A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the -dimensional Euclidean space .

+ Regular polytope examples160pxA regular pentagon is a polygon, a two-dimensional polytope with 5 edges, represented by Schläfli symbol 160pxA regular dodecahedron is a polyhedron, a three-dimensional polytope, with 12 pentagonal faces, represented by Schläfli symbol 160pxA

The polyhedral model (also called the polytope method) is a mathematical framework for programs that perform large numbers of operations -- too large to be explicitly enumerated -- thereby requiring a compact representation.

In mathematics, the Newton polytope is an integral polytope associated with a multivariate polynomial.

In mathematics, a cyclic polytope, denoted C(n, d), is a convex polytope formed as a convex hull of n distinct points on a rational normal curve in Rd, where n is greater than d.