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Category 2: Truncates
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Above are sections of 6 of the truncates, the number represents the sectioning realm (.0 = top, 1.0 = bottom). Tigaghi and taggix are normal truncates, tissidtixhi and tiggidtixhi are ditrigonal truncates, quit gogishi and quit gashi are quasitruncates.
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The truncates are formed by truncating the regular polychora, or even those with a uniform polyhedron for a vertex figure. Quasitruncation is a much grander form of truncation - truncating a square would get an octagon, quasitruncating a square would get an octagram. There are 12 normal truncates (20-31), 3 ditrigonal truncates (33-35), titho (32), and 5 quasitruncates (36-40) - 21 in all. They are as follows:
20. Tip (truncated pentachoron) - has a triangular pyramid vertex figure, cells are 5 tets (tet = tetrahedron) and 5 tuts (tut = truncated tetrahedron).
21. Tat (truncated tesseract) - has a triangular pyramid vertex figure, cells are 16 tets and 8 tics (tic = truncated cube).
22. Thex (truncated hexadecachoron) - has a square pyramid vertex figure, cells are 8 octs (oct = octahedron) and 16 tuts.
23. Tico (truncated icosatetrachoron) - has a trianglar pyramid vertex figure, cells are 24 cubes and 24 toes (toe = truncated octahedron).
24. Thi (truncated hecatonicosachoron) - has a tall triangular pyramid vertex figure, cells are 600 tets and 120 tids (tid = truncated dodecahedron).
25. Tex (truncated hexacosichoron) - has a pentagonal pyramid vertex figure, cells are 120 ikes (ike = icosahedron) and 600 tuts.
26. Tiffix (truncated fix) - has a star pyramid vertex figure, cells are 120 gads (gad = great dodecahedron) and 120 tis (ti = truncated icosahedron).
27. Tighi (truncated gohi) - has a long pentagonal pyramid v.f., cells are 120 sissids (sissid = small stellated dodecahedron) and 120 tigids (tigid = truncated gad).
28. Taghi (truncated gahi) - has a long star pyramid v.f., cells are 120 gikes (gike = great ike) and 120 tids.
29. Tigaghi (truncated gaghi) - has a long triangular pyramid v.f., cells are 120 gissids (gissid = great stellated dodecahedron) and 120 tigids. Section pictured above.
30. Tigfix (truncated gofix) - has a pentagonal pyramid v.f., cells are 120 sissids and 120 tiggies (tiggy = truncated gike).
31. Taggix (truncated gax) - has a star pyramid v.f., cells are 120 gikes and 600 tuts. Section pictured above, a quite interesting one.
32. Titho (truncated tho) - has a bowtie pyramid v.f., cells are 8 thahs (thah = tetrahemihexahedron), 8 tuts, and 4 toes. Belongs to thex regiment and has hemi-tesseract symmetry.
33. Tissidtixhi (truncated sidtixhi) - sidtixhi belongs to category 17. Has a ditrigon pyramid v.f., cells are 120 sidtids (sidtid = small ditrigonary icosidodecahedron), 120 tiggies, and 600 tuts. Section pictured above.
34. Tidtidohi (truncated dittady) - dittady belongs to cat. 17. Has a "propellar" pyramid v.f., cells are 120 ditdids (ditdid = ditrigonary dodecadodecahedron), 120 tiggies, and 120 tis.
35. Tiggidtixhi (truncated gidtixhi) - gidtixhi belongs to cat. 17. Has a tripod pyramid v.f., cells are 120 gidtids (gidtid = great ditrigonary icosidodecahedron), 600 tuts, and 120 tis. Section pictured above.
36. Quitit (quasitruncated tesseract) - has a flat triangular pyramid v.f., cells are 16 tets and 8 quiths (quith = quasitruncated hexahedron).
37. Quit Sishi (quasitruncated sishi) - has a flat triangular pyramid v.f., cells are 120 does (doe = dodecahedron) and 120 quit sissids (quit sissid = quasitruncated sissid).
38. Quit Gogishi (quasitruncated gogishi) - has a triangular pyramid v.f., cells are 600 tets and 120 quit gissids (quit gissid = quasitruncated gissid). Section above.
39. Quit Gishi (quasitruncated gishi) - has flat pentagonal pyramid v.f., cells are 120 ikes and 120 quit gissids.
40. Quit Gashi (quasitruncated gashi) - has flat star pyramid v.f., cells are 120 gads and 120 quit sissids. Section above - I think this one looks the best!
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