Polytope

Summary

A polytope is a geometric figure with flat sides: a polygon in the plane, a polyhedron in space, and their analogues in any dimension. The word is used with several meanings. In convex geometry and combinatorics it usually means a convex polytope. In the wider sense used here, a polytope is a finite union of convex polytopes, so it may be non-convex. Further generalizations include star polytopes, whose faces may cross each other, and abstract polytopes, which keep only the incidence pattern of vertices, edges and faces.