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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[edit | edit source]

Elements have special names based on their dimensionality.

Rank Name
0 Vertex
1 Edge
2 Face
3 Cell
4 Teron
5 Peton
6 Exon
7 Zetton
8 Yotton
9 Xennon
n–4 Spire
n–3 Peak
n–2 Ridge
n–1 Facet