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)
  
| 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)
| 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)
 
| [(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) Im3m |
1
|
| [[4,3,4]]+ |
(211) I432 |
2
|
| [[4,3,4]+ |
(223) Pm3n |
2
|
| [[4,3+,4]] |
(204) I3 |
2
|
| [[(4,3,4,2+)]] |
(217) I43m |
2
|
| [[4,3+,4]]+ |
(197) I23 |
4
|
| [[4,3,4]++ |
(208) P4232 |
4
|
| [[4,3+,4)]+ |
(201) Pn43 |
4
|
| [[(4,3,4,2+)]+ |
(218) P43n |
4
|
[4,3,4]
|
[4,3,4] |
(221) Pm3m |
2
|
| [4,3,4]+ |
(207) P432 |
4
|
| [4,3+,4] |
(200) Pm3 |
4
|
| [4,(3,4)+ |
(226) Fm3c |
4
|
| [(4,3,4,2+)] |
(215) P43m |
4
|
| [[{4,(3}+,4)+]] |
(228) Fd3c |
4
|
| [4,3+,4]+ |
(195) P23 |
8
|
| [{4,(3}+,4)+ |
(219) F43c |
8
|
[4,31,1
 
|
[4,31,1 |
(225) Fm3m |
4
|
| [4,(31,1)+ |
(202) Fm3 |
8
|
| [4,31,1+ |
(209) F432 |
8
|
[[3[4]]]
 
|
| [(4+,2+)[3[4]]] |
(222) Pn3n |
2
|
| [[3[4]]] |
(227) Fd3m |
4
|
| [[3[4]]]+ |
(203) Fd3 |
8
|
| [[3[4]+ |
(210) F4132 |
8
|
[3[4]
|
[3[4] |
(216) F43m |
8
|
| [3[4]+ |
(196) F23 |
16
|
|