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