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, and Eric's list of uniform honeycombs.
Hyperbolic Tilings . . . Hyperbolic Tetracombs
Category 1: Regulars - The several regular honeycombs and some of their facetings.
Category 2: Truncates - These are the truncated and quasitruncated honeycombs.
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.
Category 5: Pentagonal Rectates - These are the rectates of honeycombs with pentagonal edge figures, along with their regiments.
Category 6: Hexagonal Rectates - These are the rectates of honeycombs with hexagonal edge figures, along with their regiments.
Category 7: Sphenoverts
Category 8: Bitruncates
Category 9: Grombates
Category 10: Omnitruncates
Category 11: Prismatorhombates
Category 12: Antipodiumverts
Category 13: Podiumverts
Category 14: Square Antipodiums
Category 15: Square Podiums
Category 16: Skewverts
Category 17: Antifrustaries
Category 18: Ikhon Regiment
Category 19: Ditetrahedrals
Category 20: Cuboctahedrals
Category 21: Icosidodecahedrals
Category 22: Trihexagonals
Category 23: Miscellaneous
Category 24: Pentagonal Antipodiums
Category 25: Pentagonal Podiums
Category 26: Hexagonal Antipodiums
Category 27: Hexagonal Podiums
Category 28: Ridditdih Regiment
Category 29: Triangular Cupolaverts