Facet (geometry)
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In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.
- In three-dimensional geometry a facet of a polyhedron is any polygon whose corners are vertices of the polyhedron, and is not a face.[1][2]To facet a polyhedron is to find and join such facets to form the faces of a new polyhedron; this is the reciprocal process to stellation and may also be applied to higher-dimensional polytopes.[3]
- In polyhedral combinatorics and in the general theory of polytopes, a facet of a polytope of dimension n is a face that has dimension n − 1. Facets may also be called (n − 1)-faces. In three-dimensional geometry, they are often called "faces" without qualification.[4]
- A facet of a simplicial complex is a maximal simplex, that is a simplex that is not a face of another simplex of the complex.[5] For simplicial polytopes this coincides with the meaning from polyhedral combinatorics.
References
- ↑ Bridge, N.J. Facetting the dodecahedron, Acta crystallographica A30 (1974), pp. 548–552.
- ↑ Inchbald, G. Facetting diagrams, The mathematical gazette, 90 (2006), pp. 253–261.
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External links
- Weisstein, Eric W., "Facet", MathWorld.
- Olshevsky, George, Facet at Glossary for Hyperspace.
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