Category 10: Prismatorhombates


This category deals with the polychora with trapezoid pyramid (trapyr for short) vertex figures along with their regiments. There are 30 regiments of 3. Prismatorhombates can also be called prismatotruncates and are also called cantetruncates (Norman Johnson), they have xoxx type symbols. There are other trapyr-verted polytopes mentioned here also that are not technically "prismatorhombates", but they do have similar verfs. Convex ones are prip, prit, proh, prico, prahi, and prix. They are all tame. The first two of each regiment are orientable, while the last one is non. Prip is the only pentachoric regiment, its members have 60 vertices. Prit, Proh, Quiproh, and Gichado regiments have tessic symmetry and these polychora have 192 vertices. Prico, Suti, Ditdi, and Gipti regiments have icoic symmetry with 576 vertices. All others have 7200 vertices with hyic symmetry. The regiments can be subdivided into the following groups: Convex (prip-prix), Starry (pirshi-pirgaghi), Quippirs (quiproh-quippirgax), Paquers (gichado-gippixady), Cotcoic (suti-sixathi) and Ditrigonal (gid tipathi-sphiddix). Following is a list of the 90 prismatorhombates.

Prip Regiment

Prip Regiment Verfs

Prip is the last of the pentachoric regiments currently known. This regiment shows up quite a bit in the uniform polytera as facets.

352. Prip - (PRIP) prismatorhombated pentachoron, more commonly called cantetruncated pentachoron (Norman Johnson). Its cells are 5 coes, 5 tuts, 10 trips, and 10 hips. Its symbol is xxox.

353. Pittip - (PIT tip) prismatotrispentachoron. Its cells are 5 ohoes, 5 tuts, 5 toes, and 10 trips. Its symbol is x(xo,x).

354. Ripdip - (RIP dip) rhombiprismic dispentachoron. Its cells are 5 choes, 5 toes, and 10 hips.

Sample slices of them are below in same order.

Prip Regiment Slices


Prit Regiment

Prit Regiment Verfs

The prit regiment also shows up quite a bit as polyteron facets.

355. Prit - (PRIT) prismatorhombated tesseract, more commonly called cantetruncated 16. Its cells are 8 sircoes, 16 tuts, 24 cubes, and 32 hips. Its symbol is xxo'x.

356. Sichado - (SICH a do) small cubi16disoctachoron. Its cells are 8 soccoes, 16 tuts, 24 cubes, and 8 gircoes. Its symbol is x(x'x'o,).

357. Sirpdo - (SIRP do) small rhombiprismic disoctachoron. Its cells are 8 srohs, 8 gircoes, and 32 hips.

Sample slices of them are below in same order.

Prit Regiment Slices


Proh Regiment

Proh Regiment Verfs

This regiment shows up as polyteron facets also, it is quite blockish.

358. Proh - (PRO) prismatorhombated 16, more commonly called cantetruncated tesseract. Its cells are 8 tics, 16 coes, 32 trips, and 24 ops. Its symbol is xox'x, also oo'xo.

359. Siphado - (SIFF a do) small prismato16disoctachoron. Its cells are 8 tics, 16 ohoes, 32 trips, and 8 gircoes. Its symbol is x'(xo,x).

360. Sirpith - (SIR pith) small rhombiprismic tesseracti16. Its cells are 16 choes, 24 ops, and 8 gircoes.

Sample slices of them are below in same order.

Proh Regiment Slices


Prico Regiment

Prico Regiment Verfs

Prico members below, verfs above.

361. Prico - (PRE co) prismatorhombated 24, more commonly called cantetruncated 24. Its cells are 24 sircoes, 24 toes, 96 trips, and 96 hips. Its symbol is xx'ox.

362. Sipti - (SIP tee) small prismatotris24. Its cells are 24 soccoes, 24 toes, 96 trips, and 24 gircoes. Its symbol is x(x'x,o').

363. Sirpdi - (SIRP dee) small rhombiprismic dis24. Its cells are 24 srohs, 24 gircoes, and 96 hips.

Sample slices of them are below in same order.

Prico Regiment Slices


Prahi Regiment

Prahi Regiment Verfs

Prahi members below, verfs above.

364. Prahi - (PRAH hee) prismatorhombated 120, more commonly called cantetruncated 600. Its cells are 120 srids, 600 tuts, 720 pips, and 1200 hips. Its symbol is xxo^x.

365. Spixady - (SPIX a dee) small prismato600dis120. Its cells are 120 saddids, 600 tuts, 720 pips, and 120 grids. Its symbol is x(x^x^o,).

366. Sripady - (SRIP a dee) small rhombiprismic dis120. Its cells are 120 sirds, 120 grids, and 1200 hips.

Sample slices of them are below in same order.

Prahi Regiment Slices


Prix Regiment

Prix Regiment Verfs

Prix members below, verfs above.

367. Prix - (PRIX) prismatorhombated 600, more commonly called cantetruncated 120. Its cells are 120 tids, 600 coes, 1200 trips, and 720 dips. Its symbol is xox^x.

368. Spixhihy - (spic SHI he) small prismato600-120-120. Its cells are 120 tids, 600 ohoes, 1200 trips, and 120 grids. Its symbol is x^(x,ox).

369. Sirpaxhi - (sir PAK she) small rhombiprismic 600-120. Its cells are 600 choes, 120 grids, and 720 dips.

Sample slices of them are below in same order.

Prix Regiment Slices


Pirshi Regiment

Pirshi Regiment Verfs

Pirshi members below, verfs above.

370. Pirshi - (PIR she) prismatorhombated stellated 600. Its cells are 120 radeds, 120 tis, 720 stips, and 1200 hips. Its symbol is xx^o*x.

371. Sphihix - (SRAWV a thee) small retrosphenoverted tris120. Its cells are 120 ideds, 120 tis, 720 stips, and 600 toes. Its symbol is x(xx*'o^).

372. Sriphix - (ra SHI he) rhombic small 120-120. Its cells are 120 ris, 600 toes, and 1200 hips.

Sample slices of them are below in same order.

Pirshi Regiment Slices


Pirghi Regiment

Pirghi Regiment Verfs

Pirghi members below, verfs above.

373. Pirghi - (PIRG hi) prismatorhombated great 120. Its cells are 120 radeds, 120 tigids, 720 pips, and 720 dips. Its symbol is x^x*o^x.

374. Siphidy - (sif FI dee) small prismato120dis120. Its cells are 120 ideds, 120 tigids, 720 pips, and 120 grids. Its symbol is x^(xx^o*').

375. Sirphihy - (sir FI he) small rhombiprismic 120-120. Its cells are 120 ris, 720 dips, and 120 grids.

Sample slices of them are below in same order.

Pirghi Regiment Slices


Pirgaghi Regiment

Pirgaghi Regiment Verfs

Sirghi members below, verfs above.

376. Pirgaghi - (pir GAG hi) prismatorhombated great grand 120. Its cells are 120 radeds, 120 tiggies, 720 pips, and 1200 hips. Its symbol is xx*o^x.

377. Giphihix - (GIF fee hix) great prismato120-120-600. Its cells are 120 ideds, 120 tiggies, 720 pips, and 600 toes. Its symbol is x(xx^o*').

378. Griphix - (GRIF fix) great rhombiprismic 120-600. Its cells are 120 ris, 1200 hips, and 600 toes.

Sample slices of them are below in same order.

Pirgaghi Regiment Slices


Quiproh Regiment

Quiproh Regiment Verfs

Quiproh members below, verfs above. This cool looking regiment also shows up in polytera.

379. Quiproh - (quip RO) quasiprismatorhombated 16. Its cells are 8 quiths, 16 coes, 32 trips, and 24 stops. Its symbol is xox"x.

380. Giphado - (GIF a do) great prismato16disoctachoron. Its cells are 8 quiths, 16 ohoes, 32 trips, and 8 quitcoes. Its symbol is x"(xo,x).

381. Girpith - (GIR pith) great rhombiprismic tesseracti16. Its cells are 16 choes, 24 stops, and 8 quitcoes.

Sample slices of them are below in same order.

Quiproh Regiment Slices


Quippirfix Regiment

Quippirfix Regiment Verfs

Members below, verfs above.

382. Quippirfix - (QUIP per fix) quasiprismatorhombated faceted 600. Its cells are 120 srids, 120 quit sissids, 1200 trips, and 720 stiddips. Its symbol is x*'x^ox.

383. Gipthi - (GIP thee) great prismatotris120. Its cells are 120 saddids, 120 quit sissids, 1200 trips, and 120 quitdids. Its symbol is x*'(x^x,o^).

384. Rappady - (RAP a dee) rhombiprismic dis120. Its cells are 120 sirds, 720 stiddips, and 120 quitdids.

Sample slices of them are below in same order.

Quippirfix Regiment Slices


Quippirgashi Regiment

Quippirgashi Regiment Verfs

Members below, verfs above.

385. Quippirgashi - (QUIP per GASH she) quasiprismatorhombated grand stellated 120. Its cells are 120 radeds, 120 quit sissids, 720 stips, and 720 stiddips. Its symbol is x*'x^o*x.

386. Giphidy - (gif FI de) great prismato120dis120. Its cells are 120 ideds, 120 quit sissids, 720 stips, and 120 gaquatids. Its symbol is x*'(xx*'o^).

387. Girphihy - (gir FI de) great rhombiprismic 120-120. Its cells are 120 ris, 720 stiddips, and 120 gaquatids.

Sample slices of them are below in same order.

Quippirgashi Regiment Slices


Quippirghi Regiment

Quippirghi Regiment Verfs

Members below, verfs above.

388. Quippirghi - (QUIP pirg hi) quasiprismatorhombated grand 120. Its cells are 120 srids, 120 quit gissids, 720 pips, and 720 stiddips. Its symbol is x*'xo^x.

389. Gapthi - (GAP thee) grand prismatotris120. Its cells are 120 saddids, 120 quit gissids, 720 pips, and 120 quitdids. Its symbol is x*'(x^x^o,).

390. Raphihy - (ra FI de) rhombiprismic 120-120. Its cells are 120 sirds, 720 stiddips, and 120 quitdids.

Sample slices of them are below in same order.

Quippirghi Regiment Slices


Quippirgax Regiment

Quippirgax Regiment Verfs

Members below, verfs above.

391. Quippirgax - (QUIP per gax) quasiprismatorhombated grand 600. Its cells are 600 coes, 120 quit gissids, 120 trips, and 720 stiddips. Its symbol is xox*'x.

392. Gippixhihy - (GIP pik SHI he) great prismato600-120-120. Its cells are 600 ohoes, 120 quit gissids, 1200 trips, and 120 gaquatids. Its symbol is x*'(x,ox).

393. Girpixhi - (gir PIK she) great rhombiprismic 600-120. Its cells are 600 choes, 720 stiddips, and 120 gaquatids.

Sample slices of them are below in same order.

Quippirgax Regiment Slices


Gichado Regiment

Gichado Regiment Verfs

The gichado regiment also shows up as polyteron facets.

394. Gichado - (GICH a do) great cubi16disoctachoron. Its cells are 8 goccoes, 16 tuts, 24 cubes, and 8 quitcoes. Its symbol is x(x"x'o).

395. Paqrit - (PAY krit) prismatoquasirhombated tesseract. Its cells are 8 quercoes, 16 tuts, 24 cubes, and 32 hips. Its symbol is xxo"x.

396. Girpdo - (GIRP do) great rhombiprismic disoctachoron. Its cells are 8 grohs, 8 quitcoes, and 32 hips.

Sample slices of them are below in same order.

Gichado Regiment Slices


Gipti Regiment

Gipti Regiment Verfs

Members below, verfs above.

397. Gipti - (GIP tee) great prismatotris24. Its cells are 24 goccoes, 24 quitcoes, 96 trips, and 24 toes. Its symbol is x(x"xo').

398. Paqri - (PAY kree) prismatoquasirhombated 24. Its cells are 24 quercoes, 24 toes, 96 trips, and 96 hips. Its symbol is xx"ox.

399. Girpdi - (GIRP dee) great rhombiprismic dis24. Its cells are 24 grohs, 24 quitcoes, and 96 hips.

Sample slices of them are below in same order.

Gipti Regiment Slices


Mipthi Regiment

Mipthi Regiment Verfs

Members below, verfs above.

400. Mipthi - (MIP thee) medial prismatotris120. Its cells are 120 gaddids, 120 tids, 720 stips, and 120 quitdids. Its symbol is x^(x*'x*o).

401. Paqrigshi - (pa KRIG she) prismatoquasirhombated great stellated 120. Its cells are 120 qrids, 120 tids, 720 stips, and 720 dips. Its symbol is x^xo*'x.

402. Marphihy - (mar FI he) medial rhombiprismic 120-120. Its cells are 120 girds, 720 dips, and 120 quitdids.

Sample slices of them are below in same order.

Mipthi Regiment Slices


Sipthi Regiment

Sipthi Regiment Verfs

Members below, verfs above.

403. Sipthi - (SIP thee) small prismatotris120. Its cells are 120 gaddids, 120 tigids, 1200 trips, and 120 quitdids. Its symbol is x^(x*'xo*).

404. Paqrigafix - (pa KRIG a fix) prismatoquasirhombated great faceted 600. Its cells are 120 qrids, 120 tigids, 1200 trips, and 720 dips. Its symbol is x^x*'ox.

405. Mirpady - (MIR pa dee) medial rhombiprismic dis120. Its cells are 120 girds, 720 dips, and 120 quitdids.

Sample slices of them are below in same order.

Sipthi Regiment Slices


Gippixady Regiment

Gippixady Regiment Verfs

Members below, verfs above.

406. Gippixady - (gip PIK sa dee) great prismato600dis120. Its cells are 120 gaddids, 600 tuts, 720 stips, and 120 gaquatids. Its symbol is x(x*'x*o).

407. Paqrigagishi - (pa KRIG a GISH ee) prismatoquasirhombated great grand stellated 120. Its cells are 120 qrids, 600 tuts, 720 stips, and 1200 hips. Its symbol is xxo*'x.

408. Gripady - (GRI pa de) great rhombiprismic dis120. Its cells are 120 girds, 120 gaquatids, and 1200 hips.

Sample slices of them are below in same order.

Gippixady Regiment Slices


Suti Regiment

Suti Regiment Verfs

Members below, verfs above.

409. Suti - (SU tee) small tetris120. Its cells are 24 quiths, 24 sircoes, 24 toes, and 24 quitcoes. Its symbol is (x'ox"x).

410. Diquitdi - (di QUIT dee) dis24quasitruncated dis120. Its cells are 24 quiths, 24 soccoes, 24 toes, and 24 cotcoes. Its symbol is (x"(x'x)'o,).

411. Sirti - (SIR tee) small rhombic tris120. Its cells are 24 srohs, 24 quitcoes, and 24 cotcoes.

Sample slices of them are below in same order.

Suti Regiment Slices


Ditdi Regiment

Ditdi Regiment Verfs

Members below, verfs above.

412. Ditdi - (DIT dee) dis24truncated dis120. Its cells are 24 goccoes, 24 tics, 24 toes, and 24 cotcoes. Its symbol is (x'(x"x)'o).

413. Guti - (GOO tee) great tetris120. Its cells are 24 quercoes, 24 tics, 24 toes, and 24 gircoes. Its symbol is (x'xo"x).

414. Girti - (GIR tee) great rhombic tris120. Its cells are 24 grohs, 24 cotcoes, 24 gircoes.

Sample slices of them are below in same order.

Ditdi Regiment Slices


Hixtixhi Regiment

Hixtixhi Regiment Verfs

Members below, verfs above.

415. Hixtixhi - (hix TIK she) 120-600truncated 600-120. Its cells are 120 gaddids, 600 tuts, 120 tigids, and 120 idtids. Its symbol is (x^(x*'x)o*).

416. Gixathi - (GIK sa thee) great 600tris120. Its cells are 120 qrids, 600 tuts, 120 tigids, and 120 grids. Its symbol is (x,o*x^x).

417. Grithi - (GRIH thee) great rhombic tris120. Its cells are 120 girds, 120 idtids, and 120 grids.

Sample slices of them are below in same order.

Hixtixhi Regiment Slices


Hixady Regiment

Hixady Regiment Verfs

Members below, verfs above.

418. Hixady - (HIK sa dee) 120-600dis120. Its cells are 120 quit gissids, 600 coes, 120 tids, and 120 quitdids. Its symbol is (x*'x^xo).

419. Xhidy - (ZHI dee) 600-120-dis120. Its cells are 120 quit gissids, 600 ohoes, 120 tids, and 120 idtids. Its symbol is (^x*'(xx)o,).

420. Rixady - (RIK sa dee) rhombic 600dis120. Its cells are 600 choes, 120 quitdids, and 120 idtids.

Sample slices of them are below in same order.

Hixady Regiment Slices


Sixathi Regiment

Sixathi Regiment Verfs

Members below, verfs above.

421. Sixathi - (SIK sa thee) small 600tris120. Its cells are 120 srids, 600 tuts, 120 quit sissids, and 120 gaquatids. Its symbol is (xo^x*'x).

422. Hixquitixhi - (HIX qua TIK she) 120-600quasitruncated 600-120. Its cells are 120 saddids, 600 tuts, 120 quit sissids, and 120 idtids. Its symbol is (x*'(x^x),o^).

423. Srithi - (SRIH thee) small rhombic tris120. Its cells are 120 sirds, 120 gaquatids, and 120 idtids.

Sample slices of them are below in same order.

Sixathi Regiment Slices


Gid Tipathi Regiment

Gid Tipathi Regiment Verfs

Members below, verfs above.

424. Gid Tipathi - (gid TIP a thee) great ditrigonal prismatotris120. Its cells are 120 gidditdids, 120 tis, 1200 trips, and 120 gaquatids. Its symbol is x(x*'xo^).

425. Giphixhi - (gih FIK she) great prismato120-600-120. Its cells are 120 giids, 120 tis, 1200 trips, and 600 toes. Its symbol is x(xx,o^).

426. Gasixady - (ga SIK sa dee) great small 600dis120. Its cells are 120 giddies, 120 gaquatids, and 600 toes.

Sample slices of them are below in same order.

Gid Tipathi Regiment Slices


Gid Thipady Regiment

Gid Thipady Regiment Verfs

Members below, verfs above.

427. Gid Thipady - (gid THIP a dee) great ditrigonal 120prismatodis120. Its cells are 120 gidditdids, 120 tids, 720 pips, and 120 quitdids. Its symbol is x^(x*'x^o).

428. Ghipady - (GI pa dee) great 120prismatodis120. Its cells are 120 giids, 120 tids, 720 pips, and 120 grids. Its symbol is x^(xx^o,).

429. Ghiyay - (gi YAY) great 120-120-120. Its cells are 120 giddies, 120 quitdids, and 120 grids.

Sample slices of them are below in same order.

Gid Thipady Regiment Slices


Gixipady Regiment

Gixipady Regiment Verfs

Members below, verfs above.

430. Gixipady - (gik SIP a dee) great 600prismatodis120. Its cells are 120 gidditdids, 600 tuts, 720 pips, and 120 gaquatids. Its symbol is x(x*'x^o).

431. Giphiddix - (gif FID dix) great prismato120dis600. Its cells are 120 giids, 600 tuts, 720 pips, and 600 toes. Its symbol is x(x,o^x).

432. Gigixady - (ga GIK sa dee) great great 600dis120. Its cells are 120 giddies, 600 toes, and 120 gaquatids.

Sample slices of them are below in same order.

Gixipady Regiment Slices


Sphixhi Regiment

Sphixhi Regiment Verfs

Members below, verfs above.

433. Sphixhi - (SFIK she) small prismato120-600-120. Its cells are 120 siids, 120 tiggies, 1200 trips, and 600 toes. Its symbol is x(x*ox).

434. Sid Tipathi - (sid TIP a thee) small ditrigonal prismatotris120. Its cells are 120 sidditdids, 120 tiggies, 1200 trips, and 120 grids. Its symbol is x(x^x,o*).

435. Sigixady - (sa GIK sa dee) small great 600dis120. Its cells are 120 siddies, 120 grids, and 600 toes.

Sample slices of them are below in same order.

Sphixhi Regiment Slices


Shipady Regiment

Shipady Regiment Verfs

Members below, verfs above.

436. Shipady - (SHIP a dee) small 120prismatodis120. Its cells are 120 siids, 120 quit gissids, 720 stips, and 120 gaquatids. Its symbol is x*'(xo*x).

437. Sid Thipady - (sid THIP a dee) small ditrigonal 120prismatodis120. Its cells are 120 sidditdids, 120 quit gissids, 720 stips, and 120 quitdids. Its symbol is x*'(x^x*'o).

438. Shiyay - (shi YAY) small 120-120-120. Its cells are 120 siddies, 120 quitdids, and 120 gaquatids.

Sample slices of them are below in same order.

Shipady Regiment Slices


Sphiddix Regiment

Sphiddix Regiment Verfs

Members below, verfs above.

439. Sphiddix - (SFID dix) small prismato120dis600. Its cells are 120 siids, 600 tuts, 720 stips, and 600 toes. Its symbol is x(xo*x).

440. Sixipady - (sik SIP a dee) small 600prismatodis120. Its cells are 120 sidditdids, 600 tuts, 720 stips, and 120 grids. Its symbol is x(x^x*'o).

441. Sasixady - (sa SIK sa dee) small small 600dis120. Its cells are 120 siddies, 600 toes, and 120 grids.

Sample slices of them are below in same order.

Sphiddix Regiment Slices


Conjugates

Below shows how the prismatotruncates pair up as conjugates.

Self conjugates - The following regiments have self conjugate members: prip and hixady.

Aligned Conjugates - The following paired regiments form conjugates, where their members line up as conjugates in the same order (i.e. 1-1, 2-2, 3-3): proh-quiproh, prix-quippirgax, pirshi-pirgaghi, and pirghi-quippirgashi.

Crossed Conjugates - The following paired regiments form conjugates in this way (1-2, 2-1, 3-3): prit-gichado, prico-gipti, prahi-gippixady, quippirfix-sipthi, quippirghi-mipthi, suti-ditdi, hixtixhi-sixathi, gid tipathi-sphixhi, gid thipady-shipady, and gixipady-sphiddix.

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