The lawfuls are samehirns, sameedges, and sameflats, and also have lawful flats and hirsces. The five undented ones have been known for forever, these are the Platonic shapes. The self-met ones were known but not said to be lawful until Johannas Kepler in 1619 (sistƿef, gestƿef) and Louis Poinsot in 1809 (getƿef, getƿen), and are hence named the Kepler-Poinsot shapes as to acknowledge them.
1. Fof - (FOF) fourflat. Flats are four threesides. It has four hirns and a threeside for a hirsc. Showing is x3o3o, also s4o s as a foursided twice-wedgelike and s s s as a ruted twice-wedgelike. [OBSA: tet]
2. Ƿir - (WIR) wirple. Flats are six foursides. It has eight hirns with a threeside for a hirsc. Showing is x4o3o, also x4o x as a fourside stock and x x x as a box. [OBSA: cube]
3. Eht - (EIGHT) eightflat. Flats are eight threesides and six hirns, fourside for a hirsc. Showing is o4o3x, also o3x3o as a righted fof and s6o s and s3s s as a threeside witherstock. [OBSA: oct]
4. Tƿef - (TWEF) twelveflat. Flats are twelve fivesides. This has twenty hirns and a threeside for a hirsc. Showing is x5o3o, no others. [OBSA: doe]
5. Tƿen - (TWEN) twentiflat. Flats are twenty threesides. It has twelve hirns and a fiveside for a hirsc. Showing is o5o3x, also o4s3s and s3s3s. [OBSA: ike]
6. Getƿef - (YEE twef) great twelveflat. Flats are twelve fivesides. It has twelve hirns and a fivestar for a hirsc, this is in the twen fighthede. Showing is x5o5/2o. [OBSA: gad]
7. Sistƿef - (SIS twef) small starry twelveflat. Flats are twelve fivestars. It has twelve hirns and a fiveside for a hirsc, showing is o5o5/2x. [OBSA: sissid]
8. Getƿen - (YEE twen) great twentiflat. Flats are twenty threesides with twelve hirns. It has a fivestar for a hirsc and is in the sistuf fighthede. Showing is o5/2o3x, also o4s3/2s and s3/2s3/2s. [OBSA: gike]
9. Gestƿef - (YES twef) great starry twelveflat. Flats are twelve fivestars and has twenty hirns. It has a threeside for a hirsc, showing is x5/2o3o. [OBSA: gissid]
Twins
Own Twin: fof
Twins: ƿir-eht, tƿef-tƿen, getƿef-sisƿef, getƿen-gestƿef
Other-Roots
No Other-Roots: fof, ƿir, eht
Other-Roots: tƿef-gestƿef, tƿen-getƿen, getƿuf-sistƿef