Template:List space groups Coxeter notation

Rank four groups defined the 3-dimensional space groups include:

Triclinic (1-2) Coxeter Space group [∞+,2,∞+,2,∞+] (1) P1 Monoclinic (3-15) Coxeter Space group [(∞,2,∞)+,2,∞+] (3) P2 [∞+,2,∞+,2,∞] (6) Pm [(∞,2,∞)+,2,∞] (10) P2/m Orthorhombic (16-74) File:CDel node.pngFile:CDel infin.pngFile:CDel node.pngFile:CDel 2.pngFile:CDel node.pngFile:CDel infin.pngFile:CDel node.pngFile:CDel 2.pngFile:CDel node.pngFile:CDel infin.pngFile:CDel node.png Coxeter Space group [∞,2,∞,2,∞]+ (16) P222 [[∞,2,∞,2,∞]]+ (23) I222 [∞+,2,∞,2,∞] (25) Pmm2 [∞,2,∞,2,∞] (47) Pmmm [[∞,2,∞,2,∞]] (71) Immm [∞+,2,∞+,2,∞+] [∞,2,∞,2+,∞] [∞,2+,∞,2+,∞]

Tetragonal (75-142) File:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 2.pngFile:CDel node.pngFile:CDel infin.pngFile:CDel node.png Coxeter Space group [(4,4)+,2,∞+] (75) P4 [2+[(4,4)+,2,∞+]] (79) I4 [(4,4)+,2,∞] (83) P4/m [2+[(4,4)+,2,∞]] (87) I4/m [4,4,2,∞]+ (89) P422 [2+[4,4,2,∞]]+ (97) I422 [4,4,2,∞+] (99) P4mm [4,4,2,∞] (123) P4/mmm [2+[4,4,2,∞]] (139) I4/mmm [4,(4,2)+,∞] (140) I4/mcm [4,4,2+,∞] [(4,4)+,2+,∞] [4,4,2+,∞+] [(4,4)+,2+,∞+] [4+,4+,2+,∞] [4,4+,2,∞] [4,4+,2+,∞] [((4,2+,4)),2,∞] [4,4+,2,∞+] [4,4+,2+,∞+] [((4,2+,4)),2,∞+]

Trigonal (143-167), rhombohedral Coxeter Space group Hexagonal (168-194) File:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 6.pngFile:CDel node.pngFile:CDel 2.pngFile:CDel node.pngFile:CDel infin.pngFile:CDel node.png [(6,3)+,2,∞+] (168) P6 [(6,3)+,2,∞] (175) P6/m [6,3,2,∞]+ (177) P622 [6,3,2,∞+] (183) P6mm [6,3,2,∞] (191) P6/mmm [(3[3])+,2,∞+] [3[3],2,∞] [6,3+,2,∞] [6,3+,2,∞+] [3[3],2,∞]+ [3[3],2,∞+] [(3[3])+,2,∞]

Cubic (195-230) Group Coxeter Space group Index [[4,3,4]] [[4,3,4]] (229) ImTemplate:Overlinem 1 [[4,3,4]]+ (211) I432 2 [[4,3,4]+] (223) PmTemplate:Overlinen 2 [[4,3+,4]] (204) ITemplate:Overline 2 [[(4,3,4,2+)]] (217) ITemplate:Overline3m 2 [[4,3+,4]]+ (197) I23 4 [[4,3,4]+]+ (208) P4232 4 [[4,3+,4)]+] (201) PnTemplate:Overline3 4 [[(4,3,4,2+)]+] (218) PTemplate:Overline3n 4 [4,3,4] File:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node.png [4,3,4] (221) PmTemplate:Overlinem 2 [4,3,4]+ (207) P432 4 [4,3+,4] (200) PmTemplate:Overline 4 [4,(3,4)+] (226) FmTemplate:Overlinec 4 [(4,3,4,2+)] (215) PTemplate:Overline3m 4 [[{4,(3}+,4)+]] (228) FdTemplate:Overlinec 4 [4,3+,4]+ (195) P23 8 [{4,(3}+,4)+] (219) FTemplate:Overline3c 8 [4,31,1] File:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes.png File:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node h0.png [4,31,1] (225) FmTemplate:Overlinem 4 [4,(31,1)+] (202) FmTemplate:Overline 8 [4,31,1]+ (209) F432 8 [[3[4]]] File:CDel branch.pngFile:CDel 3ab.pngFile:CDel branch.png [(4+,2+)[3[4]]] (222) PnTemplate:Overlinen 2 [[3[4]]] (227) FdTemplate:Overlinem 4 [[3[4]]]+ (203) FdTemplate:Overline 8 [[3[4]]+] (210) F4132 8 [3[4]] File:CDel branch.pngFile:CDel 3ab.pngFile:CDel branch.png File:CDel node h0.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node h0.png [3[4]] (216) FTemplate:Overline3m 8 [3[4]]+ (196) F23 16