Orbiform

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

In 3D
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
If an orbiform polytope has a circumradius of less than its edge length, its pyramid is also orbiform.