In geometry, a hypercell is a descriptive term for an element of a polytope or tessellation, usually representing an element one dimension higher than a cell. The most generally accepted term is 4-face because it contains a 4-dimensional interior. Another proposed name in use is teron, shortened from tetron, constructed from the prefix tetra meaning four.

A 5-dimensional polytope or 4-dimensional tessellation can be considered constructed of 4-dimensional hypercells, 3-dimensional cells, 2-dimensional faces, 1-dimensional edges, and 0-dimensional vertices.

For example the 5-dimensional penteract (5-hypercube) is constructed from 10 tesseractic hypercells. Also the 4-dimensional tesseractic honeycomb is constructed from tesseract hypercells. In the context of these figures, hypercells can also be called facets representing the highest dimensional elements of the figures.

See also

* Face (geometry)

* 5-polytope

* List of regular polytopes

Links

* Eric W. Weisstein, Facet at MathWorld.

* Olshevsky, George, Facet at Glossary for Hyperspace.

Geometry