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.

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