Trivial group

The trivial group also known as the zero group, is the simplest possible group. It contains 1 element, its identity. Polytopes whose symmetry group are isomorphic to the trivial group are called asymmetrical.

Symmetries Isomorphic to the trivial group

 * Pointic symmetry
 * I
 * I×I
 * I×I×I
 * I×I×I×I

Notable asymmetrical polytopes
Most classes of polytopes that are objects of study (regular, uniform, noble, etc.) are symmetrical.

Asymmetrical polyhedra with all regular faces are believed to have a minimum possible face count of 9. An example is a square prism blended with a pentagonal prism.

All Johnson solids are symmetrical, but there are asymmetrical Blind polytopes, all of which are special cuts of the hexacosichoron.