In elementary geometry, a polytope is a geometric object with flat sides, which exists in any general number of dimensions. A polygon is a polytope in two dimensions, a polyhedron in three dimensions, and so on in higher dimensions (such as a polychoron in four dimensions). Some theories further generalize the idea to include such things as unbounded polytopes (apeirotopes and tessellations), and abstract polytopes.
When referring to an n-dimensional generalization, the term n-polytope is used. For example, a polygon is a 2-polytope, a polyhedron is a 3-polytope, and a polychoron is a 4-polytope.
The term was coined by the mathematician Hoppe, writing in German, and was later introduced to the English Mathematicians by Alicia Boole Stott, the daughter of logician George Boole.