This is a (forever) incomplete list of hyperbolic honeycombs. The style of this list and the names were inspired by Jonathan Bowers' list of uniform polychora, Eric's list of uniform honeycombs, and ThePokemonkey123's other list of uniform honeycombs.
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Category A: Borromeachora - These have infinite stacks of prisms, connected by cubes in a pyritic icosahedron vertex figure.
Category B: Prismatic Honeycombs - These have isosceles triangular tiling vertex figures.
Category C: Antiprismatic Honeycombs - These have trapezoid tiling vertex figures.
Category D: Snub Cube Borromeachora - Similar to Category A, but some of the cubes are replaced with square tilings.
Category E: Square Tiling Borromeachora - Category D, but all cubes are replaced with square tilings.
Category 1: Regulars - The several regular honeycombs and some of their facetings.
Category 2: Truncates - These are the truncated and quasitruncated honeycombs. Some of these have verfs outside hyperbolic space.
Category 3: Triangular Rectates - These are the rectates of honeycombs with triangular edge figures.
Category 4: Square Rectates - These are the rectates of honeycombs with square edge figures, along with their regiments. This mimics the ico regiment of spherical space.
Category 5: Pentagonal Rectates - These are the rectates of honeycombs with pentagonal edge figures, along with their regiments. This mimics the rox regiment.
Category 6: Hexagonal Rectates - These are the rectates of honeycombs with hexagonal edge figures, along with their regiments. The closest analog of this is the rissidtixhi regiment of spherical space.
Category 7: Sphenoverts - These are the cantellates (or small rhombates) of the honeycombs along with others with similar verfs. Verfs are wedges and their facetings, each of the many regiments have at most 7 members.
Category 8: Bitruncates - These have disphenoid verfs. There are many double-symmetric honeycombs, like batih and batped.
Category 9: Grombates - These have scalene-containing sphenoid verfs.
Category 10: Omnitruncates - These have tetrahedral verfs containing only even sided polygons. There are a lot more of these now.
Category 11: Prismatorhombates - These have trapezoid pyramid verfs. There are probably many of these guys.
Category 12: Triangular Antipodiumverts - The various small prismates belong here, along with some others.
Category 13: Triangular Podiumverts - These have triangular podiums as verfs. Some rectates have new members in here.
Category 14: Square Antipodiums - These are like the spic and giddic polychora of spherical space.
Category 15: Square Podiums - This category contains brand new types of honeycombs. Some overlap with category 17.
Category 16: Skewverts - These contained skewed wedges with up to 15 members per regiment.
Category 17: Antifrustaries - These are analogs of the afdec and affixthi regiments of spherical space.
Category 18: Ikhon Regiment - This is the analog of the sishi regiment. It gets a category to itself because it's so special.
Category 19: Ditetrahedrals - These are similar to sidtaxhi/dattady/gadtaxady. They contain tetrahedral symmetric verfs. Things like ahexah (alternated hexah) exist here.
Category 20: Cuboctahedrals - These contain cubic symmetric verfs. Here some more alternated honeycombs exist.
Category 21: Icosidodecahedrals - These contain dodecahedral symmetric verfs. There exists a honeycomb with a semuniform grid verf here too. It's not dangerous thankfully. There is another one that is dangerous, but that's not important.
Category 22: Trihexagonals - The trah regiment is placed here. These contain various honeycombs with verfs with hexagonal tiling symmetry.
Category 23: Tetratetragonals - These contain various honeycombs with verfs with square tiling symmetry.
Category 24: Miscellaneous - The ultimate "random stuff that doesn't fit anywhere else" category. Things like snadih, a honeycomb with sesides, sidtids, and tets, go here.
Category 25: Pentagonal Antipodiums - Analogs of padohi. The small prismated icosahedral honeycomb is here (spih).
Category 26: Pentagonal Podiums - Analogs of gidipthi.
Category 27: Hexagonal Antipodiums - Hexagonal antipodium. Spitrah (small prismated triangular tiling honeycomb) is here.
Category 28: Hexagonal Podiums - These are somewhat like the ditrigonal antifrustaries later on.
Category 29: Ditrigonal Prismverts - This is the true analog of the rissidtixhi regiment, making them the true knockoffs of rissidtixhi.
Category 30: Ditetragonal Prismverts - Upgraded version of the ditrigonal prismverts
Category 31: Dipentagonal Prismverts - Stop upgrading.
Category 32: Dihexagonal Prismverts - I SAID STOP.
Category 33: Triangular Cupolaverts - Analog of stut phiddix/getit xethi.
Category 34: Square Cupolaverts - Here we go again.
Category 35: Pentagonal Cupolaverts
Category 36: Hexagonal Cupolaverts
Category 37: Ditrigonal Frustaries - Not even the afdec knockoffs are safe.
Category 38: Ditetragonal Frustaries
Category 39: Dipentagonal Frustaries
Category 40: Dihexagonal Frustaries
Category 41: Tetradigonaries - These have rectangular tiling verfs, they have non-simplicial fundamental domains. Octh and sisquah fit here as well.
Category 42: Small Rhombic Tetradigonaries - These have trapezoid tiling verfs, with infinite stacks of alternating trapezoids connected together.
Category 43: Truncate Tetradigonaries - These have isosceles triangle tiling verfs, like the trapezoid tilings but some of trapezoids degenerate into triangles.
Category 44: Great Rhombic Tetradigonaries - These have chiral verfs and are technically omnitruncates of a non-simplicial fundamental domain.
Category 45: Pyriticaries - Honeycombs with pyritic symmetric verfs. These are related to the borromeachora infinite category A.
Category 46: Square Tiling Ionicaries - Related to category E.
Category 47: Triangular Tiling Ionicaries - Have verfs with triangular tiling ionic symmetry.
Category 48: Snub Polyhedronaries - Somehow, snub polyhedra can be used as verfs. Their rectates will also be listed here.
Category 49: x(oo^x^)/o(oo^x^) Blends - This regiment has a verf that is a tut with four tricus blended to it. The colonel has srids, pips, and tets. It seems to be convex.
Category 50: x*(oox^)/o*(xoo^) Blends - This regiment has a verf that is a ditrigonal prism with two tricu caps added to it. Its colonel has gissids, radeds, trips, dids, and gids
Category 51: Phexah Compound Regiment - This regiment has a verf that is a hexagonal prism with two hexagonal podium caps. It has a compound of phexahs inside, and its colonel has trats, gidditdids, and dids.
Category 52: Ahexah Blends - The first of the alternated blends. This has a tutet verf.
Category 53: Ashexah Blends - The second of the alternated blends. This has a tutoe verf.
Category 54: Aphexah Blends - The last and scariest of the alternated blends. This has a verf that is the blend of two tis, which is concerning.