Cell (geometry)

In geometry, a cell is a three-dimensional element that is part of a higher-dimensional object.

In polytopes

A cell is a three-dimensional polyhedron element that is part of the boundary of a higher-dimensional polytope, such as a polychoron (4-polytope) or honeycomb (3-space tessellation).

For example, a cubic honeycomb is made of cubic cells, with 4 cubes on each edge. A tesseract is also made of cubic cells, but only has 3 cubes on each edge.

In polychoron names

Regular convex polychora are sometimes named by how many cells they contain, just like "n"-gon and "n"-hedron are used as a shorthand for polygonal and polyhedral names. For example, the tesseract can also be called an "octachoron" or an 8-cell because it contains 8 cubic cells.

ee also

*Face (geometry) - the two-dimensional element analogue of cells for polyhedra and planar tilings.
* Facet (geometry) as the highest dimensional subelements in a 4-polytope or 3-space tessellation, and "3-faces" more systematically.
* Hypercells, or more clearly "4-faces", are four-dimensional elements (5-polytopes and higher). Systematically "n-faces" are elements in "(n+1)-polytopes" and higher.
*Cell complex

External links

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* (An incorrect definition: "a finite regular polytope")