Cubic symmetry

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

 * 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
 * Bilateral symmetry
 * Identity symmetry

Convex polytopes with B3 symmetry

 * 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)