Cell (geometry)

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Cubic honeycomb - four cubic cells per edge

hypercube - three cubic cells per edge

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

[edit] 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 hypercube is also made of cubic cells, but only has 3 cubes on each edge.

Faces are the two-dimensional element analogue of cells for polyhedra and planar tilings.

Cells can be called facets as the highest dimensional subelements in a 4-polytope or 3-space tessellation, and 3-faces more systematically.

Sometimes four-dimensional elements (5-polytopes and higher) are called hypercells, or more clearly 4-faces. Systematically n-faces are elements in (n+1)-polytopes and higher.