# polytope

A polytope is a higher-dimensional analogue of a polygon or polyhedron. The number of possible
regular polytopes depends on the number of dimensions. In two dimensions
there are infinitely many possible regular polygons; in three dimensions
there are five possible regular polyhedra; in four dimensions there are
six possible regular polytopes; and in each number of dimensions higher
than four, there are just three possible regular polytopes, analogous to
the three-dimensional tetrahedron, cube, and octahedron. A four-dimensional
polytope is also sometimes called a **polyhedroid** or a **polychoron**.
Just as a polygon has vertices and edges, and a polyhedron has vertices,
edges, and faces, a four-dimensional polytope has vertices, edges, faces,
and *cells*, where a cell is a three-dimensional figure.

### reference

1. Coxeter, H. S. M. *Regular Polytopes*, 3rd ed. New York: Dover
Publications, 1973.