Polychoron Categories
1. Regulars - this includes the 16 regular polychora and 3 facetings that didn't fit anywhere else. (19 total).
2. Truncates - this includes truncates, quasitruncates, and other truncates (21 total).
3. Triangular Rectates - this includes 7 regiments of 3 polychora - which have vertex figures resembling the triangular prism and it's facetings. (21 total).
4. Ico Regiment - this includes the 13 polychora that share the same vertices and edges as the 24-cell (ico). (13 total).
5. Pentagonal Rectates - this includes 4 regiments of 22 polychora which have vertex figures shaped like the pentagonal prism and its facetings. (88 total).
6. Sphenoverts - this includes the polychora with wedge shaped vertex figures and their facetings (sirgax is one). (165 total).
7. Bitruncates - this includes polychora with disphenoid vertex figures, (11 total).
8. Great Rhombates - this includes those with vertex figures shaped like tetrahedra with bilateral symmetry. (23 total).
9. Maximized - this includes the polychora with irregular tetrahedra vertex figures, these have the maximum number of vertices for their symmetry groups. (22 total).
10. Prismatorhombates - this includes those with trapezoid pyramid vertex figures and their facetings. Contains 30 regiments of 3, (90 total).
11. Triangular Antipodiumverts - this includes those with triangular antipodium (looks like antiprism) vertex figures and their facetings. (40 total).
12. Frustrumverts - this includes those with triangular frustum vertex figures and their facetings. (30 total).
13. Spic and Giddic Regiments - Spic and Giddic both have square antiprism shaped vertex figures, each regiment contains 22 polychora. (44 total).
14. Skewverts - these are 4 regiments of 15, which have skewed wedge (and facetings) shaped vertex figures. (60 total).
15. Afdec Regiment - this regiment has icoic (24-cell) symmetry, and contains 54 polychora.
16. Affixthi Regiment - this regiment has hyic (120-cell) symmetry, and contains 100 polychora.
17. Sishi Regiment - Sishi is the small stellated 120-cell, its regiment contains 2 regulars, 8 swirlprisms, and 34 others - the "others" are mentioned here. (34 total).
18. Ditetrahedrals - this group contains those with vertex figures shaped like the truncated tetrahedron, and the "small rhombitetratetrahedron" (looks like cuboctahedron), and their facetings. (213 total).
19. Prisms - this contains the prisms of the uniform polyhedra, I also call them "Hedrisms". (74 total).
20. Miscellaneous - this contains the 6 antiprisms (includes grand antiprism), the 6 normal snubs, the 10 swirlprisms, and 2 recent discoveries with 4,4 duoprism symmetry. (24 total).
21. Padohi Super Regiment - padohi has a pentagonal antipodium vertex figure, its regiment contains a whopping 354 polychora.
22. Gidipthi Super Regiment - gidipthi has a pentagonal frustrum vertex figure, its regiment also contains 354 polychora. Many of these are very intricate.
23. Rissidtixhi Super Regiment - rissidtixhi has a ditrigon prism vertex figure, its regiment contains 316 polychora.
24. Stut Phiddix Super Regiment - stut phiddix has a triagular cupola shaped vertex figure and its regiment contains 238 polychora.
25. Getit Xethi Super Regiment - getit xethi has a vertex figure which resembles stut phiddix's but sort of squashed a bit, this regiment has 238 polychora.
26. Blends - this contains a non-Wythoffian regiment of 16 polychora.
27. Baby Monster Snubs - this contains 2 regiments of 15 non-Wythoffian snubs, many are chiral.
28. Idcossids - this is one of the grandest regiments of all, containing a whopping 2749 non-Wythoffian snubs - these are horrificly complex, nearly all are chiral. Based on the compound of 10 padohis.
29. Dircospids - this is another horrific regiment of 2749 non-Wythoffian snubs, nearly all are chiral. This regiment most likely contains the most complex polychoron. Based on the compound of 10 gidipthis.
Page wrote by HedronDude, a.k.a. Jonathan Bowers
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