Uniform polytope

A uniform polytope is an isogonal polytope that can be represented with only one edge length and whose elements are also uniform geometrically. Regular polytopes are also uniform polytopes. Most uniform polytopes can be derived from a Wythoffian construction, but there are some uniform polytopes, such as the grand antiprism, that are not Wythoffian-constructible. Infinite sets of uniform polytopes can be created from the Cartesian product of two uniform polytopes, with one either being a regular polygon or a line, in which case the latter results in the prism of the other polytope.

Besides the infinite sets mentioned above, there are an infinite number of uniform polytopes in 2D (the regular polygons), 75 in 3D, and atleast 1849 in 4D. It is not known how many uniform polytopes are there in 5D and above.