The truncates are formed by truncating or quasitruncating objects with uniform verfs. These would be chon, cuhsquah, octet, tehtrah, and ohtrah. The only bitruncate, batch, is thrown in here as well, as one honeycomb isn't really enough to get its own category, and i wouldn't describe a bitruncate as "greater" either.
33. Tich - Truncated cubic honeycomb. Cells are octs and tics. Its verf is a tall square pyramid. Symbols are x4x3o4o and x4x3o *b3o.
34. Ticuhsquah - Truncated cubihemisquare honeycomb. Cells are thahs, tics, and tosquats. Its verf is a tall bowtie pyramid. This can be seen as analogous to titho. Like for the demicrosses, the hemihypercubic honeycombs get more valid truncations as dimension increases.
35. Tatoh - Truncated tetrahedral-octahedral honeycomb. Cells are coes, tuts, and toes. Its verf is a rectangle pyramid. Symbols are x3x3o *b4o and x3x3x3o3*a.
36. Tutehtrah - Truncated tetrahemitriangular honeycomb. Cells are ohoes, tuts, and hexats. Its verf is a bowtie pyramid. Symbol is x3x3x3o3/2*a3*c. As with tetrah itself, this is only wythoffian under cyclotettic symmetry, as ohoes are only wythoffian under tettic. Not to be confused with a compound or blend of two tetrahs.
37. Tohtrah - Truncated octahemitriangular honeycomb. Cells are choes, toes, and hexats. Its verf is a bowtie pyramid.
Chon, being made of squares, has the ability to be quasitruncated! The other primaries are made of triangles and thus do not get this luxury.
38. Quitch - Quasitruncated cubic honeycomb. Cells are octs and quiths. Its verf is a very short square pyramid. Symbol is x4/3x3o4o. The very short height of the pyramidal verfs of the quasitruncated hypercubic honeycombs is constant across dimensions, so these won't be getting any taller.
39. Quitcuhsquah - Quasitruncated cubihemisquare honeycomb. Cells are thahs, quiths, and quitsquats. Its verf is a very short bowtie pyramid. This one might win the "most spikiest" award. It's pretty rare to see a non-orientable quasitruncate, it never happens in the sphericals, but will keep happening for higher analogues of this.
Batch is a bitruncate. Bitruncates are not truncates, but he doesn't really have any associates, so he'll go here.
40. Batch - Bitruncated cubic honeycomb. Cells are toes. Its verf is a tetragonal disphenoid. Symbols are o4x3x4o, x3x3x *b4o, and x3x3x3x3*a. This one is noble! It has "batchic symmetry", which is doubled chonnic in the same way that doubled pennic is decaic. This is a slightly weird name, but it should be fine. This symmetry doesn't matter that much and won't be appearing very often.
The following honeycombs are self conjugate: tatoh, tutehtrah, tohtrah, batch
The following form conjugate pairs: tich-quitch, ticuhsquah-quitcuhsquah
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