Purity

A skew polytope is pure if it cannot be expressed as the blend of two polytopes in a non-trivial way.

Trivial blends
A blend is considered trivial if the result is one of the arguments. For example any polytope is the result of the blend $$\mathcal{P}\#\mathcal{P}$$, thus this blend is trivial. Similarly any polytope is a blend of itself with the point.

A non-trivial blend is simply any blend that isn't trivial.

Examples

 * The mucube is a pure apeirohedron.
 * The square duocomb is pure.
 * The Petrial tetrahedron is pure.
 * The blended square tiling is not pure, because it is the blend of the square tiling and a digon.

Properties

 * There are no regular pure polygons. Any regular polygon is either planar or a non-trivial blend.
 * All the regular pure polyhedra in 3-dimensional Euclidean space are, either the Petrial of a non-skew regular polyhedron or an apeirohedron. They are collectively refered to as the "pure apeirohedra".