Uniform dual polytope

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The rhombic dodecahedron is the dual of cuboctahedron, a uniform polyhedron.

A uniform dual polytope is a polytope whose dual is uniform. Since uniform polytopes are isogonal, uniform dual polytopes are isotopic.

3D[edit | edit source]

The Catalan solids are the convex uniform-dual polyhedra whose highest symmetry isn't prismatic or antiprismatic. They are the duals of the Archimedean solids.

The uniform dual polyhedra also include infinite families of polygonal tegums and antitegums; the latter may also be called "trapezohedra".

Convex uniform-dual polyhedra are often used as fair dice.

Uniform dual polyhedra whose duals are hemipolyhedra have faces that extend out to infinity. These are typically named with "-cron" as a suffix instead of "-hedron".

4D[edit | edit source]

The triangular-antitegmatic hexacontatetrachoron is the dual of the small disprismatotesseractihexadecachoron, a uniform polychoron.