Seonglae ChoA polytope is a geometric shape that extends polygons and polyhedra into arbitrary dimensions. An n-dimensional polytope is defined in n dimensions. For example, a polygon is a 2-dimensional polytope, a polyhedron is a 3-dimensional polytope, and a polychoron is a 4-dimensional polytope.
Polytopes
Polytope Notion
Polytope
In elementary geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any number of dimensions. Polytopes 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. In this context, "flat sides" means that the sides of a (k + 1)-polytope consist of k-polytopes that may have (k – 1)-polytopes in common.
https://en.wikipedia.org/wiki/Polytope