Pyritohedral symmetry

A3+×2, also known as pyritic symmetry or pyritohedral symmetry, is a 3D spherical Coxeter group. It is the symmetry group of the pyritohedral icosahedron and its dual pyritohedron. It is similar to cubic symmetry, but the square axes turn into rectangular axes and the triangular axes turn into chiral triangular ones..

Subgroups

 * A3+ (maximal)
 * (G2+×A1)/2 (maximal)
 * A2+×I
 * K3 (maximal)
 * K3+
 * K2×I
 * K2+×A1
 * K2+×I
 * ±(I×I×I) (maximal)
 * A1×I×I
 * I×I×I

Convex polytopes with A3+×2 symmetry

 * Cube (regular)/Octahedron (regular)
 * Cuboctahedron (isogonal)/Rhombic dodecahedron (isotopic)
 * Truncated cube (isogonal)/Triakis octahedron (isotopic)
 * Pyritohedral icosahedron (isogonal)/Pyritohedron (isotopic)
 * Pyritosnub cube (isogonal)/Tetragonal icositetrahedron (isotopic)