Planarity

A polytope of rank n is planar if its vertices lie in n-dimensional Euclidean space and the vertices of each proper element of rank r lie in an r-dimensional affine subspace. It is a common condition imposed on polytopes realized in Euclidean space.

Planarity assists with ensuring that polytopes have defined interiors (although it does not guarantee it, see filling method), and presents one way for polytope definitions to "recurse" so that proper elements are themselves valid polytopes. Planarity is part of typical definitions of regular, uniform, and CRF polytopes.

One definition of a skew polytope is simply any polytope realized in Euclidean space which is not planar.