Hypercell

Hypercell

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.

ee also

*Face (geometry)
*5-polytope
*List of regular polytopes

References

External links

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