Kind A: Stocks - The unending set of stocks. For every manyside there is a stock with that can be thought of as the manyedge stretched to have a third width.
Kind B: Witherstocks - The unending set of witherstocks, these have sideways threesides instead of foursides.
Kind 1: Lawfuls - (#1 - 9) The lawful manysides include the five undented Platonic and four self-met Kepler-Poinsot shapes. These have regular hirscs and are samehirns, samedges, and sameflats.
Kind 2: Cuts - (#10 - 19) The seven cuts and three kind-of cuts of the lawfuls. These have same-legged threesides for hirscs.
Kind 3: Near Lawfuls - (#20 - 35) These have samehirned hirscs and are sameedges, but are not lawfuls. Among these are nine out of the ten steadsamehirned halfflats.
Kind 4: Rutes - (#36 - 56) These are the steadsamehirns with table hirscs and their fighthedes.
Kind 5: Full Cuts - (#57 - 63) These are the steadsamehirns with the most score of hirns not forbidden by their sameness.
Kind 6: Snubs - (#64 - 75) These are generally handed and all have flats not where any twist is. Here the last of the steadsamehirned halfflats live - the beast that is gitrinf.