Scaliform polytope

A scaliform polytope is an isogonal polytope in four dimensions or greater that can be represented with only one edge length, without the consideration that the elements themselves are uniform. The elements of a scaliform polytope are all orbiform, however, so only Johnson solids that have a circumscribed sphere are valid cells. Infinite sets of scaliform polytopes can be created from the Cartesian product of a scaliform polytope and either a regular polygon or a 3D antiprism.

In 4D, there are only four convex scaliform polytopes: the truncated tetrahedral cupoliprism, the bi-icositetradiminished hexacosichoron, the prismatorhombisnub icositetrachoron, and the swirlprismatodiminished rectified hexacosichoron. In 5D, the duoantiwedges form an infinite family of scaliform polytera.