User:Double sharp/Polyhedra categorisation

Bowers' categorisation:

1. Regulars
   • All the regular polyhedra, plus thah (which is a faceting of oct and doesn't fit anywhere else).
2. Truncates
   • Truncates and quasitruncates of the regular polyhedra.
3. Quasiregulars
   • Rectified regular polyhedra plus their facetings (the hemipolyhedra). Also here are the three ditrigonal polyhedra: sidtid, ditdid and gidtid.
4. Trapeziverts
   • Cantellated regular polyhedra plus their facetings. Their facetings include both socco-type and sroh-type (blended) polyhedra.
5. Omnitruncates
   • Omnitruncated regular polyhedra. Includes great rhombates, great quasirhombates, and cotco and idtid as special cases.
6. Snubs
   • Alternated great rhombates. Includes Miller's monster.
7. Prisms
   • The infinite set of prisms.
8. Antiprisms
   • The infinite set of antiprisms and crossed-antiprisms.

Johnson's categorisation:

1. Regulars
   • The regular polyhedra only.
2. Quasiregulars
   • Rectified regular polyhedra plus the ditrigonal polyhedra.
3. Hemipolyhedra
   • The nine hemipolyhedra only.
4. Truncates
   • Truncates and quasitruncates of the regulars.
5. Cantellates
   • The cantellates of the regular polyhedra, together with their socco-like facetings.
6. Other even-faced polyhedra
   • The sroh-like facetings of the cantellates.
7. Omnitruncates
   • The great rhombates, great quasirhombates and cotco and idtid.
8. Snubs
   • Alternated great rhombates. Includes Miller's monster.
9. Prisms
   • The infinite set of prisms.
10. Antiprisms
    • The infinite set of antiprisms and crossed-antiprisms.