Category 8: Great Rhombates

grip grit grico grahi grix girfix graghi graggix gaqrit gaqri gaqrigaghi gaqrigafix gaqrisashi gaqrigagishi gaqrigashi thatoth thaquitoth iquatoc hixthix dahitady hihiquatady dahiquatady hixquathix


There are 23 great rhombates (also called cantitruncates or even shortened to "grombates"). Of the great rhombates, 5 are convex, 3 are starry, 7 are great quasirhombates, and 8 are like cotco and idtid. They all have "scalenoid" verfs (where a scalenoid is a tetrahedron with only bilateral symmetry). Below are the 23 great rhombates.
Great Rhombates

Convex Great Rhombates

Verfs of the Convex Great Rhombates

These five are convex.

307. Grip - (GRIP) great rhombated pentachoron better known as cantitruncated pentachoron. Its symbol is oxxx, it has 60 verts. Its cells are 5 tuts, 5 toes, and 10 trips. It has 20 pieces of three types and has pennic symmetry, LOC = 12.

308. Grit - (GRIT) great rhombated tesseract (cantitruncated tesseract). Its symbol is oxx'x, it has 192 verts. Its cells are 8 gircoes, 16 tuts, and 32 trips. It has 56 pieces of three types and has tessic symmetry, LOC = 12.

309. Grico - (GRE ko) great rhombated icositetrachoron (cantitruncated 24). It's symbol is ox'xx, and it has 576 verts. It has 24 gircoes, 24 tics, and 96 trips. It has 144 pieces of three types and has icoic symmetry, LOC = 12.

310. Grahi - (GRAH he) great rhombated 120 (cantitruncated 120). Its symbol is oxx^x and it has 7200 verts. Its cells are 120 grids, 600 tuts, and 1200 trips. It has 1920 pieces of three types and has hyic symmetry, LOC = 12.

311. Grix - (GRIKS) great rhombated 600 (cantitruncated 600). Its symbol is xxx^o and it has 7200 verts. Its cells are 120 tis, 600 toes, and 720 pips. It has 1440 pieces of three types and has hyic symmetry, LOC = 12.


Starry Great Rhombates

Verfs of the Starry Great Rhombates

These three are the starry ones. All of these have hyic symmetry and 7200 vertices.

312. Girfix - (GUR fix) great rhombated fix. Its symbol is xx^x*o. It has 120 grids, 120 tigids, and 720 stips. It has 3240 pieces of three types, LOC = 29.

313. Graghi - (GRAG hi) great rhombated gahi. Its symbol is o*xx^x. The cells are 120 grids, 120 tiggies, and 720 stips. It has 22440 pieces of five types, LOC = 87.

314. Graggix - (GRAG gix) great rhombated gax. Its symbol is xxx*o. Its cells are 600 toes, 120 tiggies, and 720 stips. It has 294,480 pieces of 31 types, LOC = 1052.


Great Quasirhombates

Verfs of the Great Quasirhombates

There are seven of these, all of which look quite interesting, gaqrit has tessic symmetry, gaqri has icoic symmetry, all others have hyic symmetry.

315. Gaqrit - (GAY krit) great quasirhombated tesseract. Its symbol is oxx"x, and it has 192 verts. Its cells are 8 quitcoes, 16 tuts, and 32 trips. It has 512 pieces of 7 types, LOC = 80.

316. Gaqri - (GAH kree) great quasirhombated ico. Its symbol is ox"xx, and it has 576 verts. Its cells are 24 quitcoes, 24 quiths, and 96 trips. It has 2856 pieces of eight types, LOC = 105.

317. Gaqrigaghi - (ga KRIG ga gee) great quasirhombated gaghi. Its symbol is ox*'x^x, and it has 7200 verts. Its cells are 120 quitdids, 120 quit gissids, and 1200 trips. It has 205,320 pieces of 23 types, LOC = 795.

318. Gaqrigafix - (ga KRIG ga fix) great quasirhombated gofix. Its symbol is o^x*'xx, and it has 7200 verts. Its cells are 120 gaquatids, 120 quit sissids, and 720 pips. It has 468,240 pieces of 44 types, LOC = 1316. This one looks amazing.

319. Gaqrisashi - (GAH krih SAS she) great quasirhombated sishi. Its symbol is ox^x*'x, and it has 7200 verts. Its cells are 120 quitdids, 120 tids, and 1200 trips. It has 20640 pieces of 7 types, LOC = 89.

320. Gaqrigagishi - (ga KRIG ga GISH she) great quasirhombated gogishi. Its symbol is oxx*'x, and it has 7200 verts. Its cells are 120 gaquatids, 600 tuts, and 1200 trips. This one has 786,000 pieces of 70 types, LOC = 1997 - which makes it the most complex one of this category.

321. Gaqrigashi - (ga KRIG ga she) great quasirhombated gishi. Its symbol is o^xx*'x, and it has 7200 verts. Its cells are 120 gaquatids, 120 tis, and 720 pips. It has 119,880 pieces of 21 types, LOC = 367.


Cotcoics

Verfs of the Cotcoics

Lets define the word "cotcoic" to represent any simplex vertex figured polytope which contains either cotcoes or idtids in them. There are eight cotcoics in this category. Thatoth and thaquitoth have tessic symmetry, iquatoc has icoic symmetry, while the remaining five have hyic symmetry.

322. Thatoth - (THAT oth) tesseracti16truncated tesseract16. Its symbol is o(x'x"x), it has 192 verts. Its cells are 8 cotcoes, 8 tics, and 16 tuts. This simple one has 152 pieces of four types, LOC = 36.

323. Thaquitoth - (THAK kwih toth) tesseracti16quasitruncated tesseracti16. Its symbol is o(x"x'x), it has 192 verts. Its cells are 8 cotcoes, 8 quiths, and 16 tuts. It has 392 pieces of 7 types, LOC = 70.

324. Iquatoc - (I kwa toc) 24quasitruncated 48. Its symbol is o(x"xx'), it has 576 verts. Its cells are 24 cotcoes, 24 quiths, and 24 tics. It has 528 pieces of four types, LOC = 56.

325. Hixthix - (HIX thix) 120-600truncated 120-600. Its symbol is o(x^x*'x), it has 7200 verts. Its cells are 120 idtids, 120 tids, and 600 tuts. It has 5520 pieces of four types, LOC = 36.

326. Dahitady - (da HIT a dee) dis120truncated dis120. Its symbol is o*(x^x*'x), it has 7200 verts. Its cells are 120 idtids, 120 tigids, and 120 tiggies. It has 82440 pieces of 12 types, LOC = 406.

327. Hihiquatady - (HI he QUAT a dee) 120-120quasitruncated dis120. Its symbol is o(x*'xx^), it has 7200 verts. Its cells are 120 idtids, 120 tids, and 120 quit gissids. It has 8520 pieces of four types, LOC = 57.

328. Dahiquatady - (DA he QUAT a dee) dis120quasitruncated dis120. Its symbol is o^(x*'x^x), it has 7200 verts. Its cells are 120 idtids, 120 tis, and 120 quit sissids. It has 13560 pieces of six types, LOC = 65.

329. Hixquathix - (HIX qua thix) 120-600quasitruncated 120-600. Its symbol is o(x*'x^x), it has 7200 verts. Its cells are 120 idtids, 120 quit gissids, and 600 tuts. It has 108,120 pieces with 13 types, LOC = 342.


Conjugates

Below shows how the great rhombates pair up as conjugates.

Conjugates

The following are self conjugates: grip, iquatoc, and hihiquatady.

The following are conjugate pairs: grit-gaqrit, grico-gaqri, grahi-gaqrigagishi, grix-graggix, girfix-gaqrigafix, graghi-gaqrigashi, gaqrigaghi-gaqrisashi, thatoth-thaquitoth, hixthix-hixquathix, dahitady-dahiquatady.

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