Ike has 30 edge facetings plus a compound, 8 belong here as well as the compound. The first two have doic symmetry and are regular, the next one has pappic symmetry as well as the following compound, and the remaining 5 have peppyric symmetry. All are orientable except gadcone.
1. Ike - (IKE / icosahedron). It has 20 trigs and has doic symmetry and is regular. It has only one orientation.
2. Gad - (GAD / great dodecahedron). It has 12 pegs and has doic symmetry and is regular. It has one orientation.
3. Pap - (PAP / pentagonal antiprism) It has 10 trigs and 2 pegs. It has pappic symmetry, it is uniform with six possible orientations, one having the same symmetry.
C. 2Peppy - (TOO peh pee / compound of 2 pentagonal pyramids) It has 10 trigs and 2 pegs. It has pappic symmetry. It is the compound of two peppies. It has six possible orientations, one with the same symmetry.
4. Peppy - (PEH pee / pentagonal pyramid). It has 5 trigs and 1 peg. It has peppyric symmetry and is a Johnson solid. It has 12 orientations, two with the same symmetry.
5. Gadcone - (GAD kone / gad cone). It has 5 trigs and 5 pegs. It has peppyric symmetry. 12 possible orientations, two with same symmetry.
6. Digdom - (DIG dum / diminished ike-gad morpher) It has 5 trigs and 1+1+5 pegs. It has peppyric symmetry and has 12 orientations, two having the same symmetry.
7. Igdom - (IG dum / ike-gad morpher) It has 5+5 trigs and 1+5 pegs. It has peppyric symmetry. It has 12 orientations, two with the same symmetry. The name stems from the fact that one point looks like ike and the opposite looks like gad and seems to morph from one to the other.
8. Gyepip - (JI e pap / gyroelongated pentagonal pyramid) It has 5+5+5 trigs and 1 pegs. It has peppyric symmetry. It has 12 orientations, two with the same symmetry. It is a Johnson solid.
Six ike facetings go here, the first two have trappic symmetry, the next three have trippyric symmetry, and the last one has brick symmetry.
9. Tigdaf - (TIG daff / trigonic gad faceting). It has 6 trigs and 6 pegs and looks like an accordion which is what I originally called it. It has trappic symmetry and has ten orientations, only one within the same symmetry. It is non-orientable.
10. Toif - (TOIF / toroidal ike faceting). It has 6 trigs and 6 pegs and has a toroidal look. It has trappic symmetry and has ten orientations, one within the symmetry. Originally called 'crazy tube'. It is orientable.
11. Teddi - (TED dee / tridiminished icosahedron). It has 1+1+3 trigs and 3 pegs and is a Johnson solid. It is also the verf of sadi. It has trappyric symmetry and is orientable. It has 20 orientations, two within the symmetry.
12. Scuffi - (SKUF fee / semicupulaically faceted icosahedron). It has 1+3+3 trigs and 3 pegs. It has trippyric symmetry and has 20 orientations with two having the same symmetry. It is non-orientable.
13. Ib - (IB / ike bomb). It has 1+3+3+3+3 trigs and 3 pegs. It has trippyric symmetry and is non-orientable. It has 20 orientations with two having the same symmetry.
14. Bissif - (BIS sif / brick symmetric ike faceting) It has 8 trigs and 4 pegs. It has brick symmetry and is orientable. It has 15 orientations with 3 having the same symmetry. Originally called 'spaceship'.
Eight ike facetings go here, the first six have rectpyric symmetry, and the last two have espyric symmetry. Rectpyrics have 30 orientations with two within the same symmetry, espyrics have 60 orientations with four within the same symmetry. All are orientable except for tudi and ifhah.
15. Mibdi - (MIB dee / metabidiminished icosahedron). It has 2+2+4+2 trigs and 2 pegs and is a Johnson solid.
16. Ifbah - (IF bah / ike faceting 2-6). It has 2+4 trigs and 2 pegs. Originally called 'butterfly pentagonal wedge - bupew'.
17. Ribdi - (RIB dee / retrobidiminished icosahedron). It has 2+4+4+2+2 trigs and 2 pegs.
18. Tudi - (TOO dee / tetradiminished icosahedron). It has 4+2+4+2 trigs and 2+2 pegs.
19. Iftit - (IF tit / ike faceting 4-4). It has 2+2 trigs and 2+2 pegs.
20. Ifhah - (IF hah / ike faceting 6-6) It has 4+2 trigs and 2+2+2 pegs.
21. Skif - (SKIF / small chiral ike faceting). It has 2+2+2+2 trigs and 2+2 pegs.
22. Gekif - (GEK if/ great chiral ike faceting) It has 2+2+2+2 trigs and 2+2 pegs.
Eight ike facetings go here, these have dyadic symmetry and have 60 orientations with four within the same symmetry, espyrics have 60 orientations with four within the same symmetry. The first three are orientable, the rest are not.
23. Iftes - (IF tess / ike faceting 3-7). It has 1+2+2+2 trigs and 1+2 pegs.
24. Topap - (TOE pap / toggled pentagonal antiprism). It has 2+2+2+2+1 trigs and 1+1+1 pegs.
25. Dribdi - (DRIB dee / diminished retrobidiminished icosahedron). It has 2+1+2+2+1+1 trigs and 1+2 pegs.
26. Toscuffi - (tos CUFF ee / toggled semicupulaically faceted icosahedron). It has 2+2+1+2+1 trigs and 2+1+1 pegs.
27. Dib - (DIB / diminished ike bomb). It has 1+2+2+2+1 trigs and 1+2+1 pegs. I claim dibs on this one.
28. Ditudi - (di TOO dee / diminished tetradiminished icosahedron) It has 2+2+2+1 trigs and 1+2+1+1 pegs.
29. Totigdaf - (TAH tig daf / toggled trigonic gad faceting). It has 1+1+2+1+2 trigs and 2+1+2 pegs.
30. Togadic - (toe GAD ik/ toggled gad cone) It has 1+2+2+1 trigs and 1+2+2+1 pegs.
Sissid has 30 edge facetings plus a compound, 8 belong here as well as the compound. The first two have doic symmetry and are regular, the next one has pappic symmetry as well as the following compound, and the remaining 5 have peppyric symmetry. All are orientable except sadcone.
1. Sissid - (SIS sid / small stellated dodecahedron). It has 12 stars and has doic symmetry and is regular. It has one orientation.
2. Gike - (GIKE / great icosahedron). It has 20 trigs and has doic symmetry and is regular. It has only one orientation.
3. Starp - (STARP / stellar retroprism) It has 10 trigs and 2 stars. It has pappic symmetry, it is uniform with six possible orientations, one having the same symmetry.
C. 2Stappy - (TOO stap pee / compound of 2 star pyramids) It has 10 trigs and 2 stars. It has pappic symmetry. It is the compound of two stappies. It has six possible orientations, one with the same symmetry.
4. Stappy - (STAP pee / star pyramid). It has 5 trigs and 1 star. It has peppyric symmetry. It has 12 orientations, two with the same symmetry.
5. Sadcone - (SAD kone / stelladodecahedron cone). It has 5 trigs and 5 stars. It has peppyric symmetry. 12 possible orientations, two with same symmetry.
6. Rigsisdom - (rig SIS dum / replenished gike-sissid morpher) It has 5 trigs and 1+1+5 stars. It has peppyric symmetry and has 12 orientations, two having the same symmetry.
7. Gissdom - (IG dum / gike-sissid morpher) It has 5+5 trigs and 1+5 stars. It has peppyric symmetry. It has 12 orientations, two with the same symmetry. The name stems from the fact that one point looks like gike and the opposite looks like sissid and seems to morph from one to the other.
8. Regi - (REH jee / replenished great icosahedron) It has 5+5+5 trigs and 1 star. It has peppyric symmetry. It has 12 orientations, two with the same symmetry.
Six sissid facetings go here, the first two have trappic symmetry, the next three have trippyric symmetry, and the last one has brick symmetry.
9. Tissidaf - (TISS id daff / trigonic sissid faceting). It has 6 trigs and 6 stars and originally called 'sixstarthingy'. It has trappic symmetry and has ten orientations, only one within the same symmetry. It is non-orientable.
10. Togif - (TOE jif / toroidal gike faceting). It has 6 trigs and 6 stars and is orientable. It has trappic symmetry and has ten orientations, one within the symmetry. Originally called 'sixstarthingamajig' - togif sounds so much better.
11. Targi - (TAR jee / trireplenished great icosahedron). It has 1+1+3 trigs and 3 stars and is the verf of rasdi. It has trappyric symmetry and is orientable. It has 20 orientations, two within the symmetry.
12. Scufgi - (SKUF jee / semicupulaically faceted great icosahedron). It has 1+3+3 trigs and 3 stars. It has trippyric symmetry and has 20 orientations with two having the same symmetry. It is non-orientable.
13. Gib - (GIB / great ike bomb). It has 1+3+3+3+3 trigs and 3 stars. It has trippyric symmetry and is non-orientable. It has 20 orientations with two having the same symmetry.
14. Bisgif - (BIS gif / brick symmetric gike faceting) It has 8 trigs and 4 stars. It has brick symmetry and is orientable. It has 15 orientations with 3 having the same symmetry. Originally called 'fourstarthingy'.
Eight ike facetings go here, the first six have rectpyric symmetry, and the last two have espyric symmetry. Rectpyrics have 30 orientations with two within the same symmetry, espyrics have 60 orientations with four within the same symmetry. All are orientable except for turgi and gifhah.
15. Mebergi - (MEH bur jee / metabireplenished great icosahedron). It has 2+2+4+2 trigs and 2 stars.
16. Gifbah - (GIF bah / gike faceting 2-6). It has 2+4 trigs and 2 stars. Originally called 'twostarthingy'.
17. Rebergi - (REH bur jee / retrobireplenished great icosahedron). It has 2+4+4+2+2 trigs and 2 stars.
18. Turgi - (TUR jee / tetrareplenished great icosahedron). It has 4+2+4+2 trigs and 2+2 stars.
19. Giftit - (GIF tit / gike faceting 4-4). It has 2+2 trigs and 2+2 stars.
20. Gifhah - (GIF hah / gike faceting 6-6) It has 4+2 trigs and 2+2+2 stars.
21. Skagif - (SKAG gif / small chiral gike faceting). It has 2+2+2+2 trigs and 2+2 stars.
22. Gekgif - (GEK gif/ great chiral gike faceting) It has 2+2+2+2 trigs and 2+2 stars.
Eight ike facetings go here, these have dyadic symmetry and have 60 orientations with four within the same symmetry, espyrics have 60 orientations with four within the same symmetry. The first three are orientable, the rest are not.
23. Giftes - (GIF tess / gike faceting 3-7). It has 1+2+2+2 trigs and 1+2 stars.
24. Tostarp - (TOS tarp / toggled stellar retroprism). It has 2+2+2+2+1 trigs and 1+1+1 stars.
25. Rarbergi - (RAR bur jee / replenished retrobireplenished great icosahedron). It has 2+1+2+2+1+1 trigs and 1+2 stars.
26. Tescufgi - (tes CUFF jee / toggled semicupulaically faceted great icosahedron). It has 2+2+1+2+1 trigs and 2+1+1 star.
27. Regib - (REE jib / replenished gike bomb). It has 1+2+2+2+1 trigs and 1+2+1 stars.
28. Returgi - (re TUR jee / replenished tetrareplenished great icosahedron) It has 2+2+2+1 trigs and 1+2+1+1 stars.
29. Tot Sissidaf - (tot SIS sid daf / toggled trigonic sissid faceting). It has 1+1+2+1+2 trigs and 2+1+2 stars.
30. Tosadic - (toe SAD ik/ toggled sadcone) It has 1+2+2+1 trigs and 1+2+2+1 stars.
Conjugates
The following are self conjugates: none.
The following are conjugate pairs: ike-gike, gad-sissid, for the rest - ike faceting n - sissid faceing n (n is the number in front of name).
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