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facet$27150$ - translation to greek
FEATURE OF A POLYTOPE IN THE NEXT-LOWER DIMENSION
Facet (mathematics)
facet
n. πλευρά αδαμάντος, όψη, όψη προβλήματος
Definition
Facet
·noun The narrow plane surface between flutings of a column.
II. Facet ·vt To cut facets or small faces upon; as, to facet a diamond.
III. Facet ·noun A smooth circumscribed surface; as, the articular facet of a bone.
IV. Facet ·noun A little face; a small, plane surface; as, the facets of a diamond.
V. Facet ·noun One of the numerous small eyes which make up the compound eyes of insects and crustaceans.
Wikipedia
Facet (geometry)
In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself. More specifically:
- 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 face that has dimension n − 1 (an (n − 1)-face or hyperface) is also called a facet.
- 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.
