Identity symmetry (3D)

Three-dimensional identity symmetry, also known as monic symmetry and notated as I×I×I, is a 3D spherical symmetry group. It is the symmetry group of the irregular tetrahedron and is equivalent to the identity group which has no symmetry. It therefore appears as a subgroup of any polyhedral symmetry.

Asymmetrical polyhedra with all regular faces are believed to have a minimum possible face count of 9. Examples include a square prism blended with a pentagonal prism, and a triangular tegum blended with a square prism (to prevent coplanar faces, the square prism can be mirrored to form a self-intersecting polyhedron). All Johnson solids happen to be symmetrical.