Facet (mathematics) | Wikipedia audio article
Channel: wikipedia tts
Date: 07/10/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Facet_(geometry)





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SUMMARY
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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. 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.
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.
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. For (boundary complexes of) simplicial polytopes this coincides with the meaning from polyhedral combinatorics.