# Facet (mathematics)

﻿
Facet (mathematics)

A facet of a simplicial complex is a maximal simplex.

In the general theory of polyhedra and polytopes, two conflicting meanings are currently jostling for acceptability:

*A facet of a geometric polyhedron is traditionally any polygon whose corners are vertices of the polyhedron. By extension to higher dimensions, it is any "j"-tope ("j"-dimensional polytope) whose vertices are shared by some "n"-tope ("n"-dimensional polytope where 0<"j"<"n"). To facet a polytope is to find and join such facets to form a new polytope - this process is called facetting or faceting and is the reciprocal process to stellation.
*A facet of an "n-polytope" is, more recently, an ("n"-1)-dimensional face or ("n"-1)-face. The informal term side can mean the same thing, edges of a polygon and faces of a polyhedron.
*:For example:
*:#The facets of a polygon are edges. (1-faces)
*:#The facets of a polyhedron or tiling are faces. (2-faces)
*:#The facets of a polychoron (4-polytope) or honeycomb are cells. (3-faces)
*:#The facets of a polyteron (5-polytope) or 4-honeycomb are hypercells. (4-faces)
*:Exactly two facets meet at any ridge in a polytope. By extension, facet or "j"-facet is sometimes used to mean any "j"-dimensional element of a polytope.

*
*
*

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Facet (disambiguation) — Facet may have the following meanings. * Facet, a flat surface of a geometric shape, e.g., of a gemstone. * Facet in mathematics (topology, geometry) is a special type of face. * In anatomy::* A facet is part of a compound eye.:* A facet joint is …   Wikipedia

• List of mathematics articles (F) — NOTOC F F₄ F algebra F coalgebra F distribution F divergence Fσ set F space F test F theory F. and M. Riesz theorem F1 Score Faà di Bruno s formula Face (geometry) Face configuration Face diagonal Facet (mathematics) Facetting… …   Wikipedia

• Science and mathematics from the Renaissance to Descartes — George Molland Early in the nineteenth century John Playfair wrote for the Encyclopaedia Britannica a long article entitled ‘Dissertation; exhibiting a General View of the Progress of Mathematics and Physical Science, since the Revival of Letters …   History of philosophy

• Interval (mathematics) — This article is about intervals of real numbers. For intervals in general mathematics, see Partially ordered set. For other uses, see Interval. In mathematics, a (real) interval is a set of real numbers with the property that any number that lies …   Wikipedia

• Перестановочный многогранник — …   Википедия

• N-dimensional space — In mathematics, an n dimensional space is a topological space whose dimension is n (where n is a fixed natural number). The archetypical example is n dimensional Euclidean space, which describes Euclidean geometry in n dimensions.Many familiar… …   Wikipedia

• Colon classification — (CC) is a system of library classification developed by S. R. Ranganathan. It was the first ever faceted (or analytico synthetic) classification. The first edition was published in 1933. Since then six more editions have been published. It is… …   Wikipedia

• Convex polytope — A 3 dimensional convex polytope A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n dimensional space Rn.[1] Some authors use the terms convex polytope and convex… …   Wikipedia

• Necessary and sufficient condition — This article is about the formal terminology in logic. For causal meanings of the terms, see Causality. In logic, the words necessity and sufficiency refer to the implicational relationships between statements. The assertion that one statement is …   Wikipedia

• Robert Haralick — Robert M. Haralick was born in Brooklyn, New York, on September 30, 1943. He received a B.A. degree in mathematics from the University of Kansas in 1964, a B.S. degree in electrical engineering in 1966, and a M.S. degree in electrical engineering …   Wikipedia