Cubic symmetry

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Cubic symmetry
Rank3
SpaceSpherical
Order48
Info
Coxeter diagram
Centrally symmetricYes
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.

Subgroups[edit | edit source]

Convex polytopes with B3 symmetry[edit | edit source]

Wythoffians with B3 symmetry[edit | edit source]

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 ()