x,1/2-y,z x,1/2+y,-z -x,-y,-z x,-y,-z -x,1/2+y,-z -x,1/2-y,z 51 Pmcm x,y,z -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 51 Pmam 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 -x,-y,z 51 Pbmm x,y,z -x,1/2+y,z x,1/2-y,z x,y,-z -x,-y,-z x,1/2-y,-z -x,1/2+y,-z -x,-y,z 51 Pcmm x,y,z -x,y,1/2+z x,-y,z x,y,1/2-z -x,-y,-z x,-y,1/2-z -x,y,-z -x,-y,1/2+z 52 Pnna 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-x,-y,z 52 Pnnb 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+x,1/2-y,1/2-z 1/2-x,y,1/2-z -x,1/2-y,z 52 Pncn x,y,z 1/2-x,1/2+y,1/2+z x,-y,1/2+z 1/2+x,1/2+y,-z -x,-y,-z 1/2+x,1/2-y,1/2-z -x,y,1/2-z 1/2-x,1/2-y,z 52 Pnan 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 52 Pbnn 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 52 Pcnn x,y,z -x,y,1/2+z 1/2+x,1/2-y,1/2+z 1/2+x,1/2+y,-z -x,-y,-z x,-y,1/2-z 1/2-x,1/2+y,1/2-z 1/2-x,1/2-y,z 53 Pmna 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 53 Pnmb x,y,z -x,1/2+y,1/2+z x,-y,z x,1/2+y,1/2-z -x,-y,-z x,1/2-y,1/2-z -x,y,-z -x,1/2-y,1/2+z 53 Pncm 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 -x,-y,z 53 Pman x,y,z -x,y,z 1/2+x,1/2-y,z 1/2+x,1/2+y,-z -x,-y,-z x,-y,-z 1/2-x,1/2+y,-z 1/2-x,1/2-y,z 53 Pbmn x,y,z 1/2-x,1/2+y,z x,-y,z 1/2+x,1/2+y,-z -x,-y,-z 1/2+x,1/2-y,-z -x,y,-z 1/2-x,1/2-y,z 53 Pcnm 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 -x,-y,z 54 Pcca x,y,z 1/2-x,y,1/2+z x,-y,1/2+z 1/2+x,y,-z -x,-y,-z 1/2+x,-y,1/2-z -x,y,1/2-z 1/2-x,-y,z 54 Pccb x,y,z -x,y,1/2+z x,1/2-y,1/2+z x,1/2+y,-z -x,-y,-z x,-y,1/2-z -x,1/2+y,1/2-z -x,1/2-y,z 54 Pbcb x,y,z -x,1/2+y,z x,-y,1/2+z x,1/2+y,1/2-z -x,-y,-z x,1/2-y,-z -x,y,1/2-z -x,1/2-y,1/2+z 54 Pbab 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-x,y,-z -x,1/2-y,z 54 Pbaa 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 54 Pcaa x,y,z -x,y,1/2+z 1/2+x,-y,z 1/2+x,y,1/2-z -x,-y,-z x,-y,1/2-z 1/2-x,y,-z 1/2-x,-y,1/2+z 55 Pbam x,y,z 1/2-x,1/2+y,z 1/2+x,1/2-y,z x,y,-z -x,-y,-z 1/2+x,1/2-y,-z 1/2-x,1/2+y,-z -x,-y,z 55 Pcma x,y,z 1/2-x,y,1/2+z x,-y,z 1/2+x,y,1/2-z -x,-y,-z 1/2+x,-y,1/2-z -x,y,-z 1/2-x,-y,1/2+z 55 Pmcb 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 56 Pccn x,y,z 1/2-x,y,1/2+z x,1/2-y,1/2+z 1/2+x,1/2+y,-z -x,-y,-z 1/2+x,-y,1/2-z -x,1/2+y,1/2-z 1/2-x,1/2-y,z 56 Pbnb x,y,z 1/2-x,1/2+y,z 1/2+x,-y,1/2+z x,1/2+y,1/2-z -x,-y,-z 1/2+x,1/2-y,-z 1/2-x,y,1/2-z -x,1/2-y,1/2+z 56 Pnaa x,y,z -x,1/2+y,1/2+z 1/2+x,1/2-y,z 1/2+x,y,1/2-z -x,-y,-z x,1/2-y,1/2-z 1/2-x,1/2+y,-z 1/2-x,-y,1/2+z 57 Pbcm x,y,z -x,1/2+y,z x,1/2-y,1/2+z x,y,1/2-z -x,-y,-z x,1/2-y,-z -x,1/2+y,1/2-z -x,-y,1/2+z 57 Pcam x,y,z 1/2-x,y,1/2+z 1/2+x,-y,z x,y,1/2-z -x,-y,-z 1/2+x,-y,1/2-z 1/2-x,y,-z -x,-y,1/2+z 57 Pbma x,y,z 1/2-x,1/2+y,z x,1/2-y,z 1/2+x,y,-z -x,-y,-z 1/2+x,1/2-y,-z -x,1/2+y,-z 1/2-x,-y,z 57 Pcmb x,y,z -x,y,1/2+z x,1/2-y,z x,1/2+y,1/2-z -x,-y,-z x,-y,1/2-z -x,1/2+y,-z -x,1/2-y,1/2+z 57 Pmca x,y,z 1/2-x,y,z x,-y,1/2+z 1/2+x,y,1/2-z -x,-y,-z 1/2+x,-y,-z -x,y,1/2-z 1/2-x,-y,1/2+z 57 Pmab x,y,z 1/2-x,y,z 1/2+x,1/2-y,z x,1/2+y,-z -x,-y,-z 1/2+x,-y,-z 1/2-x,1/2+y,-z -x,1/2-y,z 58 Pnnm x,y,z 1/2-x,1/2+y,1/2+z 1/2+x,1/2-y,1/2+z x,y,-z -x,-y,-z 1/2+x,1/2-y,1/2-z 1/2-x,1/2+y,1/2-z -x,-y,z 58 Pnmn x,y,z 1/2-x,1/2+y,1/2+z x,-y,z 1/2+x,1/2+y,1/2-z -x,-y,-z 1/2+x,1/2-y,1/2-z -x,y,-z 1/2-x,1/2-y,1/2+z 58 Pmnn x,y,z -x,y,z 1/2+x,1/2-y,1/2+z 1/2+x,1/2+y,1/2-z -x,-y,-z x,-y,-z 1/2-x,1/2+y,1/2-z 1/2-x,1/2-y,1/2+z 59 Pmmn (mm2 origin) x,y,z -x,y,z x,-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 -x,-y,z 59 Pmmn (-1 origin) x,y,z 1/2-x,y,z x,1/2-y,z 1/2+x,1/2+y,-z -x,-y,-z 1/2+x,-y,-z -x,1/2+y,-z 1/2-x,1/2-y,z 59 Pmnm (m2m origin) x,y,z -x,y,z 1/2+x,-y,1/2+z x,y,-z 1/2-x,-y,1/2-z 1/2+x,-y,1/2-z -x,y,-z 1/2-x,-y,1/2+z 59 Pmnm (-1 origin) x,y,z 1/2-x,y,z 1/2+x,-y,1/2+z x,y,1/2-z -x,-y,-z 1/2+x,-y,-z 1/2-x,y,1/2-z -x,-y,1/2+z 59 Pnmm (2mm origin) x,y,z -x,1/2+y,1/2+z x,-y,z x,y,-z -x,1/2-y,1/2-z x,-y,-z -x,1/2+y,1/2-z -x,1/2-y,1/2+z 59 Pnmm (-1 origin) 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 60 Pbcn x,y,z 1/2-x,1/2+y,z x,-y,1/2+z 1/2+x,1/2+y,1/2-z -x,-y,-z 1/2+x,1/2-y,-z -x,y,1/2-z 1/2-x,1/2-y,1/2+z 60 Pcan x,y,z -x,y,1/2+z 1/2+x,1/2-y,z 1/2+x,1/2+y,1/2-z -x,-y,-z x,-y,1/2-z 1/2-x,1/2+y,-z 1/2-x,1/2-y,1/2+z 60 Pbna x,y,z -x,1/2+y,z 1/2+x,1/2-y,1/2+z 1/2+x,y,1/2-z -x,-y,-z x,1/2-y,-z 1/2-x,1/2+y,1/2-z 1/2-x,-y,1/2+z 60 Pcnb x,y,z 1/2-x,y,1/2+z 1/2+x,1/2-y,1/2+z x,1/2+y,-z -x,-y,-z 1/2+x,-y,1/2-z 1/2-x,1/2+y,1/2-z -x,1/2-y,z 60 Pnca x,y,z 1/2-x,1/2+y,1/2+z x,1/2-y,1/2+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,-y,z 60 Pnab x,y,z 1/2-x,1/2+y,1/2+z 1/2+x,-y,z x,1/2+y,1/2-z -x,-y,-z 1/2+x,1/2-y,1/2-z 1/2-x,y,-z -x,1/2-y,1/2+z 61 Pbca x,y,z 1/2-x,1/2+y,z x,1/2-y,1/2+z 1/2+x,y,1/2-z -x,-y,-z 1/2+x,1/2-y,-z -x,1/2+y,1/2-z 1/2-x,-y,1/2+z 61 Pcab x,y,z 1/2-x,y,1/2+z 1/2+x,1/2-y,z x,1/2+y,1/2-z -x,-y,-z 1/2+x,-y,1/2-z 1/2-x,1/2+y,-z -x,1/2-y,1/2+z 62 Pnma x,y,z 1/2-x,1/2+y,1/2+z x,1/2-y,z 1/2+x,y,1/2-z -x,-y,-z 1/2+x,1/2-y,1/2-z -x,1/2+y,-z 1/2-x,-y,1/2+z 62 Pnam x,y,z 1/2-x,1/2+y,1/2+z 1/2+x,1/2-y,z x,y,1/2-z -x,-y,-z 1/2+x,1/2-y,1/2-z 1/2-x,1/2+y,-z -x,-y,1/2+z 62 Pmcn x,y,z 1/2-x,y,z x,1/2-y,1/2+z 1/2+x,1/2+y,1/2-z -x,-y,-z 1/2+x,-y,-z -x,1/2+y,1/2-z 1/2-x,1/2-y,1/2+z 62 Pcmn x,y,z 1/2-x,y,1/2+z x,1/2-y,z 1/2+x,1/2+y,1/2-z -x,-y,-z 1/2+x,-y,1/2-z -x,1/2+y,-z 1/2-x,1/2-y,1/2+z 62 Pbnm x,y,z 1/2-x,1/2+y,z 1/2+x,1/2-y,1/2+z x,y,1/2-z -x,-y,-z 1/2+x,1/2-y,-z 1/2-x,1/2+y,1/2-z -x,-y,1/2+z 62 Pnmb 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,-y,-z 1/2+x,-y,-z 1/2-x,1/2+y,1/2-z -x,1/2-y,1/2+z 63 Cmcm x,y,z -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 +(1/2,1/2,0) 63 Ccmm x,y,z -x,y,1/2+z x,-y,z x,y,1/2-z -x,-y,-z x,-y,1/2-z -x,y,-z -x,-y,1/2+z +(1/2,1/2,0) 64 Cmca 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 +(1/2,1/2,0) 64 Ccma x,y,z -x,1/2+y,1/2+z x,-y,z x,1/2+y,1/2-z -x,-y,-z x,1/2-y,1/2-z -x,y,-z -x,1/2-y,1/2+z +(1/2,1/2,0) 65 Cmmm x,y,z -x,y,z x,-y,z x,y,-z -x,-y,-z x,-y,-z -x,y,-z -x,-y,z +(1/2,1/2,0) 66 Cccm (2/m origin) 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 +(1/2,1/2,0) 66 Cccm (222 origin) x,y,z -x,y,1/2+z x,-y,1/2+z x,y,1/2-z -x,-y,1/2-z x,-y,-z -x,y,-z -x,-y,z +(1/2,1/2,0) 67 Cmma x,y,z -x,y,z x,1/2-y,z x,1/2+y,-z -x,-y,-z x,-y,-z -x,1/2+y,-z -x,1/2-y,z +(1/2,1/2,0) 67 Cmma (alt.) 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 +(1/2,1/2,0) 68 Ccca (222 origin) 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 x,-y,-z -x,y,-z -x,-y,z +(1/2,1/2,0) 68 Ccca (-1 origin) 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 +(1/2,1/2,0) 68 Ccca (-1 origin, alt.) x,y,z -x,y,1/2+z x,1/2-y,1/2+z x,1/2+y,-z -x,-y,-z x,-y,1/2-z -x,1/2+y,1/2-z -x,1/2-y,z +(1/2,1/2,0) 69 Fmmm x,y,z -x,y,z x,-y,z x,y,-z -x,-y,-z x,-y,-z -x,y,-z -x,-y,z +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 70 Fddd (222 origin) x,y,z 1/4-x,1/4+y,1/4+z 1/4+x,1/4-y,1/4+z 1/4+x,1/4+y,1/4-z 1/4-x,1/4-y,1/4-z x,-y,-z -x,y,-z -x,-y,z +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 70 Fddd (-1 origin) x,y,z -x,1/4+y,1/4+z 1/4+x,-y,1/4+z 1/4+x,1/4+y,-z -x,-y,-z x,1/4-y,1/4-z 1/4-x,y,1/4-z 1/4-x,1/4-y,z +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 71 Immm x,y,z -x,y,z x,-y,z x,y,-z -x,-y,-z x,-y,-z -x,y,-z -x,-y,z +(1/2,1/2,1/2) 72 Ibam 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 +(1/2,1/2,1/2) 72 Ibma 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 +(1/2,1/2,1/2) 72 Imaa 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 +(1/2,1/2,1/2) 73 Ibca x,y,z -x,y,1/2+z 1/2+x,-y,z x,1/2+y,-z -x,-y,-z x,-y,1/2-z 1/2-x,y,-z -x,1/2-y,z +(1/2,1/2,1/2) 73 Ibca (alt.) x,y,z -x,1/2+y,z x,-y,1/2+z 1/2+x,y,-z -x,-y,-z x,1/2-y,-z -x,y,1/2-z 1/2-x,-y,z +(1/2,1/2,1/2) 74 Imma x,y,z -x,y,z x,1/2-y,z x,1/2+y,-z -x,-y,-z x,-y,-z -x,1/2+y,-z -x,1/2-y,z +(1/2,1/2,1/2) 74 Imma (alt.) x,y,z 1/2-x,y,z x,-y,z 1/2+x,y,-z -x,-y,-z 1/2+x,-y,-z -x,y,-z 1/2-x,-y,z +(1/2,1/2,1/2) 74 Imam 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 -x,-y,z +(1/2,1/2,1/2) 74 Imam (alt.) x,y,z -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 +(1/2,1/2,1/2) [Tetragonal] 75 P4 x,y,z -x,-y,z -y,x,z y,-x,z 76 P4(1) x,y,z -x,-y,1/2+z -y,x,1/4+z y,-x,3/4+z 77 P4(2) x,y,z -x,-y,z -y,x,1/2+z y,-x,1/2+z 78 P4(3) x,y,z -x,-y,1/2+z -y,x,3/4+z y,-x,1/4+z 79 I4 x,y,z -x,-y,z -y,x,z y,-x,z +(1/2,1/2,1/2) 80 I4(1) (2 origin) x,y,z -x,-y,z -y,1/2+x,1/4+z y,1/2-x,1/4+z +(1/2,1/2,1/2) 80 I4(1) (4(1) origin) x,y,z -x,-y,1/2+z -y,x,1/4+z y,-x,3/4+z +(1/2,1/2,1/2) 81 P-4 x,y,z -x,-y,z y,-x,-z -y,x,-z 82 I-4 x,y,z -x,-y,z y,-x,-z -y,x,-z +(1/2,1/2,1/2) 83 P4/m x,y,z -x,-y,z -y,x,z y,-x,z -x,-y,-z x,y,-z y,-x,-z -y,x,-z 84 P4(2)/m x,y,z -x,-y,z -y,x,1/2+z y,-x,1/2+z -x,-y,-z x,y,-z y,-x,1/2-z -y,x,1/2-z 85 P4/n (-4 origin) x,y,z -x,-y,z 1/2-y,1/2+x,z 1/2+y,1/2-x,z 1/2-x,1/2-y,-z 1/2+x,1/2+y,-z y,-x,-z -y,x,-z 85 P4/n (-1 origin) x,y,z 1/2-x,1/2-y,z 1/2-y,x,z y,1/2-x,z -x,-y,-z 1/2+x,1/2+y,-z 1/2+y,-x,-z -y,1/2+x,-z 85 P4/n (-1 origin, alt.) x,y,z 1/2-x,1/2-y,z -y,1/2+x,z 1/2+y,-x,z -x,-y,-z 1/2+x,1/2+y,-z y,1/2-x,-z 1/2-y,x,-z 85 P4/n (4/n origin) x,y,z -x,-y,z -y,x,z y,-x,z 1/2-x,1/2-y,-z 1/2+x,1/2+y,-z 1/2+y,1/2-x,-z 1/2-y,1/2+x,-z 86 P4(2)/n (-4 origin) x,y,z -x,-y,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+x,1/2+y,1/2-z y,-x,-z -y,x,-z 86 P4(2)/n (-1 origin) x,y,z 1/2-x,1/2-y,z -y,1/2+x,1/2+z 1/2+y,-x,1/2+z -x,-y,-z 1/2+x,1/2+y,-z y,1/2-x,1/2-z 1/2-y,x,1/2-z 86 P4(2)/n (-1 origin, alt.) x,y,z 1/2-x,1/2-y,z 1/2-y,x,1/2+z y,1/2-x,1/2+z -x,-y,-z 1/2+x,1/2+y,-z 1/2+y,-x,1/2-z -y,1/2+x,1/2-z 86 P4(2)/n (4(2)/n origin) x,y,z -x,-y,z -y,x,1/2+z y,-x,1/2+z 1/2-x,1/2-y,-z 1/2+x,1/2+y,-z 1/2+y,1/2-x,1/2-z 1/2-y,1/2+x,1/2-z 87 I4/m x,y,z -x,-y,z -y,x,z y,-x,z -x,-y,-z x,y,-z y,-x,-z -y,x,-z +(1/2,1/2,1/2) 88 I4(1)/a (-4 origin) x,y,z -x,-y,z -y,1/2+x,1/4+z y,1/2-x,1/4+z -x,1/2-y,1/4-z x,1/2+y,1/4-z y,-x,-z -y,x,-z +(1/2,1/2,1/2) 88 I4(1)/a (-1 origin) x,y,z -x,1/2-y,z 1/4-y,3/4+x,3/4+z 1/4+y,1/4-x,1/4+z -x,-y,-z x,1/2+y,-z 1/4+y,3/4-x,3/4-z 1/4-y,1/4+x,1/4-z +(1/2,1/2,1/2) 88 I4(1)/a (4(1)/a origin) x,y,z -x,-y,1/2+z -y,x,1/4+z y,-x,3/4+z -x,1/2-y,-z 1/2+x,y,-z 1/2+y,-x,1/4-z -y,1/2+x,1/4-z +(1/2,1/2,1/2) 88 I4(1)/a (4(1)/b origin) x,y,z -x,-y,1/2+z -y,x,1/4+z y,-x,3/4+z 1/2-x,-y,-z x,1/2+y,-z y,1/2-x,1/4-z 1/2-y,x,1/4-z +(1/2,1/2,1/2) 89 P422 x,y,z -x,-y,z -y,x,z y,-x,z x,-y,-z -x,y,-z -y,-x,-z y,x,-z 90 P42(1)2 (222 origin) x,y,z -x,-y,z 1/2-y,1/2+x,z 1/2+y,1/2-x,z 1/2+x,1/2-y,-z 1/2-x,1/2+y,-z -y,-x,-z y,x,-z 90 P42(1)2 (42(1)2(1) origin) x,y,z -x,-y,z -y,x,z y,-x,z 1/2+x,1/2-y,-z 1/2-x,1/2+y,-z 1/2-y,1/2-x,-z 1/2+y,1/2+x,-z 91 P4(1)22 x,y,z -x,-y,1/2+z -y,x,1/4+z y,-x,3/4+z x,-y,1/2-z -x,y,-z -y,-x,1/4-z y,x,3/4-z 92 P4(1)2(1)2 (origin 2(1)12) x,y,z -x,-y,1/2+z 1/2-y,1/2+x,1/4+z 1/2+y,1/2-x,3/4+z 1/2+x,1/2-y,3/4-z 1/2-x,1/2+y,1/4-z -y,-x,1/2-z y,x,-z 92 P4(1)2(1)2 (origin 4(1)12(1)) x,y,z -x,-y,1/2+z -y,x,1/4+z y,-x,3/4+z 1/2+x,1/2-y,3/4-z 1/2-x,1/2+y,1/4-z 1/2-y,1/2-x,1/2-z 1/2+y,1/2+x,-z 92 P4(1)2(1)2 (origin as P2(1)2(1)2(1)) x,y,z 1/2-x,-y,1/2+z 1/4-y,3/4+x,1/4+z 1/4+y,1/4-x,3/4+z 1/2+x,1/2-y,-z -x,1/2+y,1/2-z 3/4-y,3/4-x,3/4-z 3/4+y,1/4+x,1/4-z 93 P4(2)22 x,y,z -x,-y,z -y,x,1/2+z y,-x,1/2+z x,-y,-z -x,y,-z -y,-x,1/2-z y,x,1/2-z 94 P4(2)2(1)2 (222 origin) x,y,z -x,-y,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-x,1/2+y,1/2-z -y,-x,-z y,x,-z 94 P4(2)2(1)2 (4(2)2(1)2(1) origin) x,y,z -x,-y,z -y,x,1/2+z y,-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,1/2-x,-z 1/2+y,1/2+x,-z 95 P4(3)22 x,y,z -x,-y,1/2+z -y,x,3/4+z y,-x,1/4+z x,-y,1/2-z -x,y,-z -y,-x,3/4-z y,x,1/4-z 96 P4(3)2(1)2 (2(1)12 origin) 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,1/4-z 1/2-x,1/2+y,3/4-z -y,-x,1/2-z y,x,-z 96 P4(3)2(1)2 (4(3)12(1) origin) x,y,z -x,-y,1/2+z -y,x,3/4+z y,-x,1/4+z 1/2+x,1/2-y,1/4-z 1/2-x,1/2+y,3/4-z 1/2-y,1/2-x,1/2-z 1/2+y,1/2+x,-z 96 P4(3)2(1)2 (origin as P2(1)2(1)2(1)) x,y,z 1/2-x,-y,1/2+z 1/4-y,3/4+x,3/4+z 1/4+y,1/4-x,1/4+z 1/2+x,1/2-y,-z -x,1/2+y,1/2-z 3/4-y,3/4-x,1/4-z 3/4+y,1/4+x,3/4-z 97 I422 x,y,z -x,-y,z -y,x,z y,-x,z x,-y,-z -x,y,-z -y,-x,-z y,x,-z +(1/2,1/2,1/2) 98 I4(1)22 (222 origin) x,y,z -x,-y,z -y,1/2+x,1/4+z y,1/2-x,1/4+z x,1/2-y,1/4-z -x,1/2+y,1/4-z -y,-x,-z y,x,-z +(1/2,1/2,1/2) 98 I4(1)22 (4(1)12 origin) x,y,z -x,-y,1/2+z -y,x,1/4+z y,-x,3/4+z x,-y,1/2-z -x,y,-z -y,-x,1/4-z y,x,3/4-z +(1/2,1/2,1/2) 99 P4mm x,y,z -x,-y,z -y,x,z y,-x,z -x,y,z x,-y,z y,x,z -y,-x,z 100 P4bm x,y,z -x,-y,z -y,x,z y,-x,z 1/2-x,1/2+y,z 1/2+x,1/2-y,z 1/2+y,1/2+x,z 1/2-y,1/2-x,z 101 P4(2)cm x,y,z -x,-y,z -y,x,1/2+z y,-x,1/2+z -x,y,1/2+z x,-y,1/2+z y,x,z -y,-x,z 102 P4(2)nm x,y,z -x,-y,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+x,1/2-y,1/2+z y,x,z -y,-x,z 103 P4cc x,y,z -x,-y,z -y,x,z y,-x,z -x,y,1/2+z x,-y,1/2+z y,x,1/2+z -y,-x,1/2+z 104 P4nc x,y,z -x,-y,z -y,x,z y,-x,z 1/2-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 105 P4(2)mc x,y,z -x,-y,z -y,x,1/2+z y,-x,1/2+z -x,y,z x,-y,z y,x,1/2+z -y,-x,1/2+z 106 P4(2)bc x,y,z -x,-y,z -y,x,1/2+z y,-x,1/2+z 1/2-x,1/2+y,z 1/2+x,1/2-y,z 1/2+y,1/2+x,1/2+z 1/2-y,1/2-x,1/2+z 107 I4mm x,y,z -x,-y,z -y,x,z y,-x,z -x,y,z x,-y,z y,x,z -y,-x,z +(1/2,1/2,1/2) 108 I4cm x,y,z -x,-y,z -y,x,z y,-x,z -x,y,1/2+z x,-y,1/2+z y,x,1/2+z -y,-x,1/2+z +(1/2,1/2,1/2) 109 I4(1)md x,y,z -x,-y,z -y,1/2+x,1/4+z y,1/2-x,1/4+z -x,y,z x,-y,z y,1/2+x,1/4+z -y,1/2-x,1/4+z +(1/2,1/2,1/2) 110 I4(1)cd x,y,z -x,-y,z -y,1/2+x,1/4+z y,1/2-x,1/4+z -x,y,1/2+z x,-y,1/2+z 1/2+y,x,1/4+z 1/2-y,-x,1/4+z +(1/2,1/2,1/2) 111 P-42m x,y,z -x,-y,z y,-x,-z -y,x,-z x,-y,-z -x,y,-z y,x,z -y,-x,z 112 P-42c x,y,z -x,-y,z y,-x,-z -y,x,-z x,-y,1/2-z -x,y,1/2-z y,x,1/2+z -y,-x,1/2+z 113 P-42(1)m x,y,z -x,-y,z y,-x,-z -y,x,-z 1/2+x,1/2-y,-z 1/2-x,1/2+y,-z 1/2+y,1/2+x,z 1/2-y,1/2-x,z 114 P-42(1)c x,y,z -x,-y,z y,-x,-z -y,x,-z 1/2+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 115 P-4m2 x,y,z -x,-y,z y,-x,-z -y,x,-z -x,y,z x,-y,z -y,-x,-z y,x,-z 116 P-4c2 x,y,z -x,-y,z y,-x,-z -y,x,-z -x,y,1/2+z x,-y,1/2+z -y,-x,1/2-z y,x,1/2-z 117 P-4b2 (-4 origin) x,y,z -x,-y,z y,-x,-z -y,x,-z 1/2-x,1/2+y,z 1/2+x,1/2-y,z 1/2-y,1/2-x,-z 1/2+y,1/2+x,-z 117 P-4b2 (222 origin) x,y,z -x,-y,z 1/2+y,1/2-x,-z 1/2-y,1/2+x,-z 1/2-x,1/2+y,z 1/2+x,1/2-y,z -y,-x,-z y,x,-z 118 P-4n2 (-4 origin) x,y,z -x,-y,z y,-x,-z -y,x,-z 1/2-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 118 P-4n2 (222 origin) x,y,z -x,-y,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+x,1/2-y,1/2+z -y,-x,-z y,x,-z 119 I-4m2 x,y,z -x,-y,z y,-x,-z -y,x,-z -x,y,z x,-y,z -y,-x,-z y,x,-z +(1/2,1/2,1/2) 120 I-4c2 x,y,z -x,-y,z y,-x,-z -y,x,-z -x,y,1/2+z x,-y,1/2+z -y,-x,1/2-z y,x,1/2-z +(1/2,1/2,1/2) 121 I-42m x,y,z -x,-y,z y,-x,-z -y,x,-z x,-y,-z -x,y,-z y,x,z -y,-x,z +(1/2,1/2,1/2) 122 I-42d x,y,z -x,-y,z y,-x,-z -y,x,-z x,1/2-y,1/4-z -x,1/2+y,1/4-z y,1/2+x,1/4+z -y,1/2-x,1/4+z +(1/2,1/2,1/2) 123 P4/mmm 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 y,-x,-z -y,x,-z x,-y,-z -x,y,-z -y,-x,-z y,x,-z 124 P4/mcc (4/m origin) x,y,z -x,-y,z -y,x,z y,-x,z -x,y,1/2+z x,-y,1/2+z y,x,1/2+z -y,-x,1/2+z -x,-y,-z x,y,-z y,-x,-z -y,x,-z x,-y,1/2-z -x,y,1/2-z -y,-x,1/2-z y,x,1/2-z 124 P4/mcc (422 origin) x,y,z -x,-y,z -y,x,z y,-x,z -x,y,1/2+z x,-y,1/2+z y,x,1/2+z -y,-x,1/2+z -x,-y,1/2-z x,y,1/2-z y,-x,1/2-z -y,x,1/2-z x,-y,-z -x,y,-z -y,-x,-z y,x,-z 125 P4/nbm (422 origin) x,y,z -x,-y,z -y,x,z y,-x,z 1/2-x,1/2+y,z 1/2+x,1/2-y,z 1/2+y,1/2+x,z 1/2-y,1/2-x,z 1/2-x,1/2-y,-z 1/2+x,1/2+y,-z 1/2+y,1/2-x,-z 1/2-y,1/2+x,-z x,-y,-z -x,y,-z -y,-x,-z y,x,-z 125 P4/nbm (2/m origin) x,y,z 1/2-x,1/2-y,z 1/2-y,x,z y,1/2-x,z -x,1/2+y,z 1/2+x,-y,z 1/2+y,1/2+x,z -y,-x,z -x,-y,-z 1/2+x,1/2+y,-z 1/2+y,-x,-z -y,1/2+x,-z x,1/2-y,-z 1/2-x,y,-z 1/2-y,1/2-x,-z y,x,-z 125 P4/nbm (2/m origin, alt.) x,y,z 1/2-x,1/2-y,z -y,1/2+x,z 1/2+y,-x,z -x,1/2+y,z 1/2+x,-y,z y,x,z 1/2-y,1/2-x,z -x,-y,-z 1/2+x,1/2+y,-z y,1/2-x,-z 1/2-y,x,-z x,1/2-y,-z 1/2-x,y,-z -y,-x,-z 1/2+y,1/2+x,-z 125 P4/nbm (-42m origin) x,y,z -x,-y,z 1/2-y,1/2+x,z 1/2+y,1/2-x,z 1/2-x,1/2+y,z 1/2+x,1/2-y,z y,x,z -y,-x,z 1/2-x,1/2-y,-z 1/2+x,1/2+y,-z y,-x,-z -y,x,-z x,-y,-z -x,y,-z 1/2-y,1/2-x,-z 1/2+y,1/2+x,-z 126 P4/nnc (422 origin) x,y,z -x,-y,z -y,x,z y,-x,z 1/2-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-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 x,-y,-z -x,y,-z -y,-x,-z y,x,-z 126 P4/nnc (-1 origin) x,y,z 1/2-x,1/2-y,z 1/2-y,x,z y,1/2-x,z -x,1/2+y,1/2+z 1/2+x,-y,1/2+z 1/2+y,1/2+x,1/2+z -y,-x,1/2+z -x,-y,-z 1/2+x,1/2+y,-z 1/2+y,-x,-z -y,1/2+x,-z x,1/2-y,1/2-z 1/2-x,y,1/2-z 1/2-y,1/2-x,1/2-z y,x,1/2-z 126 P4/nnc (-1 origin, alt.) x,y,z 1/2-x,1/2-y,z -y,1/2+x,z 1/2+y,-x,z -x,1/2+y,1/2+z 1/2+x,-y,1/2+z y,x,1/2+z 1/2-y,1/2-x,1/2+z -x,-y,-z 1/2+x,1/2+y,-z y,1/2-x,-z 1/2-y,x,-z x,1/2-y,1/2-z 1/2-x,y,1/2-z -y,-x,1/2-z 1/2+y,1/2+x,1/2-z 126 P4/nnc (-4 origin) x,y,z -x,-y,z 1/2-y,1/2+x,z 1/2+y,1/2-x,z 1/2-x,1/2+y,1/2+z 1/2+x,1/2-y,1/2+z y,x,1/2+z -y,-x,1/2+z 1/2-x,1/2-y,-z 1/2+x,1/2+y,-z y,-x,-z -y,x,-z x,-y,1/2-z -x,y,1/2-z 1/2-y,1/2-x,1/2-z 1/2+y,1/2+x,1/2-z 127 P4/mbm (4/m origin) x,y,z -x,-y,z -y,x,z y,-x,z 1/2-x,1/2+y,z 1/2+x,1/2-y,z 1/2+y,1/2+x,z 1/2-y,1/2-x,z -x,-y,-z x,y,-z y,-x,-z -y,x,-z 1/2+x,1/2-y,-z 1/2-x,1/2+y,-z 1/2-y,1/2-x,-z 1/2+y,1/2+x,-z 127 P4/mbm (mmm origin) x,y,z -x,-y,z 1/2-y,1/2+x,z 1/2+y,1/2-x,z 1/2-x,1/2+y,z 1/2+x,1/2-y,z y,x,z -y,-x,z -x,-y,-z x,y,-z 1/2+y,1/2-x,-z 1/2-y,1/2+x,-z 1/2+x,1/2-y,-z 1/2-x,1/2+y,-z -y,-x,-z y,x,-z 128 P4/mnc (4/m origin) x,y,z -x,-y,z -y,x,z y,-x,z 1/2-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 -x,-y,-z x,y,-z y,-x,-z -y,x,-z 1/2+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 128 P4/mnc (222 origin) x,y,z -x,-y,z 1/2-y,1/2+x,z 1/2+y,1/2-x,z 1/2-x,1/2+y,1/2+z 1/2+x,1/2-y,1/2+z y,x,1/2+z -y,-x,1/2+z -x,-y,1/2-z x,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,-z 1/2-x,1/2+y,-z -y,-x,-z y,x,-z 129 P4/nmm (-4m2 origin) x,y,z -x,-y,z 1/2-y,1/2+x,z 1/2+y,1/2-x,z -x,y,z x,-y,z 1/2+y,1/2+x,z 1/2-y,1/2-x,z 1/2-x,1/2-y,-z 1/2+x,1/2+y,-z y,-x,-z -y,x,-z 1/2+x,1/2-y,-z 1/2-x,1/2+y,-z -y,-x,-z y,x,-z 129 P4/nmm (2/m origin) x,y,z 1/2-x,1/2-y,z 1/2-y,x,z y,1/2-x,z 1/2-x,y,z x,1/2-y,z y,x,z 1/2-y,1/2-x,z -x,-y,-z 1/2+x,1/2+y,-z 1/2+y,-x,-z -y,1/2+x,-z 1/2+x,-y,-z -x,1/2+y,-z -y,-x,-z 1/2+y,1/2+x,-z 129 P4/nmm (2/m origin, alt.) x,y,z 1/2-x,1/2-y,z -y,1/2+x,z 1/2+y,-x,z 1/2-x,y,z x,1/2-y,z 1/2+y,1/2+x,z -y,-x,z -x,-y,-z 1/2+x,1/2+y,-z y,1/2-x,-z 1/2-y,x,-z 1/2+x,-y,-z -x,1/2+y,-z 1/2-y,1/2-x,-z y,x,-z 129 P4/nmm (4mm origin) x,y,z -x,-y,z -y,x,z y,-x,z -x,y,z x,-y,z y,x,z -y,-x,z 1/2-x,1/2-y,-z 1/2+x,1/2+y,-z 1/2+y,1/2-x,-z 1/2-y,1/2+x,-z 1/2+x,1/2-y,-z 1/2-x,1/2+y,-z 1/2-y,1/2-x,-z 1/2+y,1/2+x,-z 130 P4/ncc (-4 origin) x,y,z -x,-y,z 1/2-y,1/2+x,z 1/2+y,1/2-x,z -x,y,1/2+z x,-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,-z 1/2+x,1/2+y,-z y,-x,-z -y,x,-z 1/2+x,1/2-y,1/2-z 1/2-x,1/2+y,1/2-z -y,-x,1/2-z y,x,1/2-z 130 P4/ncc (-1 origin) x,y,z 1/2-x,1/2-y,z 1/2-y,x,z y,1/2-x,z 1/2-x,y,1/2+z x,1/2-y,1/2+z y,x,1/2+z 1/2-y,1/2-x,1/2+z -x,-y,-z 1/2+x,1/2+y,-z 1/2+y,-x,-z -y,1/2+x,-z 1/2+x,-y,1/2-z -x,1/2+y,1/2-z -y,-x,1/2-z 1/2+y,1/2+x,1/2-z 130 P4/ncc (-1 origin, alt.) x,y,z 1/2-x,1/2-y,z -y,1/2+x,z 1/2+y,-x,z 1/2-x,y,1/2+z x,1/2-y,1/2+z 1/2+y,1/2+x,1/2+z -y,-x,1/2+z -x,-y,-z 1/2+x,1/2+y,-z y,1/2-x,-z 1/2-y,x,-z 1/2+x,-y,1/2-z -x,1/2+y,1/2-z 1/2-y,1/2-x,1/2-z y,x,1/2-z 130 P4/ncc (222 origin) x,y,z -x,-y,z 1/2-y,1/2+x,z 1/2+y,1/2-x,z -x,y,1/2+z x,-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+x,1/2+y,1/2-z y,-x,1/2-z -y,x,1/2-z 1/2+x,1/2-y,-z 1/2-x,1/2+y,-z -y,-x,-z y,x,-z 131 P4(2)/mmc x,y,z -x,-y,z -y,x,1/2+z y,-x,1/2+z -x,y,z x,-y,z y,x,1/2+z -y,-x,1/2+z -x,-y,-z x,y,-z y,-x,1/2-z -y,x,1/2-z x,-y,-z -x,y,-z -y,-x,1/2-z y,x,1/2-z 132 P4(2)/mcm x,y,z -x,-y,z -y,x,1/2+z y,-x,1/2+z -x,y,1/2+z x,-y,1/2+z y,x,z -y,-x,z -x,-y,-z x,y,-z y,-x,1/2-z -y,x,1/2-z x,-y,1/2-z -x,y,1/2-z -y,-x,-z y,x,-z 133 P4(2)/nbc (-4 origin) x,y,z -x,-y,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,z 1/2+x,1/2-y,z y,x,1/2+z -y,-x,1/2+z 1/2-x,1/2-y,1/2-z 1/2+x,1/2+y,1/2-z y,-x,-z -y,x,-z x,-y,1/2-z -x,y,1/2-z 1/2-y,1/2-x,-z 1/2+y,1/2+x,-z 133 P4(2)/nbc (-1 origin) x,y,z 1/2-x,1/2-y,z 1/2-y,x,1/2+z y,1/2-x,1/2+z -x,1/2+y,z 1/2+x,-y,z 1/2+y,1/2+x,1/2+z -y,-x,1/2+z -x,-y,-z 1/2+x,1/2+y,-z 1/2+y,-x,1/2-z -y,1/2+x,1/2-z x,1/2-y,-z 1/2-x,y,-z 1/2-y,1/2-x,1/2-z y,x,1/2-z 133 P4(2)/nbc (-1 origin, alt.) x,y,z 1/2-x,1/2-y,z -y,1/2+x,1/2+z 1/2+y,-x,1/2+z -x,1/2+y,z 1/2+x,-y,z y,x,1/2+z 1/2-y,1/2-x,1/2+z -x,-y,-z 1/2+x,1/2+y,-z y,1/2-x,1/2-z 1/2-y,x,1/2-z x,1/2-y,-z 1/2-x,y,-z -y,-x,1/2-z 1/2+y,1/2+x,1/2-z 133 P4(2)/nbc (222 origin) x,y,z -x,-y,z -y,x,1/2+z y,-x,1/2+z 1/2-x,1/2+y,z 1/2+x,1/2-y,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,-z 1/2+x,1/2+y,-z 1/2+y,1/2-x,1/2-z 1/2-y,1/2+x,1/2-z x,-y,-z -x,y,-z -y,-x,1/2-z y,x,1/2-z 134 P4(2)/nnm (-42m origin) x,y,z -x,-y,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+x,1/2-y,1/2+z y,x,z -y,-x,z 1/2-x,1/2-y,1/2-z 1/2+x,1/2+y,1/2-z y,-x,-z -y,x,-z x,-y,-z -x,y,-z 1/2-y,1/2-x,1/2-z 1/2+y,1/2+x,1/2-z 134 P42/nnm (2/m origin) x,y,z 1/2-x,1/2-y,z 1/2-y,x,1/2+z y,1/2-x,1/2+z -x,1/2+y,1/2+z 1/2+x,-y,1/2+z 1/2+y,1/2+x,z -y,-x,z -x,-y,-z 1/2+x,1/2+y,-z 1/2+y,-x,1/2-z -y,1/2+x,1/2-z x,1/2-y,1/2-z 1/2-x,y,1/2-z 1/2-y,1/2-x,-z y,x,-z 134 P4(2)/nnm (2/m origin, alt.) x,y,z 1/2-x,1/2-y,z -y,1/2+x,1/2+z 1/2+y,-x,1/2+z -x,1/2+y,1/2+z 1/2+x,-y,1/2+z y,x,z 1/2-y,1/2-x,z -x,-y,-z 1/2+x,1/2+y,-z y,1/2-x,1/2-z 1/2-y,x,1/2-z x,1/2-y,1/2-z 1/2-x,y,1/2-z -y,-x,-z 1/2+y,1/2+x,-z 134 P4(2)/nnm (4(2)22 origin) x,y,z -x,-y,z -y,x,1/2+z y,-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,1/2+x,z 1/2-y,1/2-x,z 1/2-x,1/2-y,1/2-z 1/2+x,1/2+y,1/2-z 1/2+y,1/2-x,-z 1/2-y,1/2+x,-z x,-y,-z -x,y,-z -y,-x,1/2-z y,x,1/2-z 135 P4(2)/mbc (4(2)/m origin) x,y,z -x,-y,z -y,x,1/2+z y,-x,1/2+z 1/2-x,1/2+y,z 1/2+x,1/2-y,z 1/2+y,1/2+x,1/2+z 1/2-y,1/2-x,1/2+z -x,-y,-z x,y,-z y,-x,1/2-z -y,x,1/2-z 1/2+x,1/2-y,-z 1/2-x,1/2+y,-z 1/2-y,1/2-x,1/2-z 1/2+y,1/2+x,1/2-z 135 P4(2)/mbc (222 origin) x,y,z -x,-y,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,z 1/2+x,1/2-y,z y,x,1/2+z -y,-x,1/2+z -x,-y,1/2-z x,y,1/2-z 1/2+y,1/2-x,-z 1/2-y,1/2+x,-z 1/2+x,1/2-y,1/2-z 1/2-x,1/2+y,1/2-z -y,-x,-z y,x,-z 136 P4(2)/mnm (mmm origin) x,y,z -x,-y,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+x,1/2-y,1/2+z y,x,z -y,-x,z -x,-y,-z x,y,-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-x,1/2+y,1/2-z -y,-x,-z y,x,-z 136 P4(2)/mnm (4(2)/m origin) x,y,z -x,-y,z -y,x,1/2+z y,-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,1/2+x,z 1/2-y,1/2-x,z -x,-y,-z x,y,-z y,-x,1/2-z -y,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,1/2-x,-z 1/2+y,1/2+x,-z 137 P4(2)/nmc (-4m2 origin) x,y,z -x,-y,z 1/2-y,1/2+x,1/2+z 1/2+y,1/2-x,1/2+z -x,y,z x,-y,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+x,1/2+y,1/2-z y,-x,-z -y,x,-z 1/2+x,1/2-y,1/2-z 1/2-x,1/2+y,1/2-z -y,-x,-z y,x,-z 137 P4(2)/nmc (-1 origin) x,y,z 1/2-x,1/2-y,z 1/2-y,x,1/2+z y,1/2-x,1/2+z 1/2-x,y,z x,1/2-y,z y,x,1/2+z 1/2-y,1/2-x,1/2+z -x,-y,-z 1/2+x,1/2+y,-z 1/2+y,-x,1/2-z -y,1/2+x,1/2-z 1/2+x,-y,-z -x,1/2+y,-z -y,-x,1/2-z 1/2+y,1/2+x,1/2-z 137 P4(2)/nmc (-1 origin, alt.) x,y,z 1/2-x,1/2-y,z -y,1/2+x,1/2+z 1/2+y,-x,1/2+z 1/2-x,y,z x,1/2-y,z 1/2+y,1/2+x,1/2+z -y,-x,1/2+z -x,-y,-z 1/2+x,1/2+y,-z y,1/2-x,1/2-z 1/2-y,x,1/2-z 1/2+x,-y,-z -x,1/2+y,-z 1/2-y,1/2-x,1/2-z y,x,1/2-z 137 P4(2)/nmc (4(2)/n origin) x,y,z -x,-y,z -y,x,1/2+z y,-x,1/2+z -x,y,z x,-y,z y,x,1/2+z -y,-x,1/2+z 1/2-x,1/2-y,-z 1/2+x,1/2+y,-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,-z 1/2-x,1/2+y,-z 1/2-y,1/2-x,1/2-z 1/2+y,1/2+x,1/2-z 138 P4(2)/ncm (-4 origin) x,y,z -x,-y,z 1/2-y,1/2+x,1/2+z 1/2+y,1/2-x,1/2+z -x,y,1/2+z x,-y,1/2+z 1/2+y,1/2+x,z 1/2-y,1/2-x,z 1/2-x,1/2-y,1/2-z 1/2+x,1/2+y,1/2-z y,-x,-z -y,x,-z 1/2+x,1/2-y,-z 1/2-x,1/2+y,-z -y,-x,1/2-z y,x,1/2-z 138 P4(2)/ncm (2/m origin) x,y,z 1/2-x,1/2-y,z 1/2-y,x,1/2+z y,1/2-x,1/2+z 1/2-x,y,1/2+z x,1/2-y,1/2+z y,x,z 1/2-y,1/2-x,z -x,-y,-z 1/2+x,1/2+y,-z 1/2+y,-x,1/2-z -y,1/2+x,1/2-z 1/2+x,-y,1/2-z -x,1/2+y,1/2-z -y,-x,-z 1/2+y,1/2+x,-z 138 P4(2)/ncm (2/m origin, alt.) x,y,z 1/2-x,1/2-y,z -y,1/2+x,1/2+z 1/2+y,-x,1/2+z 1/2-x,y,1/2+z x,1/2-y,1/2+z 1/2+y,1/2+x,z -y,-x,z -x,-y,-z 1/2+x,1/2+y,-z y,1/2-x,1/2-z 1/2-y,x,1/2-z 1/2+x,-y,1/2-z -x,1/2+y,1/2-z 1/2-y,1/2-x,-z y,x,-z 138 P4(2)/ncm (222 origin) x,y,z -x,-y,z 1/2-y,1/2+x,1/2+z 1/2+y,1/2-x,1/2+z -x,y,1/2+z x,-y,1/2+z 1/2+y,1/2+x,z 1/2-y,1/2-x,z 1/2-x,1/2-y,-z 1/2+x,1/2+y,-z y,-x,1/2-z -y,x,1/2-z 1/2+x,1/2-y,1/2-z 1/2-x,1/2+y,1/2-z -y,-x,-z y,x,-z 138 P4(2)/ncm (4(2)/n origin) x,y,z -x,-y,z -y,x,1/2+z y,-x,1/2+z -x,y,1/2+z x,-y,1/2+z y,x,z -y,-x,z 1/2-x,1/2-y,-z 1/2+x,1/2+y,-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-x,1/2+y,1/2-z 1/2-y,1/2-x,-z 1/2+y,1/2+x,-z 139 I4/mmm 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 y,-x,-z -y,x,-z x,-y,-z -x,y,-z -y,-x,-z y,x,-z +(1/2,1/2,1/2) 140 I4/mcm x,y,z -x,-y,z -y,x,z y,-x,z -x,y,1/2+z x,-y,1/2+z y,x,1/2+z -y,-x,1/2+z -x,-y,-z x,y,-z y,-x,-z -y,x,-z x,-y,1/2-z -x,y,1/2-z -y,-x,1/2-z y,x,1/2-z +(1/2,1/2,1/2) 141 I4(1)/amd (-4m2 origin) x,y,z -x,-y,z -y,1/2+x,1/4+z y,1/2-x,1/4+z y,1/2-x,1/4+z -x,y,z x,-y,z y,1/2+x,1/4+z -y,1/2-x,1/4+z -x,1/2-y,1/4-z x,1/2+y,1/4-z y,-x,-z -y,x,-z x,1/2-y,1/4-z -x,1/2+y,1/4-z -y,-x,-z y,x,-z +(1/2,1/2,1/2) 141 I4(1)/amd (2/m origin) x,y,z -x,1/2-y,z 3/4-y,1/4+x,3/4+z 3/4+y,3/4-x,1/4+z -x,y,z x,1/2-y,z 1/4+y,1/4+x,3/4+z 1/4-y,3/4-x,1/4+z -x,-y,-z x,1/2+y,-z 3/4+y,1/4-x,3/4-z 3/4-y,3/4+x,1/4-z x,-y,-z -x,1/2+y,-z 1/4-y,1/4-x,3/4-z 1/4+y,3/4+x,1/4-z +(1/2,1/2,1/2) 142 I4(1)/acd (-4 origin) x,y,z -x,-y,z -y,1/2+x,1/4+z y,1/2-x,1/4+z -x,y,1/2+z x,-y,1/2+z 1/2+y,x,1/4+z 1/2-y,-x,1/4+z -x,1/2-y,1/4-z x,1/2+y,1/4-z y,-x,-z -y,x,-z 1/2+x,-y,1/4-z 1/2-x,y,1/4-z -y,-x,1/2-z y,x,1/2-z +(1/2,1/2,1/2) 142 I4(1)/acd (-1 origin) x,y,z -x,1/2-y,z 3/4-y,1/4+x,3/4+z 3/4+y,3/4-x,1/4+z -x,y,1/2+z 1/2+x,-y,z 1/4+y,1/4+x,1/4+z 1/4-y,3/4-x,3/4+z -x,-y,-z x,1/2+y,-z 3/4+y,1/4-x,3/4-z 3/4-y,3/4+x,1/4-z x,-y,1/2-z 1/2-x,y,-z 1/4-y,1/4-x,1/4-z 1/4+y,3/4+x,3/4-z +(1/2,1/2,1/2) [Trigonal] 143 P3 x,y,z -y,x-y,z -x+y,-x,z 143 H3 x,y,z -y,x-y,z -x+y,-x,z +(2/3,1/3,0),(1/3,2/3,0) 144 P3(1) x,y,z -y,x-y,1/3+z -x+y,-x,2/3+z 144 H3(1) x,y,z -y,x-y,1/3+z -x+y,-x,2/3+z +(2/3,1/3,0),(1/3,2/3,0) 145 P3(2) x,y,z -y,x-y,2/3+z -x+y,-x,1/3+z 145 H3(2) x,y,z -y,x-y,2/3+z -x+y,-x,1/3+z +(2/3,1/3,0),(1/3,2/3,0) 146 R3 x,y,z z,x,y y,z,x 146 R3 (hexagonal axes) x,y,z -y,x-y,z -x+y,-x,z +(2/3,1/3,1/3),(1/3,2/3,2/3) 147 P-3 x,y,z -y,x-y,z -x+y,-x,z -x,-y,-z y,-x+y,-z x-y,x,-z 147 H-3 x,y,z -y,x-y,z -x+y,-x,z -x,-y,-z y,-x+y,-z x-y,x,-z +(2/3,1/3,0),(1/3,2/3,0) 148 R-3 x,y,z z,x,y y,z,x -x,-y,-z -z,-x,-y -y,-z,-x 148 R-3 (hexagonal axes) x,y,z -y,x-y,z -x+y,-x,z -x,-y,-z y,-x+y,-z x-y,x,-z +(2/3,1/3,1/3),(1/3,2/3,2/3) 149 P312 x,y,z -y,x-y,z -x+y,-x,z -y,-x,-z -x+y,y,-z x,x-y,-z 149 H321 x,y,z -y,x-y,z -x+y,-x,z y,x,-z x-y,-y,-z -x,-x+y,-z +(2/3,1/3,0),(1/3,2/3,0) 150 P321 x,y,z -y,x-y,z -x+y,-x,z y,x,-z x-y,-y,-z -x,-x+y,-z 150 H312 x,y,z -y,x-y,z -x+y,-x,z -y,-x,-z -x+y,y,-z x,x-y,-z +(2/3,1/3,0),(1/3,2/3,0) 151 P3(1)12 x,y,z -y,x-y,1/3+z -x+y,-x,2/3+z -y,-x,2/3-z -x+y,y,1/3-z x,x-y,-z 151 H3(1)21 x,y,z -y,x-y,1/3+z -x+y,-x,2/3+z y,x,-z x-y,-y,2/3-z -x,-x+y,1/3-z +(2/3,1/3,0),(1/3,2/3,0) 152 P3(1)21 x,y,z -y,x-y,1/3+z -x+y,-x,2/3+z y,x,-z x-y,-y,2/3-z -x,-x+y,1/3-z 152 H3(1)12 x,y,z -y,x-y,1/3+z -x+y,-x,2/3+z -y,-x,2/3-z -x+y,y,1/3-z x,x-y,-z +(2/3,1/3,0),(1/3,2/3,0) 153 P3(2)12 x,y,z -y,x-y,2/3+z -x+y,-x,1/3+z -y,-x,1/3-z -x+y,y,2/3-z x,x-y,-z 153 H3(2)21 x,y,z -y,x-y,2/3+z -x+y,-x,1/3+z y,x,-z x-y,-y,1/3-z -x,-x+y,2/3-z +(2/3,1/3,0),(1/3,2/3,0) 154 P3(2)21 x,y,z -y,x-y,2/3+z -x+y,-x,1/3+z y,x,-z x-y,-y,1/3-z -x,-x+y,2/3-z 154 H3(2)12 x,y,z -y,x-y,2/3+z -x+y,-x,1/3+z -y,-x,1/3-z -x+y,y,2/3-z x,x-y,-z +(2/3,1/3,0),(1/3,2/3,0) 155 R32 x,y,z z,x,y y,z,x -x,-z,-y -z,-y,-x -y,-x,-z 155 R32 (hexagonal axes) x,y,z -y,x-y,z -x+y,-x,z y,x,-z x-y,-y,-z -x,-x+y,-z +(2/3,1/3,1/3),(1/3,2/3,2/3) 156 P3m1 x,y,z -y,x-y,z -x+y,-x,z -y,-x,z -x+y,y,z x,x-y,z 156 H31m x,y,z -y,x-y,z -x+y,-x,z y,x,z x-y,-y,z -x,-x+y,z +(2/3,1/3,0),(1/3,2/3,0) 157 P31m x,y,z -y,x-y,z -x+y,-x,z y,x,z x-y,-y,z -x,-x+y,z 157 H3m1 x,y,z -y,x-y,z -x+y,-x,z -y,-x,z -x+y,y,z x,x-y,z +(2/3,1/3,0),(1/3,2/3,0) 158 P3c1 x,y,z -y,x-y,z -x+y,-x,z -y,-x,1/2+z -x+y,y,1/2+z x,x-y,1/2+z 158 P31c x,y,z -y,x-y,z -x+y,-x,z y,x,1/2+z x-y,-y,1/2+z -x,-x+y,1/2+z +(2/3,1/3,0),(1/3,2/3,0) 159 P31c x,y,z -y,x-y,z -x+y,-x,z y,x,1/2+z x-y,-y,1/2+z -x,-x+y,1/2+z 159 H3c1 x,y,z -y,x-y,z -x+y,-x,z -y,-x,1/2+z -x+y,y,1/2+z x,x-y,1/2+z +(2/3,1/3,0),(1/3,2/3,0) 160 R3m x,y,z z,x,y y,z,x x,z,y z,y,x y,x,z 160 R3m (hexagonal axes) x,y,z -y,x-y,z -x+y,-x,z -y,-x,z -x+y,y,z x,x-y,z +(2/3,1/3,1/3),(1/3,2/3,2/3) 161 R3c x,y,z z,x,y y,z,x 1/2+x,1/2+z,1/2+y 1/2+z,1/2+y,1/2+x 1/2+y,1/2+x,1/2+z 161 R3c (hexagonal axes) x,y,z -y,x-y,z -x+y,-x,z -y,-x,1/2+z -x+y,y,1/2+z x,x-y,1/2+z +(2/3,1/3,1/3),(1/3,2/3,2/3) 162 P-31m 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 162 H-3m1 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 +(2/3,1/3,0),(1/3,2/3,0) 163 P-31c (-3 origin) x,y,z -y,x-y,z -x+y,-x,z y,x,1/2+z x-y,-y,1/2+z -x,-x+y,1/2+z -x,-y,-z y,-x+y,-z x-y,x,-z -y,-x,1/2-z -x+y,y,1/2-z x,x-y,1/2-z 163 P-31c (32 origin) x,y,z -y,x-y,z -x+y,-x,z y,x,1/2+z x-y,-y,1/2+z -x,-x+y,1/2+z -x,-y,1/2-z y,-x+y,1/2-z x-y,x,1/2-z -y,-x,-z -x+y,y,-z x,x-y,-z 163 H-3c1 x,y,z -y,x-y,z -x+y,-x,z -y,-x,1/2+z -x+y,y,1/2+z x,x-y,1/2+z -x,-y,-z y,-x+y,-z x-y,x,-z y,x,1/2-z x-y,-y,1/2-z -x,-x+y,1/2-z +(2/3,1/3,0),(1/3,2/3,0) 164 P-3m1 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 164 H-31m 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 +(2/3,1/3,0),(1/3,2/3,0) 165 P-3c1 (-3 origin) x,y,z -y,x-y,z -x+y,-x,z -y,-x,1/2+z -x+y,y,1/2+z x,x-y,1/2+z -x,-y,-z y,-x+y,-z x-y,x,-z y,x,1/2-z x-y,-y,1/2-z -x,-x+y,1/2-z 165 P-3c1 (32 origin) x,y,z -y,x-y,z -x+y,-x,z -y,-x,1/2+z -x+y,y,1/2+z x,x-y,1/2+z -x,-y,1/2-z y,-x+y,1/2-z x-y,x,1/2-z y,x,-z x-y,-y,-z -x,-x+y,-z 165 H-31c x,y,z -y,x-y,z -x+y,-x,z y,x,1/2+z x-y,-y,1/2+z -x,-x+y,1/2+z -x,-y,-z y,-x+y,-z x-y,x,-z -y,-x,1/2-z -x+y,y,1/2-z x,x-y,1/2-z +(2/3,1/3,0),(1/3,2/3,0) 166 R-3m x,y,z z,x,y y,z,x x,z,y z,y,x y,x,z -x,-y,-z -z,-x,-y -y,-z,-x -x,-z,-y -z,-y,-x -y,-x,-z 166 R-3m (hexagonal axes) 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 +(2/3,1/3,1/3),(1/3,2/3,2/3) 167 R-3c x,y,z z,x,y y,z,x 1/2+x,1/2+z,1/2+y 1/2+z,1/2+y,1/2+x 1/2+y,1/2+x,1/2+z -x,-y,-z -z,-x,-y -y,-z,-x 1/2-x,1/2-z,1/2-y 1/2-z,1/2-y,1/2-x 1/2-y,1/2-x,1/2-z 167 R-3c (hexagonal axes) x,y,z -y,x-y,z -x+y,-x,z -y,-x,1/2+z -x+y,y,1/2+z x,x-y,1/2+z -x,-y,-z y,-x+y,-z x-y,x,-z y,x,1/2-z x-y,-y,1/2-z -x,-x+y,1/2-z +(2/3,1/3,1/3),(1/3,2/3,2/3) [Hexagonal] 168 P6 x,y,z -y,x-y,z -x+y,-x,z -x,-y,z x-y,x,z y,-x+y,z 169 P6(1) x,y,z -y,x-y,1/3+z -x+y,-x,2/3+z -x,-y,1/2+z x-y,x,1/6+z y,-x+y,5/6+z 170 P6(5) x,y,z -y,x-y,2/3+z -x+y,-x,1/3+z -x,-y,1/2+z x-y,x,5/6+z y,-x+y,1/6+z 171 P6(2) x,y,z -y,x-y,2/3+z -x+y,-x,1/3+z -x,-y,z x-y,x,1/3+z y,-x+y,2/3+z 172 P6(4) x,y,z -y,x-y,1/3+z -x+y,-x,2/3+z -x,-y,z x-y,x,2/3+z y,-x+y,1/3+z 173 P6(3) x,y,z -y,x-y,z -x+y,-x,z -x,-y,1/2+z x-y,x,1/2+z y,-x+y,1/2+z 174 P-6 x,y,z -y,x-y,z -x+y,-x,z x,y,-z -x+y,-x,-z -y,x-y,-z 175 P6/m x,y,z -y,x-y,z -x+y,-x,z -x,-y,z x-y,x,z y,-x+y,z -x,-y,-z y,-x+y,-z x-y,x,-z x,y,-z -x+y,-x,-z -y,x-y,-z 176 P6(3)/m x,y,z -y,x-y,z -x+y,-x,z -x,-y,1/2+z x-y,x,1/2+z y,-x+y,1/2+z -x,-y,-z y,-x+y,-z x-y,x,-z x,y,1/2-z -x+y,-x,1/2-z -y,x-y,1/2-z 177 P622 x,y,z -y,x-y,z -x+y,-x,z -x,-y,z x-y,x,z y,-x+y,z y,x,-z x-y,-y,-z -x,-x+y,-z -y,-x,-z -x+y,y,-z x,x-y,-z 178 P6(1)22 x,y,z -y,x-y,1/3+z -x+y,-x,2/3+z -x,-y,1/2+z x-y,x,1/6+z y,-x+y,5/6+z y,x,1/3-z x-y,-y,-z -x,-x+y,2/3-z -y,-x,5/6-z -x+y,y,1/2-z x,x-y,1/6-z 179 P6(5)22 x,y,z -y,x-y,2/3+z -x+y,-x,1/3+z -x,-y,1/2+z x-y,x,5/6+z y,-x+y,1/6+z y,x,2/3-z x-y,-y,-z -x,-x+y,1/3-z -y,-x,1/6-z -x+y,y,1/2-z x,x-y,5/6-z 180 P6(2)22 x,y,z -y,x-y,2/3+z -x+y,-x,1/3+z -x,-y,z x-y,x,1/3+z y,-x+y,2/3+z y,x,2/3-z x-y,-y,-z -x,-x+y,1/3-z -y,-x,2/3-z -x+y,y,-z x,x-y,1/3-z 181 P6(4)22 x,y,z -y,x-y,1/3+z -x+y,-x,2/3+z -x,-y,z x-y,x,2/3+z y,-x+y,1/3+z y,x,1/3-z x-y,-y,-z -x,-x+y,2/3-z -y,-x,1/3-z -x+y,y,-z x,x-y,2/3-z 182 P6(3)22 x,y,z -y,x-y,z -x+y,-x,z -x,-y,1/2+z x-y,x,1/2+z y,-x+y,1/2+z y,x,-z x-y,-y,-z -x,-x+y,-z -y,-x,1/2-z -x+y,y,1/2-z x,x-y,1/2-z 183 P6mm x,y,z -y,x-y,z -x+y,-x,z -x,-y,z x-y,x,z y,-x+y,z -y,-x,z -x+y,y,z x,x-y,z y,x,z x-y,-y,z -x,-x+y,z 184 P6cc x,y,z -y,x-y,z -x+y,-x,z -x,-y,z x-y,x,z y,-x+y,z -y,-x,1/2+z -x+y,y,1/2+z x,x-y,1/2+z y,x,1/2+z x-y,-y,1/2+z -x,-x+y,1/2+z 185 P6(3)cm x,y,z -y,x-y,z -x+y,-x,z -x,-y,1/2+z x-y,x,1/2+z y,-x+y,1/2+z -y,-x,1/2+z -x+y,y,1/2+z x,x-y,1/2+z y,x,z x-y,-y,z -x,-x+y,z 186 P6(3)mc x,y,z -y,x-y,z -x+y,-x,z -x,-y,1/2+z x-y,x,1/2+z y,-x+y,1/2+z -y,-x,z -x+y,y,z x,x-y,z y,x,1/2+z x-y,-y,1/2+z -x,-x+y,1/2+z 187 P-6m2 x,y,z -y,x-y,z -x+y,-x,z x,y,-z -x+y,-x,-z -y,x-y,-z -y,-x,z -x+y,y,z x,x-y,z -y,-x,-z -x+y,y,-z x,x-y,-z 188 P-6c2 (312 origin) x,y,z -y,x-y,z -x+y,-x,z x,y,1/2-z -x+y,-x,1/2-z -y,x-y,1/2-z -y,-x,1/2+z -x+y,y,1/2+z x,x-y,1/2+z -y,-x,-z -x+y,y,-z x,x-y,-z 188 P-6c2 (-6 origin) x,y,z -y,x-y,z -x+y,-x,z x,y,-z -x+y,-x,-z -y,x-y,-z -y,-x,1/2+z -x+y,y,1/2+z x,x-y,1/2+z -y,-x,1/2-z -x+y,y,1/2-z x,x-y,1/2-z 189 P-62m x,y,z -y,x-y,z -x+y,-x,z x,y,-z -x+y,-x,-z -y,x-y,-z y,x,-z x-y,-y,-z -x,-x+y,-z y,x,z x-y,-y,z -x,-x+y,z 190 P-62c (321 origin) x,y,z -y,x-y,z -x+y,-x,z x,y,1/2-z -x+y,-x,1/2-z -y,x-y,1/2-z y,x,-z x-y,-y,-z -x,-x+y,-z y,x,1/2+z x-y,-y,1/2+z -x,-x+y,1/2+z 190 P-62c (-6 origin) x,y,z -y,x-y,z -x+y,-x,z x,y,-z -x+y,-x,-z -y,x-y,-z y,x,1/2-z x-y,-y,1/2-z -x,-x+y,1/2-z y,x,1/2+z x-y,-y,1/2+z -x,-x+y,1/2+z 191 P6/mmm x,y,z -y,x-y,z -x+y,-x,z -x,-y,z x-y,x,z y,-x+y,z -y,-x,z -x+y,y,z x,x-y,z 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 -x+y,-x,-z -y,x-y,-z y,x,-z x-y,-y,-z -x,-x+y,-z -y,-x,-z -x+y,y,-z x,x-y,-z 192 P6/mcc x,y,z -y,x-y,z -x+y,-x,z -x,-y,z x-y,x,z y,-x+y,z -y,-x,1/2+z -x+y,y,1/2+z x,x-y,1/2+z y,x,1/2+z x-y,-y,1/2+z -x,-x+y,1/2+z -x,-y,-z y,-x+y,-z x-y,x,-z x,y,-z -x+y,-x,-z -y,x-y,-z y,x,1/2-z x-y,-y,1/2-z -x,-x+y,1/2-z -y,-x,1/2-z -x+y,y,1/2-z x,x-y,1/2-z 193 P6(3)/mcm x,y,z -y,x-y,z -x+y,-x,z -x,-y,1/2+z x-y,x,1/2+z y,-x+y,1/2+z -y,-x,1/2+z -x+y,y,1/2+z x,x-y,1/2+z y,x,z x-y,-y,z -x,-x+y,z -x,-y,-z y,-x+y,-z x-y,x,-z x,y,1/2-z -x+y,-x,1/2-z -y,x-y,1/2-z y,x,1/2-z x-y,-y,1/2-z -x,-x+y,1/2-z -y,-x,-z -x+y,y,-z x,x-y,-z 194 P6(3)/mmc x,y,z -y,x-y,z -x+y,-x,z -x,-y,1/2+z x-y,x,1/2+z y,-x+y,1/2+z -y,-x,z -x+y,y,z x,x-y,z y,x,1/2+z x-y,-y,1/2+z -x,-x+y,1/2+z -x,-y,-z y,-x+y,-z x-y,x,-z x,y,1/2-z -x+y,-x,1/2-z -y,x-y,1/2-z y,x,-z x-y,-y,-z -x,-x+y,-z -y,-x,1/2-z -x+y,y,1/2-z x,x-y,1/2-z [Cubic] 195 P23 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 196 F23 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 +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 197 I23 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 +(1/2,1/2,1/2) 198 P2(1)3 x,y,z 1/2+x,1/2-y,-z -x,1/2+y,1/2-z 1/2-x,-y,1/2+z z,x,y 1/2-z,-x,1/2+y 1/2+z,1/2-x,-y -z,1/2+x,1/2-y y,z,x -y,1/2+z,1/2-x 1/2-y,-z,1/2+x 1/2+y,1/2-z,-x 199 I2(1)3 x,y,z 1/2+x,1/2-y,-z -x,1/2+y,1/2-z 1/2-x,-y,1/2+z z,x,y 1/2-z,-x,1/2+y 1/2+z,1/2-x,-y -z,1/2+x,1/2-y y,z,x -y,1/2+z,1/2-x 1/2-y,-z,1/2+x 1/2+y,1/2-z,-x +(1/2,1/2,1/2) 200 Pm-3 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 -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 201 Pn-3 (23 origin) 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 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+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+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-y,1/2+z,1/2+x 201 Pn-3 (-3 origin) x,y,z x,1/2-y,1/2-z 1/2-x,y,1/2-z 1/2-x,1/2-y,z z,x,y 1/2-z,1/2-x,y z,1/2-x,1/2-y 1/2-z,x,1/2-y y,z,x 1/2-y,z,1/2-x 1/2-y,1/2-z,x y,1/2-z,1/2-x -x,-y,-z -x,1/2+y,1/2+z 1/2+x,-y,1/2+z 1/2+x,1/2+y,-z -z,-x,-y 1/2+z,1/2+x,-y -z,1/2+x,1/2+y 1/2+z,-x,1/2+y -y,-z,-x 1/2+y,-z,1/2+x 1/2+y,1/2+z,-x -y,1/2+z,1/2+x 202 Fm-3 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 -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 +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 203 Fd-3 (23 origin) 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 1/4-x,1/4-y,1/4-z 1/4-x,1/4+y,1/4+z 1/4+x,1/4-y,1/4+z 1/4+x,1/4+y,1/4-z 1/4-z,1/4-x,1/4-y 1/4+z,1/4+x,1/4-y 1/4-z,1/4+x,1/4+y 1/4+z,1/4-x,1/4+y 1/4-y,1/4-z,1/4-x 1/4+y,1/4-z,1/4+x 1/4+y,1/4+z,1/4-x 1/4-y,1/4+z,1/4+x +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 203 Fd-3 (-3 origin) x,y,z x,1/4-y,1/4-z 1/4-x,y,1/4-z 1/4-x,1/4-y,z z,x,y 1/4-z,1/4-x,y z,1/4-x,1/4-y 1/4-z,x,1/4-y y,z,x 1/4-y,z,1/4-x 1/4-y,1/4-z,x y,1/4-z,1/4-x -x,-y,-z -x,1/4+y,1/4+z 1/4+x,-y,1/4+z 1/4+x,1/4+y,-z -z,-x,-y 1/4+z,1/4+x,-y -z,1/4+x,1/4+y 1/4+z,-x,1/4+y -y,-z,-x 1/4+y,-z,1/4+x 1/4+y,1/4+z,-x -y,1/4+z,1/4+x +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 204 Im-3 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 -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 +(1/2,1/2,1/2) 205 Pa-3 x,y,z 1/2+x,1/2-y,-z -x,1/2+y,1/2-z 1/2-x,-y,1/2+z z,x,y 1/2-z,-x,1/2+y 1/2+z,1/2-x,-y -z,1/2+x,1/2-y y,z,x -y,1/2+z,1/2-x 1/2-y,-z,1/2+x 1/2+y,1/2-z,-x -x,-y,-z 1/2-x,1/2+y,z x,1/2-y,1/2+z 1/2+x,y,1/2-z -z,-x,-y 1/2+z,x,1/2-y 1/2-z,1/2+x,y z,1/2-x,1/2+y -y,-z,-x y,1/2-z,1/2+x 1/2+y,z,1/2-x 1/2-y,1/2+z,x 206 Ia-3 x,y,z x,-y,1/2-z 1/2-x,y,-z -x,1/2-y,z z,x,y -z,1/2-x,y z,-x,1/2-y 1/2-z,x,-y y,z,x 1/2-y,z,-x -y,1/2-z,x y,-z,1/2-x -x,-y,-z -x,y,1/2+z 1/2+x,-y,z x,1/2+y,-z -z,-x,-y z,1/2+x,-y -z,x,1/2+y 1/2+z,-x,y -y,-z,-x 1/2+y,-z,x y,1/2+z,-x -y,z,1/2+x +(1/2,1/2,1/2) 207 P432 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 x,-z,y x,z,-y -x,-z,-y -x,z,y z,y,-x -z,y,x -z,-y,-x z,-y,x -y,x,z y,-x,z -y,-x,-z y,x,-z 208 P4(2)32 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 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-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+z,1/2-y,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+y,1/2+x,1/2-z 209 F432 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 x,-z,y x,z,-y -x,-z,-y -x,z,y z,y,-x -z,y,x -z,-y,-x z,-y,x -y,x,z y,-x,z -y,-x,-z y,x,-z +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 210 F4(1)32 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 1/4+x,1/4-z,1/4+y 1/4+x,1/4+z,1/4-y 1/4-x,1/4-z,1/4-y 1/4-x,1/4+z,1/4+y 1/4+z,1/4+y,1/4-x 1/4-z,1/4+y,1/4+x 1/4-z,1/4-y,1/4-x 1/4+z,1/4-y,1/4+x 1/4-y,1/4+x,1/4+z 1/4+y,1/4-x,1/4+z 1/4-y,1/4-x,1/4-z 1/4+y,1/4+x,1/4-z +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 211 I432 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 x,-z,y x,z,-y -x,-z,-y -x,z,y z,y,-x -z,y,x -z,-y,-x z,-y,x -y,x,z y,-x,z -y,-x,-z y,x,-z +(1/2,1/2,1/2) 212 P4(3)32 x,y,z 1/2+x,1/2-y,-z -x,1/2+y,1/2-z 1/2-x,-y,1/2+z z,x,y 1/2-z,-x,1/2+y 1/2+z,1/2-x,-y -z,1/2+x,1/2-y y,z,x -y,1/2+z,1/2-x 1/2-y,-z,1/2+x 1/2+y,1/2-z,-x 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+y 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+x 3/4-y,1/4+x,3/4+z 3/4+y,3/4-x,1/4+z 1/4-y,1/4-x,1/4-z 1/4+y,3/4+x,3/4-z 213 P4(1)32 x,y,z 1/2+x,1/2-y,-z -x,1/2+y,1/2-z 1/2-x,-y,1/2+z z,x,y 1/2-z,-x,1/2+y 1/2+z,1/2-x,-y -z,1/2+x,1/2-y y,z,x -y,1/2+z,1/2-x 1/2-y,-z,1/2+x 1/2+y,1/2-z,-x 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+z,1/4+y 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+x 1/4-y,3/4+x,1/4+z 1/4+y,1/4-x,3/4+z 3/4-y,3/4-x,3/4-z 3/4+y,1/4+x,1/4-z 214 I4(1)32 x,y,z x,-y,1/2-z 1/2-x,y,-z -x,1/2-y,z z,x,y -z,1/2-x,y z,-x,1/2-y 1/2-z,x,-y y,z,x 1/2-y,z,-x -y,1/2-z,x y,-z,1/2-x 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+y 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+x 3/4-y,1/4+x,3/4+z 3/4+y,3/4-x,1/4+z 1/4-y,1/4-x,1/4-z 1/4+y,3/4+x,3/4-z +(1/2,1/2,1/2) 215 P-43m 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 -x,z,-y -x,-z,y x,z,y x,-z,-y -z,-y,x z,-y,-x z,y,x -z,y,-x y,-x,-z -y,x,-z y,x,z -y,-x,z 216 F-43m 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 -x,z,-y -x,-z,y x,z,y x,-z,-y -z,-y,x z,-y,-x z,y,x -z,y,-x y,-x,-z -y,x,-z y,x,z -y,-x,z +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 217 I-43m 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 -x,z,-y -x,-z,y x,z,y x,-z,-y -z,-y,x z,-y,-x z,y,x -z,y,-x y,-x,-z -y,x,-z y,x,z -y,-x,z +(1/2,1/2,1/2) 218 P-43n 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 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+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-z,1/2+y,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-y,1/2-x,1/2+z 219 F-43c 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 -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 -z,y,1/2-x y,-x,1/2-z -y,x,1/2-z y,x,1/2+z -y,-x,1/2+z +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 220 I-43d x,y,z x,-y,1/2-z 1/2-x,y,-z -x,1/2-y,z z,x,y -z,1/2-x,y z,-x,1/2-y 1/2-z,x,-y y,z,x 1/2-y,z,-x -y,1/2-z,x y,-z,1/2-x 1/4-x,1/4+z,3/4-y 1/4-x,3/4-z,3/4+y 1/4+x,1/4+z,1/4+y 1/4+x,3/4-z,1/4-y 1/4-z,3/4-y,3/4+x 1/4+z,3/4-y,1/4-x 1/4+z,1/4+y,1/4+x 1/4-z,1/4+y,3/4-x 1/4+y,3/4-x,1/4-z 3/4-y,3/4+x,1/4-z 1/4+y,1/4+x,1/4+z 1/4-y,3/4-x,3/4+z +(1/2,1/2,1/2) 221 Pm-3m 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 x,-z,y x,z,-y -x,-z,-y -x,z,y z,y,-x -z,y,x -z,-y,-x z,-y,x -y,x,z y,-x,z -y,-x,-z y,x,-z -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 -x,z,-y -x,-z,y x,z,y x,-z,-y -z,-y,x z,-y,-x z,y,x -z,y,-x y,-x,-z -y,x,-z y,x,z -y,-x,z 222 Pn-3n (432 origin) 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 x,-z,y x,z,-y -x,-z,-y -x,z,y z,y,-x -z,y,x -z,-y,-x z,-y,x -y,x,z y,-x,z -y,-x,-z y,x,-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+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+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-y,1/2+z,1/2+x 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+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-z,1/2+y,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-y,1/2-x,1/2+z 222 Pn-3n (-3 origin) x,y,z x,1/2-y,1/2-z 1/2-x,y,1/2-z 1/2-x,1/2-y,z z,x,y 1/2-z,1/2-x,y z,1/2-x,1/2-y 1/2-z,x,1/2-y y,z,x 1/2-y,z,1/2-x 1/2-y,1/2-z,x y,1/2-z,1/2-x x,1/2-z,y x,z,1/2-y 1/2-x,1/2-z,1/2-y 1/2-x,z,y z,y,1/2-x 1/2-z,y,x 1/2-z,1/2-y,1/2-x z,1/2-y,x 1/2-y,x,z y,1/2-x,z 1/2-y,1/2-x,1/2-z y,x,1/2-z -x,-y,-z -x,1/2+y,1/2+z 1/2+x,-y,1/2+z 1/2+x,1/2+y,-z -z,-x,-y 1/2+z,1/2+x,-y -z,1/2+x,1/2+y 1/2+z,-x,1/2+y -y,-z,-x 1/2+y,-z,1/2+x 1/2+y,1/2+z,-x -y,1/2+z,1/2+x -x,1/2+z,-y -x,-z,1/2+y 1/2+x,1/2+z,1/2+y 1/2+x,-z,-y -z,-y,1/2+x 1/2+z,-y,-x 1/2+z,1/2+y,1/2+x -z,1/2+y,-x 1/2+y,-x,-z -y,1/2+x,-z 1/2+y,1/2+x,1/2+z -y,-x,1/2+z 223 Pm-3n 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 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-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+z,1/2-y,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+y,1/2+x,1/2-z -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 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+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-z,1/2+y,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-y,1/2-x,1/2+z 224 Pn-3m (-43m origin) 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 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-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+z,1/2-y,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+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+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+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+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 -x,z,-y -x,-z,y x,z,y x,-z,-y -z,-y,x z,-y,-x z,y,x -z,y,-x y,-x,-z -y,x,-z y,x,z -y,-x,z 224 Pn-3m (-3m origin) x,y,z x,1/2-y,1/2-z 1/2-x,y,1/2-z 1/2-x,1/2-y,z z,x,y 1/2-z,1/2-x,y z,1/2-x,1/2-y 1/2-z,x,1/2-y y,z,x 1/2-y,z,1/2-x 1/2-y,1/2-z,x y,1/2-z,1/2-x 1/2+x,-z,1/2+y 1/2+x,1/2+z,-y -x,-z,-y -x,1/2+z,1/2+y 1/2+z,1/2+y,-x -z,1/2+y,1/2+x -z,-y,-x 1/2+z,-y,1/2+x -y,1/2+x,1/2+z 1/2+y,-x,1/2+z -y,-x,-z 1/2+y,1/2+x,-z -x,-y,-z -x,1/2+y,1/2+z 1/2+x,-y,1/2+z 1/2+x,1/2+y,-z -z,-x,-y 1/2+z,1/2+x,-y -z,1/2+x,1/2+y 1/2+z,-x,1/2+y -y,-z,-x 1/2+y,-z,1/2+x 1/2+y,1/2+z,-x -y,1/2+z,1/2+x 1/2-x,z,1/2-y 1/2-x,1/2-z,y x,z,y x,1/2-z,1/2-y 1/2-z,1/2-y,x z,1/2-y,1/2-x z,y,x 1/2-z,y,1/2-x y,1/2-x,1/2-z 1/2-y,x,1/2-z y,x,z 1/2-y,1/2-x,z 225 Fm-3m 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 x,-z,y x,z,-y -x,-z,-y -x,z,y z,y,-x -z,y,x -z,-y,-x z,-y,x -y,x,z y,-x,z -y,-x,-z y,x,-z -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 -x,z,-y -x,-z,y x,z,y x,-z,-y -z,-y,x z,-y,-x z,y,x -z,y,-x y,-x,-z -y,x,-z y,x,z -y,-x,z +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 226 Fm-3c 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 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 z,-y,1/2+x -y,x,1/2+z y,-x,1/2+z -y,-x,1/2-z y,x,1/2-z -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 -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 -z,y,1/2-x y,-x,1/2-z -y,x,1/2-z y,x,1/2+z -y,-x,1/2+z +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 227 Fd-3m (-43m origin) 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 1/4+x,1/4-z,1/4+y 1/4+x,1/4+z,1/4-y 1/4-x,1/4-z,1/4-y 1/4-x,1/4+z,1/4+y 1/4+z,1/4+y,1/4-x 1/4-z,1/4+y,1/4+x 1/4-z,1/4-y,1/4-x 1/4+z,1/4-y,1/4+x 1/4-y,1/4+x,1/4+z 1/4+y,1/4-x,1/4+z 1/4-y,1/4-x,1/4-z 1/4+y,1/4+x,1/4-z 1/4-x,1/4-y,1/4-z 1/4-x,1/4+y,1/4+z 1/4+x,1/4-y,1/4+z 1/4+x,1/4+y,1/4-z 1/4-z,1/4-x,1/4-y 1/4+z,1/4+x,1/4-y 1/4-z,1/4+x,1/4+y 1/4+z,1/4-x,1/4+y 1/4-y,1/4-z,1/4-x 1/4+y,1/4-z,1/4+x 1/4+y,1/4+z,1/4-x 1/4-y,1/4+z,1/4+x -x,z,-y -x,-z,y x,z,y x,-z,-y -z,-y,x z,-y,-x z,y,x -z,y,-x y,-x,-z -y,x,-z y,x,z -y,-x,z +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 227 Fd-3m (-3 origin) x,y,z x,1/4-y,1/4-z 1/4-x,y,1/4-z 1/4-x,1/4-y,z z,x,y 1/4-z,1/4-x,y z,1/4-x,1/4-y 1/4-z,x,1/4-y y,z,x 1/4-y,z,1/4-x 1/4-y,1/4-z,x y,1/4-z,1/4-x 1/4+x,-z,1/4+y 1/4+x,1/4+z,-y -x,-z,-y -x,1/4+z,1/4+y 1/4+z,1/4+y,-x -z,1/4+y,1/4+x -z,-y,-x 1/4+z,-y,1/4+x -y,1/4+x,1/4+z 1/4+y,-x,1/4+z -y,-x,-z 1/4+y,1/4+x,-z -x,-y,-z -x,1/4+y,1/4+z 1/4+x,-y,1/4+z 1/4+x,1/4+y,-z -z,-x,-y 1/4+z,1/4+x,-y -z,1/4+x,1/4+y 1/4+z,-x,1/4+y -y,-z,-x 1/4+y,-z,1/4+x 1/4+y,1/4+z,-x -y,1/4+z,1/4+x 1/4-x,z,1/4-y 1/4-x,1/4-z,y x,z,y x,1/4-z,1/4-y 1/4-z,1/4-y,x z,1/4-y,1/4-x z,y,x 1/4-z,y,1/4-x y,1/4-x,1/4-z 1/4-y,x,1/4-z y,x,z 1/4-y,1/4-x,z +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 228 Fd-3c (23 origin) 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 1/4+x,1/4-z,1/4+y 1/4+x,1/4+z,1/4-y 1/4-x,1/4-z,1/4-y 1/4-x,1/4+z,1/4+y 1/4+z,1/4+y,1/4-x 1/4-z,1/4+y,1/4+x 1/4-z,1/4-y,1/4-x 1/4+z,1/4-y,1/4+x 1/4-y,1/4+x,1/4+z 1/4+y,1/4-x,1/4+z 1/4-y,1/4-x,1/4-z 1/4+y,1/4+x,1/4-z 1/4-x,1/4-y,3/4-z 1/4-x,1/4+y,3/4+z 1/4+x,1/4-y,3/4+z 1/4+x,1/4+y,3/4-z 1/4-z,1/4-x,3/4-y 1/4+z,1/4+x,3/4-y 1/4-z,1/4+x,3/4+y 1/4+z,1/4-x,3/4+y 1/4-y,1/4-z,3/4-x 1/4+y,1/4-z,3/4+x 1/4+y,1/4+z,3/4-x 1/4-y,1/4+z,3/4+x -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 -z,y,1/2-x y,-x,1/2-z -y,x,1/2-z y,x,1/2+z -y,-x,1/2+z +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 228 Fd-3c (-3 origin) x,y,z x,1/4-y,1/4-z 1/4-x,y,1/4-z 1/4-x,1/4-y,z z,x,y 1/4-z,1/4-x,y z,1/4-x,1/4-y 1/4-z,x,1/4-y y,z,x 1/4-y,z,1/4-x 1/4-y,1/4-z,x y,1/4-z,1/4-x 1/4+x,-z,3/4+y 1/4+x,3/4+z,-y -x,-z,1/2-y -x,1/4+z,3/4+y 1/4+z,3/4+y,-x -z,1/4+y,3/4+x -z,-y,1/2-x 1/4+z,-y,3/4+x -y,1/4+x,3/4+z 1/4+y,-x,3/4+z -y,-x,1/2-z 1/4+y,3/4+x,-z -x,-y,-z -x,1/4+y,1/4+z 1/4+x,-y,1/4+z 1/4+x,1/4+y,-z -z,-x,-y 1/4+z,1/4+x,-y -z,1/4+x,1/4+y 1/4+z,-x,1/4+y -y,-z,-x 1/4+y,-z,1/4+x 1/4+y,1/4+z,-x -y,1/4+z,1/4+x 1/4-x,z,3/4-y 1/4-x,3/4-z,y x,z,1/2+y x,1/4-z,3/4-y 1/4-z,3/4-y,x z,1/4-y,3/4-x z,y,1/2+x 1/4-z,y,3/4-x y,1/4-x,3/4-z 1/4-y,x,3/4-z y,x,1/2+z 1/4-y,3/4-x,z +(0,1/2,1/2),(1/2,0,1/2),(1/2,1/2,0) 229 Im-3m 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 x,-z,y x,z,-y -x,-z,-y -x,z,y z,y,-x -z,y,x -z,-y,-x z,-y,x -y,x,z y,-x,z -y,-x,-z y,x,-z -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 -x,z,-y -x,-z,y x,z,y x,-z,-y -z,-y,x z,-y,-x z,y,x -z,y,-x y,-x,-z -y,x,-z y,x,z -y,-x,z +(1/2,1/2,1/2) 230 Ia-3d x,y,z x,-y,1/2-z 1/2-x,y,-z -x,1/2-y,z z,x,y -z,1/2-x,y z,-x,1/2-y 1/2-z,x,-y y,z,x 1/2-y,z,-x -y,1/2-z,x y,-z,1/2-x 1/4+x,1/4-z,3/4+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+y 1/4+z,3/4+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,1/4+x 3/4-y,1/4+x,3/4+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,1/4-z -x,-y,-z -x,y,1/2+z 1/2+x,-y,z x,1/2+y,-z -z,-x,-y z,1/2+x,-y -z,x,1/2+y 1/2+z,-x,y -y,-z,-x 1/2+y,-z,x y,1/2+z,-x -y,z,1/2+x 1/4-x,1/4+z,3/4-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-y 1/4-z,3/4-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,1/4-x 3/4+y,1/4-x,3/4-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,1/4+z +(1/2,1/2,1/2)