A Polytope is an n-dimensional generalization of the 3-dimensional polyhedron. In essence, it is any geometric object with flat sides. Since polytopes can exist in any dimension, they can be labeled as n-polytopes, with n being the dimension they're in.
In certain fields of mathematics, the terms "polytope" and "polyhedron" are used in a different sense: polyhedron refers to a generic object in any dimension, whilst a polytope means a bounded polyhedron.
| Dimension | Name |
|---|---|
| -1 | Nullitope (used in abstract theory) |
| 0 | Monon (point) |
| 1 | Dion (line segment) |
| 2 | Polygon |
| 3 | Polyhedron |
| 4 | Polychoron |