Category 9: Omnitruncates

gippid gidpith gippic gidpixhi gaquidpoth gaquapac gaquidipdy goquidipdy gaquidphihi gaquidapixhi thatpath thaquitpath iquatpic doc croc coqroc hixtaphix dohitipady hixquitphix sidhiquit paddy gidhiquit paddy xithi


There are 22 omnitruncates (also called great prismates). Of these, 4 are convex, 6 are great quasiprismates, 8 are cotcoics, and 4 are of another sort. They all have irregular tetrahedron verfs (some like gaquapac have a skewed disphenoid verf). Below are the 22 omnitruncates.
Omnitruncates

Convex Omnitruncates

Verfs of the Convex Omnitruncates

These four are convex. Of these, gippid and gippic have the skewed disphenoid verfs.

330. Gippid - (GIP pid) great prismatodecachoron better known as omnitruncated pentachoron. Its symbol is xxxx, it has 120 verts. Its cells are 10 toes and 20 hips. It has 30 pieces with two types and has deca symmetry. LOC = 12.

331. Gidpith - (GID pith) great disprismatotesseracti16 (omnitruncated tesseract). Its symbol is xxx'x, it has 384 verts. Its cells are 8 gircoes, 16 toes, 24 ops, and 32 hips. It has 80 pieces with four types and has tessic symmetry. LOC = 24.

332. Gippic - (GIP pik) great prismato48 (omnitruncated 24). It's symbol is xx'xx, and it has 1152 verts. It has 48 gircoes and 192 hips. It has 240 pieces with two types and has contic symmetry. LOC = 12.

333. Gidpixhi - (gid PIK she) great disprismato600-120 (omnitruncated 120). Its symbol is xxx^x and it has 14400 verts. Its cells are 120 grids, 600 toes, 720 dips, and 1200 hips. It has 2640 pieces with four types and has hyic symmetry. LOC = 24.


Great Quasiprismates

Verfs of the Great Quasiprismates

There are six of these. Gaquidpoth is tessic (384 verts), gaquapac is contic (1152 verts), all others are hyic (14400 verts). Gaquapac also has skewed disphenoid verf.

334. Gaquidpoth - (ga QUID poth) great quasidisprismatotesseracti16. Its symbol is xxx"x. Its cells are 8 quitcoes, 16 toes, 24 stops, and 32 hips. It has 536 pieces in 8 types. LOC = 104.

335. Gaquapac - (GA qua pak) great quasiprismato48. Its symbol is xx"xx. It has 48 quitcoes and 196 hips. It has 145,728 pieces with 77 types. LOC = 3178.

336. Gaquidipdy - (GA qua DIP dee) grand quasidisprismatodis120. Its symbol is xx*'x^x. The cells are 120 quitdids, 120 gaquatids, 720 dips, and 1200 hips. It has 1,594,080 pieces with 125 types. LOC = 5075. It ranks number two in complexity in this category.

337. Goquidipdy - (GO qua DIP dee) great quasidisprismatodis120. Its symbol is xx^x*'x. Its cells are 120 quitdids, 120 grids, 720 stiddips, and 1200 hips. It has 21,360 pieces with 8 types. LOC = 113.

338. Gaquidphihi - (GAY quid FI hee) great quasidisprismato120-120. Its symbol is x^xx*'x. Its cells are 120 gaquatids, 120 grids, 720 stiddips, and 720 dips. This one looks interesting, it has 105,240 pieces with 12 types. LOC = 363.

339. Gaquidapixhi - (ga QUID a PIK she) great quasidisprismato600-120. Its symbol is xxx*'x. Its cells are 120 gaquatids, 600 toes, 720 stiddips, and 1200 hips. It's the most complex one in this category with 1,616,400 pieces in 130 types. LOC = 6651.


Cotcoics

Verfs of the Cotcoics

There are eight of these, thatpath and thaquitpath have tessic symmetry with 384 verts, iquatpic has icoic symmetry with 1152 verts, all others have hyic symmetry with 14400 verts.

340. Thatpath - (THAT path) tesseracti16truncated prismatotesseracti16. Its symbol is x(x'x"x). Its cells are 8 cotcoes, 8 gircoes, 16 toes, and 24 stops. It has 176 pieces in 5 types. LOC = 60.

341. Thaquitpath - (THAK wit path) tesseracti16quasitruncated prismatotesseracti16. Its symbol is x(x"x'x). Its cells are 8 cotcoes, 8 quitcoes, 16 toes, and 24 ops. It has 2688 pieces with 18 types. LOC = 389.

342. Iquatpic - (i QUAT pic) 24quasitruncated prismato48. Its symbol is x(x"xx'). Its cells are 24 quitcoes, 24 cotcoes, 24 gircoes, and 96 hips. It has 1800 pieces with 8 types. LOC = 122.

343. Hixtaphix - (HIX ta fix) 120-600truncated prismato120-600. Its symbol is x(x^x*'x). Its cells are 120 idtids, 120 grids, 600 toes, and 120 stiddips. It has 6240 pieces in 5 types. LOC = 60.

344. Dohitipady - (DOE hit TIP a dee) dis120truncated prismatodis120. Its symbol is x(x*'xx^). Its cells are 120 idtids, 120 gaquatids, 120 grids, and 1200 hips. It has 100,920 pieces in 16 types. LOC = 382.

345. Hixquitphix - (HIX quit fix) 120-600quasitruncated prismato120-600. Its symbol is x(x*'x^x). Its cells are 120 idtids, 120 gaquatids, 600 toes, and 720 dips. It has 717,960 pieces with 63 types. LOC = 1883.

346. Sidhiquit Paddy - (sid HIK wit pad dee) small dis120quasitruncated prismatodis120. Its symbol is x^(x*'x^x). Its cells are 120 idtids, 120 quitdids, 120 grids, and 720 dips. It has 104,880 pieces with 18 types. LOC = 405.

347. Gidhiquit Paddy - (gid HIK wit pad dee) great dis120quasitruncated prismatodis120. Its symbol is x*'(x^x*'x). Its cells are 120 idtids, 120 quitdids, 120 gaquatids, and 720 stiddips. It has 250,920 pieces in 30 types. LOC = 931.


Others

Verfs of the Other Omnitruncates

These don't have prisms within their cells. They all have contic symmetry with 1152 verts and a skewed disphenoid verf - except for xithi which is hyic, has 14400 verts and has an irregular tet verf. Croc and coqroc can also be considered as cotcoics, but they are of another sort.

348. Doc - (DOK) dis48. Its symbol is (x'xx"x). Its cells are 48 gircoes and 48 quitcoes. It has 9120 pieces with 10 types. LOC = 197.

349. Croc - (KROK) 48rhombated 48. Its symbol is (x(x'x)"x). Its cells are 48 cotcoes and 48 gircoes. It has 1008 pieces in three types. LOC = 40.

350. Coqroc - (KO krok) 48quasirhombated 48. Its symbol is (x(x"x)'x). Its cells are 48 cotcoes and 48 quitcoes. It has 9216 pieces with 9 types. LOC = 241.

351. Xithi - (ZITH thee) 600tris120. Its symbol is (xx^x*'x). Its cells are 120 grids, 120 gaquatids, 120 quitdids, and 600 toes. It has 222,360 pieces with 29 types. LOC = 989.


Conjugates

Below shows how the omnitruncates pair up as conjugates.

Conjugates

The following are self conjugates: gippid, gaquidphihi, iquatpic, dohitipady, doc, and xithi.

The following are conjugate pairs: gidpith-gaquidpoth, gippic-gaquapac, gidpixhi-gaquidapixhi, gaquidipdy-goquidipdy, thatpath-thaquitpath, hixtaphix-hixquitphix, sidhiquit paddy-gidhiquit paddy, croc-coqroc.

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