Wiktionary
n. (context geometry English) A finite region of ''n''-dimensional space bounded by hyperplanes; the geometrical entity represented by the general term of the infinite sequence "point, line, polygon, polyhedron, ...".
Wikipedia
In elementary geometry, a polytope is a geometric object with flat sides, and may exist in any general number of dimensions n as an n-dimensional polytope or n-polytope. For example, a two-dimensional polygon is a 2-polytope and a three-dimensional polyhedron is a 3-polytope.
Some theories further generalize the idea to include such objects as unbounded ( apeirotopes and tessellations), decompositions or tilings of curved manifolds such as spherical polyhedra, and set-theoretic abstract polytopes.
Polytopes in more than three dimensions were first discovered by Ludwig Schläfli. The German term "polytop" was coined by the mathematician Reinhold Hoppe, and was introduced to English mathematicians as polytope by Alicia Boole Stott.
Usage examples of "polytope".
The point is, all the corresponding forms on the right should be the shadows of the same polytopes after a simple rotation through higher-dimensional space.
The cube was undoubtedly chosen because it is one of the three regular polytopes possible in N-dimensional space when N is greater than five.