Category 11: Antipodiumverts

The antipodiumverts (also called antipodites) have vertex figures shaped like triangle antipodia and their facetings. There are 40 polychora in this category which is divided up into 6 regiments each with 7 members, except spid which has 5. The regiments are spid, sidpith, sidpixhi, siddapady, sadixady, and gixhidy. Spid, sidpith, and sidpixhi are convex. Their 3-D counterparts are the regiments of co (as the rhombitetratetrahedron), sirco, srid, and raded. Many of them have conjugates in category 12. For each regiment (except spid), the first four are tame, while the last three are wild. Following are the antipodites.

Spid Regiment

This 5 member regiment commonly shows up in several uniform polytera as terons (4-D facets) usually acting like it has 7 members (nipdip and piphid shows up twice since they can be oriented in two ways). All of them have 20 vertices. Spid's symbol is xoox. Spid acts like a 4-D version of co. Piphid and nipdip have pennic symmetry, while spid, duhd, and phud have deca symmetry. Spid is one of the coolest looking regiments with pennic symmetry. Phud and nipdip are wild, others are tame.

Spid

442. Spid - (SPID) small prismatodecachoron. Its cells are 10 tets and 20 trips. Its verf is a long trap (trigonal antiprism). It has 30 pieces of two types, LOC = 4. It is convex.

443. Piphid - (PIF fid) prismatopentahemidecachoron. Its cells are 5 tets, 10 trips, and 5 coes. It also has 5 pseudo-tets and 10 pseduo-trips. Its verf is a stretched thah. It has 85 pieces in five types, LOC = 20.

444. Duhd - (DUD) decahemidecachoron. It has 10 tets and 5 ohoes as cells. Its verf is an triangle hourglass. Duhd is the 4-D version of oho (it's 5-D version is called dehad). This polychoron has a dangling appearance, and is one of the most interesting of this regiment. It has 50 pieces of two types, LOC = 5.

445. Phud - (FUDD - just like Elmer's last name) prismatohemidecachoron. Its cells are 20 trips and 5 ohoes. It also has 10 pseudo-tets. Its verf is a long inverted trap. It has 60 pieces in two types, LOC = 7.

446. Nipdip - (NIP dip) spinoprismatodispentachoron. It has 5 tets, 10 trips, and 5 choes as cells. Its verf is a trigonal crown. It has 45 pieces of three types and has an interesting appearance, LOC = 12.

Sidpith Regiment

The sidpith regiment which has tessic symmetry gets more interesting the more one looks at it - first it had only 7 members, then iquipadah was found as well as the compound of 2 sodips, and lately 6 scaliforms have been found in this regiment - as it turns out, the blend of four sidpiths leads to yet another regiment, the ondip regiment which is loaded with scaliforms and compounds - however only the original 7 sidpith members are counted in category 11. The conjugate of this regiment is the gittith regiment from category 12. These all have 64 vertices. Sidpith's symbol is xoo'x, it is the 4-D version of sirco. Just for fun, here are the names of the n-D versions starting with 2-D: octagon, sirco, sidpith, scant, stoxog, suposaz, and seok.

Sidpith

447. Sidpith - (SID pith) small disprismatotesseracti16. It is the 4-D version of sirco and is convex. Its cells are 8 cubes, 16 tets, 24 more cubes, and 32 trips. Its verf is a trigonal antipodium. It has 80 pieces with four types, LOC = 8.

448. Stefacoth - (STEF a coth) small tesseractifaceted cubitesseracti16. It has 16 tets, 24 cubes, and 8 sircoes - it also has 8 pseudo-cubes and 32 pseudo-trips. Its verf is a trigonal hemiantiprism (thah-like). It has 256 pieces in six types, LOC = 24.

449. Shafipto - (sha FIP toe) small 16faceted prismatotesseractioctachoron. The cells are 8 cubes, 32 trips, and 8 sircoes, it also has 16 pseudo-tets and 24 pseudo-cubes. Its verf is a trigonal hemiantiprism. It has 248 pieces in five types, LOC = 23.

450. Steth - (STETH) small tesseractitesseracti16. It is the 4-D version of socco. Its cells are 8 cubes, 16 tets, and 8 soccoes. Its verf is a trigonal retropodium. It has 136 pieces in four types, LOC = 12.

451. Dippit - (DIP pit) disprismatotesseract. It has 32 trips, 24 cubes, and 8 soccoes - it also has 8 pseudo-cubes and 16 pseudo-tets. Its verf is a trigonal inverted antipodium. It has 176 pieces in five types, LOC = 17.

452. Snappoth - (SNAP poth) small spinoprismatotesseracti16. It has 16 tets, 32 trips, and 8 srohs. Its verf is a trigonal spiky crown. It has 152 pieces in four types, LOC = 14.

453. Snipto - (SNIP toe) small spinoprismatotesseractioctachoron. The cells are 8 cubes, 24 more cubes, and 8 srohs. Its verf is a trigonal crown. It has 128 pieces of three types (136 in four types if counting the central cavity, which shows up in snipto containing polytera), LOC = 13.

Sidpixhi Regiment

This regiment has hyic symmetry, each member has 2400 vertices. Sidpixhi's symbol is xoo^x. It is the 4-D version of srid. It's conjugate regiment is gixhihy from category 12.

Sidpixhi

454. Sidpixhi - (sid PIK she) small disprismato600-120. Its cells are 120 does, 600 tets, 720 pips, and 1200 trips. Its verf is a trigonal antipodium. This convex polychoron has 2640 pieces in four types, LOC = 8.

455. Shif Phix - (SHIF FIX) small 120faceted prismato120-600. Its cells are 600 tets, 720 pips, and 120 srids, it also has 120 pseudo-does and 1200 pseudo-trips. Its verf is a trigonal hemiantipodium. It has 8880 pieces in six types, LOC = 24.

456. Six Fipady - (six FIP a dee) small 600faceted prismatodis120. Its cells are 120 does, 1200 trips, and 120 srids, it also has 600 pseudo-tets and 720 pseudo-pips. Its verf is a trigonal hemiantipodium. It has 8760 pieces in five types, LOC = 23.

457. Sixhihy - (sik SHI he) small 600-120-120. Its cells are 120 does, 600 tets, and 120 saddids. This is the 4-D version of saddid. Its verf is a trigonal retropodium. It has 4560 pieces in four types, LOC = 12.

458. Paphi - (PAF fee) prismatoprismato120. Its cells are 720 pips, 1200 trips, and 120 saddids, it also has 120 pseudo-does and 600 pseudo-tets. Its verf is a trigonal inverted antipodium. It has 5880 pieces in five types, LOC = 17.

459. Snapaxhi - (snap PAK she) small spinoprismato600-120. Its cells are 600 tets, 1200 trips, and 120 sirds. Its verf is a trigonal spiky crown. It has 5520 pieces in four types, LOC = 14. Be careful handling this polychoron, you may get pricked by the barbs.

460. Snappady - (SNAP a dee) small spinoprismatodis120. Its cells are 120 does, 720 pips, and 120 sirds. Its verf is a trigonal crown. It has 4440 pieces with three types (4560 in four types, if counting the central cavity), LOC = 13.

Siddapady Regiment

This regiment has hyic symmetry where each member has 2400 vertices. Siddapady's symbol is x*oo^x. It is the mathematical 4-D version of raded (however padohi looks more like a 4-D raded analogue). This regiment is self-conjugate. This is the regiment that blends with tigaghi and quit sishi to form the blends of category 26.

Siddapady

461. Siddapady - (sid DAP a dee) small disprismatodis120. Its cells are 120 gissids, 120 does, 720 stips, and 720 pips. Its verf is a trigonal antipodium. This is the 4-D version of raded. It has 64440 pieces with 12 types, LOC = 203. Even though it is the colonel of its regiment, it is more complex than two of its members (tahi and snaphihy).

462. Hi Fipady - (hi FIP a dee) 120faceted prismatodis120. It has 120 gissids, 720 pips, and 120 radeds, it also has 120 pseudo-does and 720 pseudo-stips. Its verf is a trigonal hemiantipodium. It has 99720 pieces with 15 types, LOC = 343.

463. Mohi Fipady - (MO hee FIP a dee) medial 120faceted prismatodis120. It has 120 does, 720 stips, and 120 radeds, it also has 120 pseudo-gissids and 720 pseudo-pips. Its verf is a trigonal hemiantipodium. It has 145,200 pieces with 23 types, LOC = 381.

464. Tahi - (TAH hee) triakis120. Its cells are 120 gissids, 120 does, and 120 ideds. Its verf is a trigonal retropodium. This is the 4-D version of ided. It has 38520 pieces with 8 types, LOC = 125.

465. Daphi - (DAF fee - just like the duck) disprismato120. It has 720 stips, 720 pips, and 120 ideds, it also has 120 pseudo-does and 120 pseudo-gissids. Its verf is a trigonal inverted antipodium. It has 115,200 pieces with 19 types, LOC = 305.

466. Snaphihy - (snaf FI he) small spinoprismato120-120. It has 120 gissids, 720 stips, and 120 ris. Its verf is a trigonal spiky crown - and you will get pricked with this one, no way around it. It has 50040 pieces with 9 types, LOC = 144.

467. Gnaphihy - (naf FI he) great spinoprismato120-120. It has 120 does, 720 pips, and 120 ris. Its verf is a trigonal crown, this one is quite attractive. It has 84000 pieces with 11 types, LOC = 220.

Sadixady Regiment

This regiment has hyic symmetry and 2400 vertices. Sadixady's symbol is (xoo*x). It's conjugate regiment is gidthixhi from category 12. Members of this regiment are usually very attractive, or very intricate.

Sadixady

468. Sadixady - (sa DIX sa dee) small dis600dis120. Its cells are 120 gissids, 600 tets, 120 tiggies, and 600 tuts. It has a long trigonal antipodium verf. It has 57120 pieces in 12 types, LOC = 293.

469. Six Fixady - (six FIX a dee) small 600faceted 600dis120. Its cells are 120 gissids, 600 tuts, and 120 siids, it also has 120 pseudo-tiggies, and 600 pseudo-tets. Its verf is a long trigonal hemiantipodium. It is very intricate with 294,120 pieces in 31 types, LOC = 925.

470. Shi Fixady - (shi FIX a dee) small 120faceted 600dis120. Its cells are 600 tets, 120 tiggies, and 120 siids, it also has 120 pseudo-gissids and 600 pseudo-tuts. Its verf is a long trigonal hemiantipodium. It has 299,040 pieces in 36 types, LOC = 955 - the two "fixady sisters" are the most complex in this category, with shi barely beating six.

471. Sidthixhi - (sid THIK she) small ditrigonary 120-600-120. Its cells are 120 gissids, 600 tets, and 120 sidditdids. Its verf is a long trigonal retropodium. It has 51120 pieces with 10 types, LOC = 214.

472. Hihix - (HI hix) 120-120-600. Its cells are 120 tiggies, 600 tuts and 120 sidditdids, it also has 120 pseudo-gissids and 600 pseudo-tets. It has a long trigonal inverted antipodium verf. It has 188,880 pieces in 29 types, LOC = 686.

473. Snathi - (SNATH thee) small spinotriakis120. Its cells are 120 gissids, 120 tiggies, and 120 siddies. Its verf is a long spiky trigonal crown - OUCH. It has 103,560 pieces with 14 types, LOC = 325.

474. Sanhiddix - (san HID dix) small spino120dis600. Its cells are 600 tets, 600 tuts, and 120 siddies. Its verf is a long trigonal crown. It has 193,800 pieces with 21 types, LOC = 625.

Gixhidy Regiment

This regiment has hyic symmetry and 2400 vertices. Gixhidy's symbol is (ox*'x^o). It's conjugate regiment is shihix.

Gixhidy

475. Gixhidy - (gik SHI dee) great 600-120dis120. Its cells are 120 does, 600 tets, 120 quit gissids, and 120 quit sissids. Its verf is a trigonal antipodium. It has 8760 pieces with 5 types, LOC = 43.

476. Gohi Fohixhi - (GO hi fo HIK she) great 120faceted 120-600-120. Its cells are 600 tets, 120 quit sissids, and 120 gidditdids, it also has 120 pseudo-quit gissids and 120 pseudo-does. Its verf is a trigonal hemiantipodium. It has 126,600 pieces with 23 types, LOC = 349.

477. Gaxifthi - (gax IF thee) great 600faceted triakis120. Its cells are 120 does, 120 quit gissids, and 120 gidditdids, it also has 600 pseudo-tets and 120 pseudo-quit sissids. Its verf is a trigonal hemiantipodium. It has 57960 pieces with 11 types, LOC = 184.

478. Gohihix - (go HI hix) great 120-120-600. Its cells are 120 does, 600 tets, and 120 giids. Its verf is a trigonal retropodium.

479. Hidy - (HI dee) 120dis120. Its cells are 120 quit gissids, 120 quit sissids, and 120 giids, it also has 120 pseudo-does and 600 pseudo-tets. Its verf is a trigonal inverted antipodium. It has 24360 pieces in 7 types, LOC = 94.

480. Ganxady - (GANK sa dee) great spino600dis120. Its cells are 600 tets, 120 quit gissids, and 120 giddies. Its verf is a trigonal crown. It has 27960 pieces with 6 types, LOC = 89.

481. Gun Hidy - (gun HI dee - just like the greeting phud had with daphi when it was duck season) great spino120dis120. Its cells are 120 does, 120 quit sissids, and 120 giddies. (I guess when you come against 120 does and 120 giddies, its time to say "gun hidy" - KAPOW! - sorry folks, just had to throw that in). Its verf is a trigonal crown. It has 69000 pieces in 12 types, LOC = 190.

Conjugates

Below shows how the antipodites pair up as conjugates.

Conjugates

The following are self conjugates: spid, piphid, duhd, phud, nipdip, siddapady, tahi and daphi. - phud and daphi are here, wonder where bugs and taz went? - OK, OK - I'll stop the Loony Toons bit.

The following are conjugate pairs: hi fipady-mohi fipady and snaphihy-gnaphihy.

The following are conjugate pairs with catgory 12 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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