Convex and discrete geometry Polytopes and polyhedra Concept
Facet
Summary
A facet of a convex polytope is a face of the largest possible dimension below that of the polytope itself. A polytope of dimension has facets of dimension . The facets determine the polytope: a full-dimensional polytope is the intersection of the closed half-spaces bounded by the hyperplanes of its facets. Counting facets and studying their shapes is a central theme of polytope combinatorics.
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| Tag | DPDXN2FJC4 |
|---|---|
| URI | m2://DPDXN2FJC4 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 52B05, 52B11 |
| Specializes | Face of a convex set |
| Same as |
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Used by
- Cross-polytope
- Simplicial polytope
- Birkhoff polytope
- Schlegel diagram
- Associahedron
- Hypercube
- Simple polytope
- Uniform polytope
- Permutohedron
- Cyclic polytope
- Schläfli symbol
- Hirsch conjecture