Polychoron Quick Reference

This page shows a series of sections of all of the uniform polychora with the lower symmetry groups - pennic, tessic, and prismattics based off of the triangle and the square. These have a chance to show up as facets of polytera, although some don't make it. Also included are a few compounds that show up within the regiments, their names are in blue.


There are 23 pennics (those with 4-simplex (pentachoric) symmetry). They come from the following categories: 1 (pen), 2 (tip), 3 (rap regiment), 6 (srip regiment), 7 (deca), 8 (grip), 9 (gippid), 10 (prip regiment), and 11 (spid regiment).

Sections of the Pennics

Convex Tessics

There are 58 convex tessics plus two compounds. These have tesseract or demitesseract symmetry, one compound as well as iquipadah has squared square symmetry. These have a convex shell (the colonel of the regiment is convex). They come from the categories: 1 (tes and hex regiments), 2 (tat, thex regiment, tico), 3 (rit and rico regiments), 4 (ico regiment), 6 (srit and rico regiments), 7 (tah), 8 (grit), 9 (gidpith), 10 (prit and proh regiments), 11 (sidpith regiment, sto and gotto), and 20 (sadi, iquipadah).

Sections of the Convex Tessics

Sections of the Convex Tessics

Star Tessics

There are 51 star tessics plus one compound (gondip regiment has yet to be sectioned). These have a starry shell (in star regiments). They come from the following categories: 2 (quitit), 6 (wavitoth regiment), 8 (gaqrit, thatoth, and thaquitoth), 9 (gaquidpoth, thatpath, and thaquitpath), 10 (quiproh and gichado regiments), 12 (gittith regiment), 14 (skiviphado regiment), and 20 (gaquipadah, rasdi, rappisdi regiment, ondip and gondip regiments).

Sections of the Star Tessics

Sections of the Star Tessics


These prisms are uniform under tet prism, cube prism, or pyritoprism symmetry and have potential of showing up as facets of uniform polytera. They come from category 19.

Sections of the Prismatics


These duoprisms have trigon and square based symmetries, also included is squappip - an antiduoprism. They come from category A and B.

Sections of the Duoprismatics

Duals and Conjugates

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