Uniform Polychoron - Convex Uniform Polychora

Convex Uniform Polychora

There are 64 convex uniform polychora, including the 6 regular convex polychora, and excluding the infinite sets of the duoprisms and the antiprismatic hyperprisms.

• 5 are polyhedral prisms based on the Platonic solids (1 overlap with regular since a cubic hyperprism is a tesseract)
• 13 are polyhedral prisms based on the Archimedean solids
• 9 are in the self-dual regular A₄ group (5-cell) family.
• 9 are in the self-dual regular F₄ group (24-cell) family. (Excluding snub 24-cell)
• 15 are in the regular BC₄ group (tesseract/16-cell) family (3 overlap with 24-cell family)
• 15 are in the regular H₄ group (120-cell/600-cell) family.
• 1 special snub form in the group (24-cell) family.
• 1 special non-Wythoffian polychoron, the grand antiprism.
• TOTAL: 68 − 4 = 64

These 64 uniform polychora are indexed below by George Olshevsky. Repeated symmetry forms are indexed in brackets.

In addition to the 64 above, there are 2 infinite prismatic sets that generate all of the remaining convex forms:

• Set of uniform antiprismatic prisms - s{p,2}x{} - Polyhedral prisms of two antiprisms.
• Set of uniform duoprisms - {p}x{q} - A product of two polygons.