polytope
Noun
Meaning
polytope (plural polytopes)
(geometry) A finite region of n-dimensional space bounded by hyperplanes (a geometric shape with flat sides, existing in any number of dimensions); the geometrical entity represented by the general term of the infinite sequence "point, line, polygon, polyhedron, ...".
Related terms
Phrases with the word
Examples
A polytope is finite if it is defined in terms of a finite number of objects, e.g., as an intersection of a finite number of half-planes.
A similar result holds for the number of vertices (of the Gaussian polytope), the number of edges, and in fact, faces of all dimensions.
Depending on circumstance, the dual figure may or may not be another geometric polytope.
Every bounded nonempty polytope is pointed.
A polytope is said to be pointed if it contains at least one vertex.
Approaches to definition The term polytope is nowadays a broad term that covers a wide class of objects, and different definitions are attested in mathematical literature.