Cubic symmetry
(Redirected from B3)
Cubic symmetry | |
---|---|
Rank | 3 |
Space | Spherical |
Order | 48 |
Info | |
Coxeter diagram | |
Centrally symmetric | Yes |
Elements | |
Axes | 3 × BC_{2}×A_{1}, 4 × (G_{2}×A_{1})/2, 6 × K_{3} |
Related polytopes | |
Omnitruncate | Great rhombicuboctahedron |
Cubic symmetry, also known as octahedral symmetry and notated B_{3} or BC_{3}, is a 3D spherical Coxeter group. It is the symmetry group of the cube and octahedron.
Subgroups[edit | edit source]
- Pyritohedral symmetry (maximal)
- Chiral cubic symmetry (maximal)
- Tetrahedral symmetry (maximal)
- Chiral tetrahedral symmetry
- Square prismatic symmetry (maximal)
- Chiral square prismatic symmetry
- Prosquare prismatic symmetry
- Square pyramidal symmetry
- Chiral square pyramidal symmetry
- Triangular antiprismatic symmetry (maximal)
- Protriangular antiprismatic symmetry
- Chiral triangular prismatic symmetry
- Triangular pyramidal symmetry
- Chiral triangular pyramidal symmetry
- Digonal prismatic symmetry
- Chiral digonal prismatic symmetry
- Prodigonal prismatic symmetry
- Digonal antiprismatic symmetry
- Prodigonal antiprismatic symmetry
- Rectangular pyramidal symmetry
- Chiral digonal pyramidal symmetry
- Inversion symmetry
- Reflection symmetry
- Identity symmetry
Convex polytopes with B_{3} symmetry[edit | edit source]
- Cube (regular)/Octahedron (regular)
- Cuboctahedron (isogonal)/Rhombic dodecahedron (isotopic)
- Truncated cube (isogonal)/Triakis octahedron (isotopic)
- Truncated octahedron (isogonal)/Tetrakis hexahedron (isotopic)
- Small rhombicuboctahedron (isogonal)/Deltoidal icositetrahedron (isotopic)
- Great rhombicuboctahedron (isogonal)/Disdyakis dodecahedron (isotopic)
Wythoffians with B_{3} symmetry[edit | edit source]
Name | OBSA | CD diagram | Picture |
---|---|---|---|
(degenerate, double cover of cube) | x4/3o3o4*a () | ||
Great cubicuboctahedron | gocco | x4/3x3o4*a () | |
(degenerate, oct+6(4)) | o4/3x3o4*a () | ||
(degenerate, double cover of cho) | o4/3x3x4*a () | ||
(degenerate, oct+6(4)) | o4/3o3x4*a () | ||
Small cubicuboctahedron | socco | x4/3o3x4*a () | |
Cuboctatruncated cuboctahedron | cotco | x4/3x3x4*a () |