In geometry, a cell is a three-dimensional element that is part of a higher-dimensional object.
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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.
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
- Olshevsky, George, Cell at Glossary for Hyperspace.
- Weisstein, Eric W., "Cell" from MathWorld. (An incorrect definition: a finite regular polytope)
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