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