Cell (geometry)

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

In polytopes

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.

See 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

• (An incorrect definition: a finite regular polytope)