# Circumscribable polytope

(Redirected from Circumradius)

A polytope is said to be **circumscribable** when all of its vertices are at a common distance from a point. This point is known as the **circumcenter**, and the distance is known as the **circumradius**. In Euclidean space, all points at the circumradius' distance from the circumcenter define a hypersphere, known as the **circumsphere** (of the polytope.

Every finite isogonal polytope in Euclidean space is circumscribable, its center being the unique fixed point of its symmetry group. Orbiform polytopes provide a further class of circumscribable polytopes. The dual of a circumscribable polytope is inscribable.

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