# Cubic symmetry

(Redirected from B3)
Cubic symmetry Rank3
SpaceSpherical
Order48
Info
Coxeter diagram     Elements
Axes3 × BC2×A1, 4 × (G2×A1)/2, 6 × K3
Related polytopes
OmnitruncateGreat rhombicuboctahedron

Cubic symmetry, also known as octahedral symmetry and notated B3 or BC3, is a 3D spherical Coxeter group. It is the symmetry group of the cube and octahedron.

## Wythoffians with B3 symmetry

o4/3o3o truncations
Name OBSA Schläfli symbol CD diagram Picture
Cube cube {4/3,3} x4/3o3o (       )
Quasitruncated hexahedron quith t{4/3,3} x4/3x3o (       )
Cuboctahedron co r{3,4/3} o4/3x3o (       )
Truncated octahedron toe t{3,4/3} o4/3x3x (       )
Octahedron oct {3,4/3} o4/3o3x (       )
Quasirhombicuboctahedron querco rr{3,4/3} x4/3o3x (       )
Quasitruncated cuboctahedron quitco tr{3,4/3} x4/3x3x (       )
(degenerate, oct+6(4)) o4/3o3ß (       )
Icosahedron ike s{3,4/3} o4/3s3s (       )
o4/3o3o4*a truncations
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 (   )