These are hyperbolic tesselations in 4D.
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Category 1: Primaries - These are the regulars, analogs of hin and cypit, and also some other weird oddballs like contit and odipt.
Category 2: Truncates - These are the truncates and quasitruncates, with uniform pyramids or polygon-dyad disphenoids.
Category 3: Triangular Rectates - These are the rectates with at most triangular symmetries in the verfs, with the verfs being tepes.
Category 4: Square Rectates - These are the rectates with at most square symmetries in the verfs, with opes, tisdips, cupes, or even copes as vertex figures.
Category 5: Pentagonal Rectates - These are the rectates with at pentagonal symmetries in the verfs, with horrifying things like ipe and dope vertex figures.
Category 6: Triangular Sphenoverts - This category has regiments of 7, with them having vertex figures of triangular prism wedges.
Category 7: Square Sphenoverts - Upgraded to square prism wedges, or even brick wedges.
Category 8: Pentagonal Sphenoverts - Upgraded to pentagonal prism wedges.
Category 9: Birhombates - Various duowedge verfed regiments appear here, some with double symmetry.
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