Pyritohedral symmetry

Pyritohedral symmetry
Rank	3
Space	Spherical
Order	24
Elements
Axes	3 × K3, 4 × (G2+×A1)/2

Pyritohedral symmetry, also known as pyritic symmetry and notated as B₃/2, is a 3D spherical symmetry 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. Unlike full cubic or tetrahedral symmetries, it is a subgroup of dodecahedral symmetry.

Subgroups

• Chiral tetrahedral symmetry (maximal)
• Protriangular antiprismatic symmetry (maximal)
• Chiral triangular prismatic symmetry
• Digonal prismatic symmetry (maximal)
• Chiral digonal prismatic symmetry
• Rectangular pyramidal symmetry
• Prodigonal prismatic symmetry
• Chiral digonal pyramidal symmetry
• Inversion symmetry
• Reflection symmetry
• Identity symmetry

Convex polytopes with B₃/2 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)