Tetrahedral symmetry
(Redirected from A3)
| Tetrahedral symmetry | |
|---|---|
 | |
| Rank | 3 |
| Space | Spherical |
| Order | 24 |
| Info | |
| Coxeter diagram |   |
| Centrally symmetric | No |
| Elements | |
| Axes | 3 × (BC2×A1)/2, 4 × A2×I |
| Related polytopes | |
| Omnitruncate | Great rhombitetratetrahedron |
Tetrahedral symmetry, also known as tettic symmetry and notated A3, is a 3D spherical Coxeter group. It is the symmetry group of the regular tetrahedron.
Subgroups[edit | edit source]
- Chiral tetrahedral symmetry (maximal)
- Triangular pyramidal symmetry (maximal)
- Chiral triangular pyramidal symmetry
- Digonal antiprismatic symmetry (maximal)
- Prodigonal antiprismatic symmetry
- Chiral digonal prismatic symmetry
- Rectangular pyramidal symmetry
- Chiral digonal pyramidal symmetry
- Reflection symmetry
- Identity symmetry
Convex polytopes with A3 symmetry[edit | edit source]
- Tetrahedron (regular)
- Tetratetrahedron (isogonal)/Rhombic hexahedron (isotopic)
- Truncated tetrahedron (isogonal)/Triakis tetrahedron (isotopic)
- Rhombitetratetrahedron (isogonal)/Deltoidal dodecahedron (isotopic)
- Great rhombitetratetrahedron (isogonal)/Disdyakis hexahedron (isotopic)
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Tetrahedron | tet | {3,3} |  |  |
| Rectified tetrahedron = Octahedron | oct | r{3,3} | |  |
| Tetrahedron | tet | {3,3} | |  |
| Truncated tetrahedron | tut | t{3,3} | |  |
| Small rhombitetratetrahedron = Cuboctahedron | co | rr{3,3} | |  |
| Truncated tetrahedron | tut | t{3,3} | |  |
| Great rhombitetratetrahedron = Truncated octahedron | toe | tr{3,3} | |  |
| Snub tetrahedron = Icosahedron | ike | sr{3,3} |  |  |