noun - An n-dimensional solid, bounded by (n-1) dimensional solids. This includes polygons in planespace, polyhedra in realmspace, polychora in tetraspace, and polytera in pentaspace.

a bounded polyhedron

a generalization of the idea of a polygon or polyhedra to any number of spatial dimensions

a set of mathematical equations that bounds a region of feasible solutions

A bounding volume defined by a closed intersection of half-spaces.

In geometry polytope means, first, the generalization to any dimension of polygon in two dimensions, polyhedron in three dimensions, and polychoron in four dimensions. Beyond that, the term is used for a variety of related mathematical concepts. This is analogous to the way the term square may be used to refer to a square-shaped region of the plane, or just to its boundary, or even to a mere list of its vertices and edges along with some information about the way they are connected.