## polytopeA 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- Coxeter, H. S. M.
*Regular Polytopes*, 3rd ed. New York: Dover Publications, 1973.
## Related entry• Boole (Stott), Alicia## Related categories• GEOMETRY• SPACE AND TIME | |||||

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