Category 12: Podiumverts

The podiumverts (also called podites or fustrumverts) have vertex figures shaped like triangle podia and their facetings. There are 30 polychora in this category which is divided up into 4 regiments of 7 and the two extra members of the rit regiment sto and gotto. The 4 main regiments are gittith, gidthixhi, gixhihy, and shihix. Their 3-D counterparts are the regiments of gocco, gidditdid, gaddid, and siid. All of them have conjugates in category 11 except for sto and gotto. Following are the podites. Sto is tame while gotto is wild, of the other regiments - the third one (has inverted trigon cupola verf) along with the last two of each regiment (which have spiky verfs) are wild, others are tame.

Rit Regiment Continued

This 5 member regiment commonly shows up in several uniform polytera as terons (4-D facets) usually acting like it has 7 members (sto and gotto shows up twice since they can be oriented in two ways). All of them have 32 vertices. While the three members from category 3 has tessic symmetry, sto and gotto has demitessic symmetry. When rit is thought of as a demitessic regiment, it acts more like a podiumvert regiment. It's demitessic symbol is x8x. Sto and gotto were discovered by George Olshevsky in Nov. 1998.

Gotto

482. Sto - (STO) small triakisoctachoron. Its cells are 8 tets, 8 ohoes, and 8 tuts. It also has 8 pseudo-tets. Its verf is a bowtie faced trip faceting. It has 248 pieces with six types, LOC = 36.

483. Gotto - (GOT toe) great triakisoctachoron. Its cells are 8 tets, 8 choes, and 8 tuts. Its verf is a crown-like trip faceting. It has 240 pieces in six types, LOC = 38.

Gittith Regiment

The gittith regiment which has tessic symmetry is the conjugate of the sidpith regiment (from cat. 11), so it has 8 uniform members (one is gaquipadah which is counted in category 20), a compound member, and 6 scaliform members - there's also the blend of four gittiths which leads to yet another regiment, the gondip regiment which is loaded with scaliforms and compounds - however only the primary 7 gittith members are counted in category 12. These all have 64 vertices. Gittith's symbol is o(o'x"x), it is the 4-D version of gocco. Just for fun, here are the names of the n-D versions of gocco starting with 2-D and going to 8-D: octagram, gocco, gittith, ginnont, goxaxog, gososaz, and gook.

Gittith

484. Gittith - (GIT tith) great tesseractitesseracti16. It is the 4-D version of gocco. Its cells are 8 goccoes, 8 cubes, and 16 tets. Its verf is a trigonal podium. It has 152 pieces in four types, LOC = 30.

485. Quidpith - (KWID pith) quasidisprismatotesseracti16. It is the 4-D version of querco. Its cells are 8 cubes, 16 tets, 24 more cubes, and 32 trips - it also has 8 pseudo-quercoes, making it fairly intricate. Its verf is a retrotrigonal antipodium. It has 23632 pieces in 91 types, LOC = 1947. This is the most complex uniform polychoron with tessic symmetry.

486. Picnut - (PIC nut) prismatocubintercepted tesseract. It has 8 goccoes, 32 trips, and 24 cubes - it also has 8 pseudo-cubes and 16 pseudo-tets. Its verf is a trigonal inverted podium. It has 456 pieces with four types, LOC = 59.

487. Gittifcoth - (git TIF cuth) great tesseractifaceted cubitesseracti16. It has 8 quercoes, 16 tets, and 24 cubes - it also has 8 pseudo-cubes and 32 pseudo-trips. Its verf is a trigonal hemipodium. It has 2968 pieces with 15 types, LOC = 361.

488. Gahfipto - (gah FIP toe) great 16faceted prismatotesseractioctachoron. The cells are 8 quercoes, 8 cubes, and 32 trips, it also has 16 pseudo-tets and 24 pseudo-cubes. Its verf is a trigonal hemipodium. It has 2824 pieces in 15 types, LOC = 343.

489. Gnappoth - (NAP poth) great spinoprismatotesseracti16. It has 8 grohs, 16 tets, and 32 trips. Its verf is a trigonal podic spiky crown. It has 2536 pieces in 15 types, LOC = 266. This one has holes.

490. Gnipto - (NIP toe) great spinoprismatotesseractioctachoron. The cells are 8 grohs, 8 cubes, and 24 more cubes. Its verf is a trigonal podic crown. It has 5592 pieces with 24 types, LOC = 559. This one has a neat looking intricate block-like appearance.

Gidthixhi Regiment

This regiment has hyic symmetry and 2400 vertices. Gidthixhi's symbol is o(o^x*'x). It's conjugate regiment is sadixady from category 11. This is the 4-D version of gidditdid.

Gidthixhi

491. Gidthixhi - (gid THIK she) great ditrigonary 120-600-120. Its cells are 120 gidditdids, 120 does, and 600 tets. Its verf is a trigonal podium. It has 5520 pieces with four types, LOC = 30.

492. Gadixady - (ga DIX sa dee) great dis600dis120. Its cells are 120 does, 600 tets, 120 tis, and 600 tuts, it also has 120 pseduo-giids and is very itricate. This is the 4-D version of giid. It has a retrotrigonal antipodium verf. It has 909,840 pieces in 95 types, LOC = 1984. In this category it has the most types of pieces, but ranks second in number of pieces and third in LOC.

493. Xhinhi - (zhen HI) 600-120intercepted 600. Its cells are 120 gidditdids, 120 tis, and 600 tuts, it also has 120 pseudo-does and 600 pseudo-tets. It has a trigonal inverted podium verf. It has 16920 pieces with four types, LOC = 59.

494. Gix Fixady - (gix FIX a dee) great 600faceted 600dis120. Its cells are 120 giids, 120 does, and 600 tuts, it also has 120 pseudo-tis, and 600 pseudo-tets. Its verf is a trigonal hemipodium. It has 107,160 pieces with 16 types, LOC = 349.

495. Gohi Fixady - (GO hee FIX a dee) great 120faceted 600dis120. Its cells are 120 giids, 600 tets, and 120 tis, it also has 120 pseudo-does and 600 pseudo-tuts. Its verf is a trigonal hemipodium. It has 112,560 pieces with 16 types, LOC = 373.

496. Gnathi - (NATH thee) great spinotriakis120. Its cells are 120 giddies, 120 does, and 120 tis. Its verf is a trigonal podic crown. It has 205,560 pieces in 24 types, LOC = 509.

497. Ganhiddix - (gan HID dix) great spino120dis600. Its cells are 120 giddies, 600 tets, and 600 tuts. Its verf is a spiky trigonal podic crown. It has 95760 pieces in 15 types, LOC = 270.

Gixhihy Regiment

This regiment has hyic symmetry, each member has 2400 vertices. Gixhihy's symbol is o(o*x*'x). It is the 4-D version of gaddid (although gidipthi (cat. 22) looks more like a 4-D gaddid). It's conjugate regiment is sidpixhi from category 11.

Gixhihy

498. Gixhihy - (gik SHI he) great 600-120-120. Its cells are 120 gaddids, 120 gissids, and 600 tets. This is the 4-D version of gaddid. Its verf is a trigonal podium. It has 18000 pieces in five types, LOC = 75.

499. Quidpixhi - (kwid PIK she) quasidisprismato600-120. Its cells are 120 gissids, 600 tets, 720 stips, and 1200 trips, it also has 120 pseudo-qrids - making it extremely intricate. Its verf is a retrotrigonal antipodium. It has 1,067,040 pieces in 89 types, LOC = 4996. This is the most complex of this category, also has the highest piece count, but in piece types it ranks in second place.

500. Dippany - (DIP a nee) prismatoprismato120. Its cells are 120 gaddids, 720 stips, and 1200 trips, it also has 120 pseudo-gissids and 600 pseudo-tets. Its verf is a trigonal inverted podium. It has 149,040 pieces with 15 types, LOC = 405.

501. Ghif Phix - (GHIF FIX) great 120faceted prismato120-600. Its cells are 120 qrids, 600 tets, and 720 stips, it also has 120 pseudo-gissids and 1200 pseudo-trips. Its verf is a trigonal hemipodium. It has 171,600 pieces with 19 types, LOC = 652.

502. Gix Fipady - (gix FIP a dee) great 600faceted prismatodis120. Its cells are 120 qrids, 120 gissids, 1200 trips, it also has 600 pseudo-tets and 720 pseudo-stips. Its verf is a trigonal hemipodium. It has 792,120 pieces in 77 types, LOC = 3048. Second place in LOC, third place in pieces and types.

503. Gnapaxhi - (nap PAK she) great spinoprismato600-120. Its cells are 120 girds, 600 tets, and 1200 trips. Its verf is a trigonal podic crown. It has 261,600 pieces with 23 types, LOC = 930.

504. Gnappady - (NAP a dee) great spinoprismatodis120. Its cells are 120 girds, 120 gissids, and 720 stips. Its verf is a trigonal podic spiky crown. It has 372,120 pieces in 35 types, LOC = 1457.

Shihix Regiment

This regiment has hyic symmetry and 2400 vertices. Shihix's symbol is o(o*xx). It's conjugate regiment is gixhidy. This is the 4-D version of siid. The members of this regiment are quite attractive.

Shihix

505. Shihix - (SHI hix) small 120-120-600. Its cells are 120 siids, 120 gissids, and 600 tets. Its verf is a long trigonal podium. It has 3120 pieces in three types, LOC = 14.

506. Sixhidy - (sik SHI dee) small 600-120dis120. Its cells are 120 gissids, 600 tets, 120 tids, and 120 tigids, it also has 120 pseudo-sidditdids. Its verf is a long retrotrigonal antipodium. This one is very attractive, and is the one pictured on the front page of this polychoron site. It has 69120 pieces in 14 types, LOC = 191.

507. Hihiny - (HI hi nee) 120-120intercepted 120. Its cells are 120 siids, 120 tids, and 120 tigids, it also has 120 pseudo-gissids and 600 pseudo-tets. Its verf is a long trigonal inverted podium. It has 46080 pieces in 10 types, LOC = 88.

508. Shi Fohixhi - (SHI fo HIK she) small 120faceted 120-600-120. Its cells are 120 sidditdids, 600 tets, and 120 tigids, it also has 120 pseudo-tids and 120 pseudo-gissids. Its verf is a long trigonal hemipodium. It has 90120 pieces with 15 types, LOC = 193.

509. Saxifthi - (sax IF thee) great 600faceted triakis120. Its cells are 120 sidditdids, 120 gissids, and 120 tids, it also has 600 pseudo-tets and 120 pseudo-tigids. Its verf is a long trigonal hemipodium. It has 82200 pieces in 14 types, LOC = 341.

510. Snaxady - (SNAK sa dee) small spino600dis120. Its cells are 120 siddies, 600 tets, and 120 tids. Its verf is a long trigonal crown. It has 37920 pieces in 9 types, LOC = 100.

511. Sun Hidy - (sun HI dee - This name really fits, it's sections have a sun-like appearance.) small spino120dis120. Its cells are 120 siddies, 120 gissids, and 120 tigids. Its verf is a long spiky trigonal crown. It has 42120 pieces in 7 types, LOC = 91.

Conjugates

Below shows how the podites pair up as conjugates.

Conjugates

The following are self conjugates: sto and gotto

The following are conjugate pairs with catgory 11 members: sidpith-quidpith, stefacoth-gittifcoth, shafipto-gahfipto, steth-gittith, dippit-picnut, snappoth-gnappoth, snipto-gnipto, sidpixhi-quidpixhi, shif phix-ghif phix, six fipady-gix fipady, sixhihy-gixhihy, paphi-dippany, snapaxhi-ganpixhi, snappady-gnappady, sadixady-gadixady, six fixady-gix fixady, shi fixady-gohi fixady, sidthixhi-gidthixhi, hihix-xhinhi, snathi-gnathi, sanhiddix-ganhiddix, gixhidy-sixhidy, gohi fohixhi-shi fohixhi, gaxifthi-saxifthi, gohihix-shihix, hidy-hihiny, ganxady-snaxady, and gun hidy-sun hidy.

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