truncates

Category 2: Truncates

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.

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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