Element

An element of a polytope P is a polytope belonging to P. It is ambiguous whether P itself counts as an element.

A pseudoelement of a polytope P is a polytope whose lower-dimensional elements are all elements of P, but which is not an element of P. For example, the octahedron has three pseudo-squares, while the tetrahemihexahedron (which has the same edges) has the same squares as faces. However, four of the octahedron's faces are pseudo-faces of the tetrahemihexahedron.

Naming
Elements have special names based on their dimensionality.