Trivial blends[edit | edit source]
A blend is considered trivial if the result is one of the arguments. For example, any polytope 𝓟 is the result of the blend , 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[edit | edit source]
- 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[edit | edit source]
- 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".