The lawfuls are samehirns, samedges, and sameflats, and also have lawful flats and hircs. 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 (sistuf, gistuf) and Louis Poinsot in 1809 (gituf, gitwen), and are hence named the Kepler-Poinsot shapes as to acknowledge them.
1. Fewf - (FEOF) fourflat. Flats are four threesides. It has four hirns and a threeside for a hirsc. Showing is x3o3o, also s4o s and s s s as a twoside withersawn. [OBSA: tet]
2. Wyr - (WÜR) wirple. Flats are six foursides. It has eight hirns with a threeside for a hirsc. Showing is x4o3o, also x4o x as a fourside sawn and x x x as a box. [OBSA: cube]
3. Aht - (AKHT) eightflat. Flats are eight threesides and six hirns, fourside for a hirsc. Showing is o4o3x, also o3x3o as a righted fewf and s6o s and s3s s as a threeside withersawn. [OBSA: oct]
4. Twef - (TWEF) twelflat. Flats are twelve fivesides. This has twenty hirns and a threeside for a hirsc. Showing is x5o3o, no others. [OBSA: doe]
5. Twen - (TWEN) twentiflat. Flats are twenty threeflats. It has twelve hirns and a fiveside for a hirsc. Showing is o5o3x, also o4s3s and s3s3s. [OBSA: ike]
6. Gituf - (YI tuf) great twelflat. Flats are twelve fiveflats. It has twelve hirns and a fivestar for a hirsc, this is in the twen foughthede. Showing is x5o5/2o. [OBSA: gad]
7. Sistuf - (SIS tuf) small starry twelflat. Flats are twelve fivestars. It has twelve hirns and a fiveflat for a hirsc, showing is o5o5/2x. [OBSA: sissid]
8. Gitwen - (YI twen) great twentiflat. Flats are twenty threesides with twelve hirns. It has a fivestar for a hirsc and is in the sistuf foughthede. Showing is o5/2o3x, also o4s3/2s and s3/2s3/2s. [OBSA: gike]
9. Gistuf - (YIS tuf) great starry twelflat. Flats are twelve twentiflats and has twenty hirns. It has a threestar for a hirsc, showing is x5/2o3o. [OBSA: gissid]
Twins
Own Twin: fewf
Twins: wyr-aht, twef-twen, gituf-sistuf, gitwen-gistuf
Other-Roots
No Other-Roots: fewf, wyr, aht
Other-Roots: twef-gistuf, twen-gitwen, gituf-sistuf