The three doic facetings of sidtid are uniform, there's also a compound. All are orientable. These only have one orientation.
1. Sidtid - (SID tid / small ditrigonary icosidodecahedron). It has 12 stars and 20 trigs, we know this guy.
2. Ditdid - (DIT did / ditrigonary dodecadodecahedron). It has 12 stars and 12 pegs.
3. Gidtid - (GID tid / great ditrigonary icosidodecahedron). It has 20 trigs and 12 pegs.
C1. Rhom - (Rhom / rhombihedron, compound of 5 cubes). It has 30 squares.
There are five pappic facetings of sidtid, two fissaries, and two compounds. The fissaries and defbideb are orientable, the others are not. These have six orientations.
4. Sifodib - (SI fo dib / sidtid faceting 0-10-20-2). It has 10 trigs, 2 pegs, and 2x10 squares.
5. Gifodib - (GI fo deb / gidtid faceting 0-10-20-2). It has 10 trigs, 2 stars, and 2x10 squares.
6. Gifdodeb - (GIF do deb / gidtid faceting 10-0-10-2). It has 2 stars, 10 pegs, and 10 squares.
7. Sifdodeb - (SIF do deb / sidtid faceting 10-0-10-2). It has 10 stars, 2 pegs, and 10 squares.
8. Defbideb - (def BI deb / ditdid faceting 2-20-10-2). It has 2 stars, 2 pegs, 20 trigs, and 10 squares.
F1. Gifdadedo - (GIF da DEE do / gidtid faceting 10-10-10-0). It has 10 trigs, 10 pegs, and 10 squares.
F2. Sifdadedo - (SIF da DEE do / gidtid faceting 10-10-10-0). It has 10 trigs, 10 stars, and 10 squares.
C2. 2Rapescu - (too RAP iss coo / compound of two rapescus). It has 10 trigs, 2 pegs, and 10 squares.
C3. 2Stiscu - (too STISS coo / compound of two stiscus). It has 10 trigs, 2 stars, and 10 squares.
There are 26 sidtid facetings that have peppyric symmetry and are legit (not fissary). They have twelve orientations with two in the same symmetry. All are non-orientable except for hagdotid and hesdotid.
9. Rapescu - (RAP iss coo / retrograde pentagonal semicupola). It has 5 trigs, 1 peg, and 5 squares.
10. Stiscu - (STISS coo / star semicupola). It has 5 trigs, 1 star, and 5 squares.
11. Gifboffu - (gif BOFF fu / gidtid faceting 2-15-15-1). It has 1 star, 1+1 pegs, 3x5 trigs, and 10+5 squares.
12. Sifboffu - (sif BOFF fu / sidtid faceting 2-15-15-1). It has 1+1 stars, 1 peg, 3x5 trigs, and 10+5 squares.
13. Gefpopfoa - (GEF pop FO wa / gidtid faceting 5-5-15-0a). It has 5 pegs, 5 trigs, and 10+5 squares.
14. Sefpopfoa - (SEF pop FO wa / sidtid faceting 5-5-15-0a). It has 5 stars, 5 trigs, and 10+5 squares.
15. Gafpipfob - (gaf PIP fob / gidtid faceting 5-5-15-0b). It has 5 pegs, 5 trigs, and 3x5 squares.
16. Safpipfob - (saf PIP fob / sidtid faceting 5-5-15-0b). It has 5 stars, 5 trigs, and 3x5 squares.
17. Gifhiddoa - (GIF hid O wa / gidtid faceting 6-10-10-0a). It has 1+5 pegs, 2x5 trigs, and 2x5 squares.
18. Sifhiddoa - (SIF his O wa / sidtid faceting 6-10-10-0a). It has 1+5 stars, 2x5 trigs, and 2x5 squares.
19. Gefpodu - (gef PO du / gidtid faceting 5-0-10-1). It has 1 star, 5 pegs, and 2x5 squares.
20. Sefpodu - (sef PO du / sidtid faceting 5-0-10-1). It has 5 stars, 1 peg, and 2x5 squares.
21. Gafheppu - (gaf HEP pu / gidtid faceting 6-5-5-1). It has 1 star, 1+5 pegs, 5 trigs, and 5 squares.
22. Safheppu - (saf HEP pu / sidtid faceting 6-5-5-1). It has 1+5 stars, 1 peg, 5 trigs, and 5 squares.
23. Gofhefpu - (goff EFF pu / gidtid faceting 6-15-5-1). It has 1 star, 1+5 pegs, 3x5 trigs, and 5 squares.
24. Sofhefpu - (soff EFF pu / sidtid faceting 6-15-5-1). It has 1+5 stars, 1 peg, 3x5 trigs, and 5 squares.
25. Hagdotid - (hag DO tid / hemi gidtid). It has 1+1 stars, 1+5 pegs, and 2x5 trigs.
26. Hesdotid - (hes DO tid / hemi sidtid). It has 1+5 stars, 1+1 pegs, and 2x5 trigs.
27. Gifspoph - (GIF spoff / gidtid faceting 7-5-5-6). It has 1+5 stars, 1+1+5 pegs, 5 trigs, and 5 squares.
28. Sifspoph - (SIF spoff / sidtid faceting 7-5-5-6). It has 1+1+5 stars, 1+5 pegs, 5 trigs, and 5 squares.
29. Gafvapoph - (gaf VAY poff / gidtid faceting 11-5-5-6). It has 1+5 stars, 1+5+5 pegs, 5 trigs, and 5 squares.
30. Safvapoph - (saf VAY poff / sidtid faceting 11-5-5-6). It has 1+5+5 pegs, 1+5 pegs, 5 trigs, and 5 squares.
31. Defhadoha - (DEF ha DO ha / ditdid faceting 6-10-0-6a). It has 1+5 stars, 1+5 pegs, and 2x5 trigs.
32. Defhadoheb - (DEF ha DO heb / ditdid faceting 6-10-0-6b). It has 1+5 stars, 1+5 pegs, and 2x5 trigs.
33. Gafiddoh - (GAFF a doe / gidtid faceting 10-10-0-6). It has 1+5 stars, 2x5 pegs, and 2x5 trigs.
34. Sefiddoh - (SEFF a doe / sidtid faceting 10-10-0-6). It has 2x5 stars, 1+5 pegs, and 2x5 trigs.
There are 20 sidtid facetings that have peppyric symmetry and are fissary. They have twelve orientations with two in the same symmetry.
F3. Giraf - (ja RAF / great rhom faceting). It has 1 peg, 5 trigs, and 3x5+10 squares.
F4. Seraf - (sa RAF / small rhom faceting). It has 1 star, 5 trigs, and 3x5+10 squares.
F5. Rafudiua - (ra FOO de wa / rhom faceting 1-10-20-1a). It has 1 star, 1 peg, 2x5 trigs, and 20 squares.
F6. Rafudiub - (ra FOO de yub / rhom faceting 1-10-20-1b). It has 1 star, 1 peg, 2x5 trigs, and 20 squares.
F7. Sifodedha - (SI fo DEH thuh / sidtid faceting 0-10-10-6a). It has 1+5 pegs, 2x5 trigs, and 10 squares.
F8. Gifodedha - (GI fo DEH thuh / gidtid faceting 0-10-10-6a). It has 1+5 stars, 2x5 trigs, and 10 squares.
F9. Gafvefop - (GAF ve fopp / gidtid faceting 11-15-0-5). It has 1+5+5 pegs, 3x5 trigs, and 5 squares.
F10. Safvefop - (SAF ve fopp / sidtid faceting 11-15-0-5). It has 1+5+5 stars, 3x5 trigs, and 5 squares.
F11. Gofpoiu - (gof POY yu / gidtid faceting 5-0-20-1). It has 1 star, 5 pegs, and 20 squares.
F12. Sofpoiu - (sof POY yu / sidtid faceting 5-0-20-1). It has 5 stars, 1 peg, 20 squares.
F13. Gafhipfu - (gaf HIP fu / gidtid faceting 6-5-15-1). It has 1 star, 1+5 pegs, 5 trigs, and 15 squares.
F14. Safhipfu - (saf HIP fu / sidtid faceting 6-5-15-1). It has 1+5 stars, 1 peg, 5 trigs, and 15 squares.
F15. Gofpeddu - (gof PED du / gidtid faceting 5-10-10-1). It has 1 star, 5 pegs, 2x5 trigs, and 10 squares.
F16. Sofpeddu - (sof PED du / sidtid faceting 5-10-10-1). It has 5 stars, 1 peg, 2x5 trigs, and 10 squares.
F17. Sifbippop - (sif BIP pop / sidtid faceting 2-5-5-5). It has 1+1 stars, 5 pegs, 5 trigs, and 5 squares.
F18. Gifbippop - (gif BIP pop / gidtid faceting 2-5-5-5). It has 5 stars, 1+1 pegs, 5 trigs, and 5 squares.
F19. Sefpopeph - (sef PO peff / sidtid faceting 5-5-5-6). It has 5 stars, 1+5 pegs, 5 trigs, and 5 squares.
F20. Gefpopeph - (gef PO peff / gidtid faceting 5-5-5-6). It has 1+5 pegs, 5 pegs, 5 trigs, and 5 squares.
F21. Defhodha - (def HAH tha / ditdid faceting 6-0-10-6a). It has 1+5 stars, 1+5 pegs, and 10 squares.
F22. Defhodhib - (def HAH thib / ditdid faceting 6-0-10-6b). It has 1+5 stars, 1+5 pegs, and 10 squares.
There are two of these plus one compound, all orientable. The cube ones have pyritic/protrappic symmetry with five orientations, quistet has kitettic symmetry and has 10 orientations, two in each symmetry.
35. Cube - (CYOOB / cube). It has 6 squares.
C4. Forcube - (FOR cyoob / compound of four cubes). It has 24 squares.
36. Quistet - (QUIZ tet / quadratisnub tetratetrahedron). It has 4+4 trigs and 12 squares.
C5. Cubinquistet - (QYOO bin QUIZ tet / cube and quistet). It has 8 trigs and 18 squares.
There are five of these, a fissary, plus two cube compounds. All are orientable except the first two and last two. They have 10 orientations.
37. Gifhahawo - (gif HA ha wo / gidtid faceting 6-6-12-0). It has 6 pegs, 6 trigs, and 12 squares.
38. Sifhahawo - (sif HA ha wo / sidtid faceting 6-6-12-0). It has 6 stars, 6 trigs, and 12 squares.
39. Gifharho - (gif HAR ho / gidtid faceting 6-14-6-0). It has 6 pegs, 14 trigs, and 6 squares.
40. Sifharho - (sif HAR ho / sidtid faceting 6-14-6-0). It has 6 stars, 14 trigs, and 6 squares.
41. Defhohah - (DEF ho hah / ditdid faceting 6-0-6-6). It has 6 stars, 6 pegs, and 6 squares.
F23. Fedifhohah - (fe DIF ho hah / fissary ditdid faceting 6-0-6-6). It has 6 stars, 6 pegs, and 6 squares.
C6. Tucube - (TOO cyoob / compound of two cubes). It has 12 squares.
C7. Threcube - (THREE cyoob / compound of three cubes). It has 18 squares.
C8. 2Trippescu - (too trip PES coo / compound of two trippescus). It has 6 pegs, 6 trigs, and 6 squares.
C9. 2Ditpascu - (too dit PAS coo / compound of two ditpascus). It has 6 stars, 6 trigs, 6 squares.
There are six of these. They have 20 orientations with two in each symmetry. Those with 12 squares are orientable, the 18 squared ones are not.
42. Gifhibwo - (gif HIB wo / gidtid faceting 6-2-12-0). It has 6 pegs, 2 trigs, and 12 squares.
43. Sifhibwo - (sif HIB wo / sidtid faceting 6-2-12-0). It has 6 stars, 2 trigs, and 12 squares.
44. Gifhibyo - (gif HIB yo / gidtid faceting 6-2-18-0). It has 6 pegs, 2 trigs, and 18 squares.
45. Sifhibyo - (sif HIB yo / sidtid faceting 6-2-18-0). It has 6 stars, 2 trigs, and 18 squares.
46. Rifowwo - (RIFF o wo / rhom faceting 0-12-12-0). It has 12 trigs and 12 squares.
47. Rifowyo - (RIFF o yo / rhom faceting 0-12-18-0). It has 12 trigs and 18 squares.
There are 33 of these. Also two compounds. They have 20 orientations with two in each symmetry.
48. Trippescu - (trip PES coo / tripod pentagonized semicupola). It has 3 pegs, 3 trigs, and 3 squares.
49. Ditpascu - (dit PAS coo / ditrigon pentagramized semicupola). It has 3 stars, 3 trigs, and 3 squares.
50. - ( / ). It has 3 pegs, 7 trigs, and 9 squares.
51. - ( / ). It has 3 stars, 7 trigs, and 9 squares.
52. - ( / ). It has 3 pegs, 7 trigs, and 9 squares.
53. - ( / ). It has 3 stars, 7 trigs, and 9 squares.
54. - ( / ). It has 3 stars, 3 pegs, and 6 squares.
55. Dritit - (DRIT it / dirhombitritrihedron). It has 3 stars, 3 pegs, and 6 squares.
56. - ( / ). It has 3 stars, 3 pegs, and 12 squares.
57. - ( / ). It has 3 stars, 3 pegs, 10 trigs, and 6 squares.
58. - ( / ). It has 3 stars, 3 pegs, 10 trigs, and 6 squares.
59. - ( / ). It has 6 pegs, 10 trigs, and 6 squares.
60. - ( / ). It has 6 stars, 10 trigs, and 6 squares.
61. - ( / ). It has 3 stars, 6 pegs, 3 trigs, and 3 squares.
62. - ( / ). It has 6 stars, 3 pegs, 3 trigs, and 3 squares.
63. - ( / ). It has 3 stars, 6 pegs, 3 trigs, and 9 squares.
64. - ( / ). It has 6 stars, 3 pegs, 3 trigs, and 9 squares.
65. - ( / ). It has 3 stars, 6 pegs, 7 trigs, and 3 squares.
66. - ( / ). It has 6 stars, 3 pegs, 7 trigs, and 3 squares.
67. - ( / ). It has 3 stars, 6 pegs, 13 trigs, and 3 squares.
68. - ( / ). It has 6 stars, 3 pegs, 13 trigs, and 3 squares.
69. - ( / ). It has 6 stars, 6 pegs, and 6 squares.
70. - ( / ). It has 6 stars, 6 pegs, and 6 squares.
71. - ( / ). It has 6 stars, 6 pegs, and 6 trigs.
72. - ( / ). It has 6 stars, 6 pegs, and 10 trigs.
73. - ( / ). It has 6 stars, 6 pegs, and 10 trigs.
74. - ( / ). It has 6 stars, 6 pegs, and 10 trigs.
75. - ( / ). It has 6 stars, 6 pegs, and 10 trigs.
76. - ( / ). It has 6 stars, 6 pegs, and 14 trigs.
77. - ( / ). It has 9 pegs, 17 trigs, and 3 squares.
78. - ( / ). It has 9 stars, 17 trigs, and 3 squares.
79. - ( / ). It has 6 stars, 9 pegs, 3 trigs, and 3 squares.
80. - ( / ). It has 9 stars, 6 pegs, 3 trigs, and 3 squares.
C10. - ( / ). It has 6 pegs, 10 trigs, and 12 squares.
C11. - ( / ). It has 6 stars, 10 trigs, and 12 squares.
There are 42 of these. They have 20 orientations with two in each symmetry.
F24. Frifowwo - (FRIF o wo / fissary rhom faceting 0-12-12-0). It has 12 trigs and 12 squares.
F25. Frifowyo - (FRIF o yo / fissary rhom faceting 0-12-18-0). It has 12 trigs and 18 squares.
F26. - ( / ). It has 3 pegs, 3 trigs, and 15 squares.
F27. - ( / ). It has 3 stars, 3 trigs, and 15 squares.
F28. - ( / ). It has 3 pegs, 7 trigs, and 9 squares.
F29. - ( / ). It has 3 stars, 7 trigs, and 9 squares.
F30. - ( / ). It has 3 pegs, 7 trigs, and 9 squares.
F31. - ( / ). It has 3 stars, 7 trigs, and 9 squares.
F32. - ( / ). It has 3 pegs, 15 trigs, and 15 squares.
F33. - ( / ). It has 3 stars, 15 trigs, and 15 squares.
F34. - ( / ). It has 3 stars, 3 pegs, and 12 squares.
F35. - ( / ). It has 3 stars, 3 pegs, 2 trigs, and 12 squares.
F36. - ( / ). It has 3 stars, 3 pegs, 2 trigs, and 12 squares.
F37. - ( / ). It has 3 stars, 3 pegs, 6 trigs, and 12 squares.
F38. - ( / ). It has 3 stars, 3 pegs, 10 trigs, and 6 squares.
F39. - ( / ). It has 3 stars, 3 pegs, 10 trigs, and 6 squares.
F40. - ( / ). It has 3 stars, 3 pegs, 12 trigs, and 12 squares.
F41. - ( / ). It has 6 pegs, 2 trigs, and 12 squares.
F42. - ( / ). It has 6 stars, 2 trigs, and 12 squares.
F43. - ( / ). It has 6 pegs, 2 trigs, and 18 squares.
F44. - ( / ). It has 6 stars, 2 trigs, and 18 squares.
F45. - ( / ). It has 6 pegs, 10 trigs, and 10 squares.
F46. - ( / ). It has 6 stars, 10 trigs, and 10 squares.
F47. - ( / ). It has 6 pegs, 10 trigs, and 6 squares.
F48. - ( / ). It has 6 stars, 10 trigs, and 6 squares.
F49. - ( / ). It has 3 stars, 6 pegs, 3 trigs, and 9 squares.
F50. - ( / ). It has 6 stars, 3 pegs, 3 trigs, and 9 squares.
F51. - ( / ). It has 3 stars, 6 pegs, 5 trigs, and 9 squares.
F52. - ( / ). It has 6 stars, 3 pegs, 5 trigs, and 9 squares.
F53. - ( / ). It has 3 stars, 6 pegs, 5 trigs, and 9 squares.
F54. - ( / ). It has 6 stars, 3 pegs, 5 trigs, and 9 squares.
F55. - ( / ). It has 3 stars, 6 pegs, 7 trigs, and 3 squares.
F56. - ( / ). It has 6 stars, 3 pegs, 7 trigs, and 3 squares.
F57. - ( / ). It has 3 stars, 6 pegs, 7 trigs, and 9 squares.
F58. - ( / ). It has 6 stars, 3 pegs, 7 trigs, and 9 squares.
F59. - ( / ). It has 3 stars, 6 pegs, 13 trigs, and 3 squares.
F60. - ( / ). It has 6 stars, 3 pegs, 13 trigs, and 3 squares.
F61. - ( / ). It has 6 stars, 6 pegs, 2 trigs, and 6 squares.
F62. - ( / ). It has 6 stars, 6 pegs, 2 trigs, and 12 squares.
F63. - ( / ). It has 6 stars, 6 pegs, 6 trigs, and 6 squares.
F64. - ( / ). It has 9 pegs, 5 trigs, and 15 squares.
F65. - ( / ). It has 9 stars, 5 trigs, and 15 squares.
There are 15 of these. They have 40 orientations with four in each symmetry.
81. - ( / ). It has 3 pegs, 7 trigs, and 9 squares.
82. - ( / ). It has 3 stars, 7 trigs, and 9 squares.
83. - ( / ). It has 3 pegs, 7 trigs, and 9 squares.
84. - ( / ). It has 3 stars, 7 trigs, and 9 squares.
85. - ( / ). It has 3 pegs, 7 trigs, and 9 squares.
86. - ( / ). It has 3 stars, 7 trigs, and 9 squares.
87. - ( / ). It has 8 trigs and 12 squares.
88. - ( / ). It has 3 pegs, 11 trigs, and 9 squares.
89. - ( / ). It has 3 stars, 11 trigs, and 9 squares.
90. - ( / ). It has 3 stars, 3 pegs, 2 trigs, and 12 squares.
91. - ( / ). It has 3 stars, 3 pegs, 6 trigs, and 6 squares.
92. - ( / ). It has 3 stars, 3 pegs, 6 trigs, and 6 squares.
93. - ( / ). It has 3 stars, 3 pegs, 8 trigs, and 6 squares.
94. - ( / ). It has 3 stars, 3 pegs, 10 trigs, and 6 squares.
95. - ( / ). It has 3 stars, 3 pegs, 10 trigs, and 6 squares.
There are six of these, a fissary, and three compounds. They have 15 orientations with three in each symmetry. All are orientable except fooo and dafoooo, that sounded weird.
96. Defquooq - (def QUOOK / ditdid faceting 4-8-0-4). It has 4 stars, 4 pegs, and 8 trigs.
97. Gifowoq - (GIF o wok / gidtid faceting 8-12-0-4). It has 4 stars, 8 pegs, and 12 trigs.
98. Sifowoq - (SIF o wok / sidtid faceting 8-12-0-4). It has 8 stars, 4 pegs, and 12 trigs.
99. Dafoooo - (da FOOOO / ditdid faceting 8-8-0-8). It has 8 stars, 8 pegs, and 8 trigs. The plural is also dafoooo (no 's'). There's a sishi scaliform with 120 dafoooo.
100. Rofquooq - (rof QUOOK / ditdid faceting 4-0-8-4). It has 4 stars, 4 pegs, and 8 squares.
101. Defquoxo - (def QUOK so / ditdid faceting 4-0-16-0). It has 4 stars, 4 pegs, and 16 squares.
F66. Fooo - (FOOO / fissary octoctoctahedron). It has 8 stars, 8 pegs, and 8 squares.
C12. 2Stopper - (TOO stop per / compound of two stoppers). It has 4 stars, 4 pegs, 8 trigs, and 8 squares.
C13. 2Gif Bhequo - (TOO gif VEE quo / compound of two gif bhequoes). It has 4 pegs, 12 trigs, and 8 squares.
C14. 2Sif Bhequo - (TOO sif VEE quo / compound of two sif bhequoes). It has 4 stars, 12 trigs, and 8 squares.
There are two of these. They have 30 orientations with six in each symmetry. Both are orientable.
102. Sifqueqdo - (sif QUEEK doe / sidtid faceting 4-4-12-0). It has 4 stars, 4 trigs, and 12 squares.
103. Gifqueqdo - (gid QUEEK doe / gidtid faceting 4-4-12-0). It has 4 pegs, 4 trigs, and 12 squares.
There are many of these. They have 30 orientations with two in each symmetry.
104. Stopper - (STOP per / star pentagonal rhombihedron). It has 2 stars, 2 pegs, 4 trigs, and 4 squares.
105. Stapper - (STAP per / star pentagonal retrohedron). It has 2 stars, 2 pegs, 4 trigs, and 2 squares.
106. Gif Bhequo - (gif VEE quo / gidtid faceting 2-6-4-0). It has 2 pegs, 6 trigs, and 4 squares.
107. Sif Bhequo - (sif VEE quo / sidtid faceting 2-6-4-0). It has 2 stars, 6 trigs, and 4 squares.
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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