From: Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry
Schoenflies | Orbifold | Order | Comments |
---|---|---|---|
C_{ n } | nn | n | Rotational symmetry of order n |
C_{nv} | *nn | 2n | Rotational symmetry of order n and reflection symmetry about n planes containing the rotation axis |
C_{nh} | n* | 2n | Rotational symmetry of order n and reflection symmetry about a plane perpendicular to the rotation axis |
S_{2n} | n× | 2n | Rotational symmetry of order 2n in which odd-numbered elements are reflected about a plane perpendicular to the rotation axis |
D_{ n } | 22n | 2n | Dihedral symmetry: rotational symmetry of order n combined with rotational symmetry of order 2 about axes that are perpendicular to the first rotation axis |
D_{nd} | 2*n | 2n | Antiprismatic symmetry: Rotation symmetry of order n and reflection symmetry about n planes containing the rotation axis, as well as rotation symmetry of order 2 about a perpendicular axis in each of the resulting sectors |
D_{nh} | *22n | 4n | Prismatic symmetry: rotational symmetry of order n and reflection symmetries about planes n passing through the rotation axis as well as the plane perpendicular to it. |
T | 332 | 12 | Tetrahedral symmetry, rotations only |
T_{d} | *332 | 24 | Complete tetrahedral symmetry, including reflection |
T_{h} | 3*2 | 24 | Pyritohedral symmetry |
O | 432 | 24 | Octahedral symmetry, rotations only (also applies to cube) |
O_{h} | *432 | 48 | Complete octahedral symmetry, icluding reflection (also applies to cube) |
I | 532 | 60 | Icosahedral symmetry, rotations only |
I_{h} | *532 | 120 | Complete icosahedral symmetry, including reflection |