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A polytope is orbiform if all its edges are of equal length and it can be inscribed in a hypersphere.[1] All uniform polytopes are orbiform.

In 3D[edit | edit source]

The orbiform polygons are simply the regular polygons, but in 3D there are many non-uniform orbiform polytopes. Examples include the square and pentagonal pyramids, the cupolae, the cuploids, and cupolaic blends.

All faces of orbiform polyhedra are regular, and thus the orbiform polyhedra are a subset of the acrohedra. Indeed, some polyhedra specifically discovered in the search for acrohedra turned out to be orbiform, such as the polyhedra produced by Green's rules.

Properties[edit | edit source]

If an orbiform polytope has a circumradius of less than its edge length, its pyramid is also orbiform.