Symmetry group (InstanceClass, 3)
From Hi.gher. Space
WIP
Three dimensions
The following table contains all the symmetry groups used by CRF polyhedra. The order of each group is given after an asterisk:
| n = | 2 | 3 | 4 | 5 |
|---|---|---|---|---|
special | Cs *2 Plane | |||
| Cn *n Chiral axial | C5 *5 Chiral rhodoaxial | |||
| Cnv *2n Axial | C2v *4 Biaxial (biplane) | C3v *6 Pyroaxial | C4v *8 Stauroaxial | C5v *10 Rhodoaxial |
| Dn *2n Chiral antiprismatic | D3 *6 Chiral pyroantiprismatic | D4 *8 Chiral stauroantiprismatic | D5 *10 Chiral rhodoantiprismatic | |
| Dnd *4n Antiprismatic | D2d *8 Biantiprismatic | D3d *12 Pyroantiprismatic | D4d *16 Stauroantiprismatic | D5d *20 Rhodoantiprismatic |
| Dnh *4n Prismatic | D2h *8 Biprismatic (triplane, brick) | D3h *12 Pyroprismatic | D4h *16 Stauroprismatic | D5h *20 Rhodoprismatic |
Chiral polyhedral | O *24 Chiral staurohedral | I *60 Chiral rhodohedral | ||
Polyhedral | Td *24 Pyrohedral | Oh *48 Staurohedral | Ih *120 Rhodohedral |
There are five more 3D symmetry groups, which are not seen in CRF polyhedra:
- C1 *1 (asymmetry)
- Cnh *2n (cyclic prismatic symmetry)
- Sn *n (for even n only) (S2 being point symmetry)
- T *12 (chiral pyrohedral symmetry)
- Th *24 (pyritohedral symmetry).
