Category 20: Miscellaneous


This category deals with the odd balls, there are two of the iquipadah type, 6 antiprismattic cases, 6 snubs, and 8 swirlprisms. There are also two fissary swirlprisms.
Fusion Miscellaneous

Above are sample slices of the members of this category in the same order as in the text. Rapsady, sidtafdip, and the gondip regiment are excluded in the graphic for I have yet to code them into my POV-Ray code.


Antiprisms

Verfs of the Antiprisms

These six are either antiprisms or duoantiprism related. The famous grand antiprism is here, which is convex. All tame.

963. Gap - (GAP) grand antiprism. It's symbol is s^sx'x. It has 100 vertices with a verf resembling an ike with 2 adjacent vertices chopped off entirely. Its cells are 20 paps (pentagonal antiprisms) and 300 tets (200 next to the pap girdles and 100 half way between them). It has pentagon duoantiprism symmetry. It is convex and has 320 pieces with 3 types. LOC = 22.

964. Padiap - (PAY de yap) pentagrammattic double antiprismoid. Its symbol is s*'sx"x. It has 100 verts with a verf resembling a gike with two points missing and with 2 crossed trapezoids instead. Its cells are 20 starps and 300 tets (200 of type 1, 100 of type 2). It has pentagon duoantiprismattic symmetry. It has 30640 pieces with 80 types. LOC = 3542.

965. Gudap - (GOO dap) great duoantiprism. Its symbol is s*'s s^s. It has 50 verts with a verf resembling a wedge fused to a crossed wedge in opposite orientations. Its cells are 10 starps, 10 paps, and 50 tets. It has pentagon-pentagon duoantiprismattic symmetry. It has 600 pieces in 8 types. LOC = 144 - This polychoron looks very different from other uniforms.

966. Sidtidap - (SID tid ap) sidtid antiprism. It's symbol is (oo*x) s. It has 40 vertices and a trigonal cupola verf. Its cells are 2 sidtids, 12 staps, and 40 tets. It has dopic symmetry (dope is the dodecahedron prism). It has 174 pieces with 4 types. LOC = 32.

967. Ditdidap - (DIT did ap) ditdid antiprism. Its symbol is (o^x*o,) s. It has 40 verts, its verf is a cupola faceting with a pseudo triangle on top and a propeller on bottom. Its cells are 2 ditdids, 12 staps, and 24 paps. It has dopic symmetry. It has 518 pieces with 6 types. LOC = 78.

968. Gidtidap - (GID tid ap) gidtid antiprism. Its symbol is (o,o^x) s. It has 40 verts, its verf is a cupla with a triangle top and a tripod bottom. Its cells are 2 gidtids, 24 paps, and 40 tets. It has dopic symmetry. It has 762 pieces with 7 types. LOC = 111. Sidtidap, ditdidap, and gidtidap are commonly referred to as the Johnson Antiprisms, for they were discovered by Norman Johnson, they also form a regiment.


Snubs

Verfs of the Snubs

There are 6 typical snubs (not included here are the 4 regiments of non-Wythoffian snubs mentioned in categories 27-29). With the exception of rapsady, all of them are icoic and can also be considered as demitessic, the icoic ones have 96 verts. Rapsady is hyic and has 2400 verts. Sadi is convex. All are tame except the two "hapsippadies" which are wild.

969. Sadi - (SAY de) snub dis24. Its symbol is s$s, it can also be oo'ss or sss'o depending on considered symmetry. It has 24 ikes and 24+96 tets. Its verf is a teddi (tridiminished ike). It has 144 pieces with 3 types. LOC = 10.

970. Rasdi - (RAS de) retrosnub dis24. It has 24 gikes and 24+96 tets. Its verf is a targi (trireplenished gike). It is quite spiky looking with 9024 pieces in 24 types. LOC = 974.

971. Rappisdi - (ra PISS de) retroantiprismatosnub dis24. Its cells are 24 ikes, 24 gikes, and 96 octs, it also has 24 pseudo-tets. Its verf is a trigon-symmetric sidtid faceting containing 3 stars, 3 pentagons, and 6 squares. The rappisdi regiment also contains sirhapsippady and girhapsippady. It has 6552 pieces with 17 types. LOC = 571.

972. Sirhapsippady - (sir hap SIP a de) small retrohemiantiprismatosnub prismatodis24. It has 24 gikes, 24 tets, 96 thahs, and 96 trips. Its verf is a faceting of the rappisdi verf. It has 8688 pieces in 21 types. LOC = 710.

973. Girhapsippady - (gir hap SIP a de) great retrohemiantiprismatosnub prismatodis24. It has 24 ikes, 24 tets, 96 thahs (oriented other way), and 96 trips. Its verf is a faceting of the rappisdi verf. It has 16200 pieces in 37 types. LOC = 1300.

974. Rapsady - (RAP sa de) retroantiprismatosnub dis120. It has 120 sirsids, 120 sesides, and 1440 paps as cells, it also has 120 pseudo-ditdids. It's verf resembles rappisdi's but with the stars changed into sirsid verfs, the pseudo-triangle turned into a pseudo-propeller and the pentagons turned into seside verfs. It has 825,960 pieces with 70 types, 120 of them being entire sirsids. LOC = 3078. This is the only non-prismattic uniform polychoron known to have dodecahedral snubs for cells. Although there are 2 snub containing scaliforms (one has sirsids while the other has sesides). Of this category, rapsady has the most pieces.


Swirlprisms

Verfs of the Swirlprisms

There are 8 swirlprisms, two are noble, the other 6 are called the hybrid swirlprisms. They all have 120 vertices. The hybrids are members of the sishi regiment, while sisp and gisp are members of the ex and gishi regiment respectively. These polychora are some of the coolest and wierdest looking ones. There are also 2 fissary swirlprisms (in sishi regiment). The swirlprisms were discovered by George Olshevsky, he and I discovered the fissary ones. Sisp and gisp are tame, the others are feral.

975. Sisp - (SISP) small swirlprism. Its cells are 120 paps that group in 12 girdles of ten which swirl about each other. Its verf is a chiral faceting of ike with 10 trapezoids. It is a noble swirlprism and has 600 pieces in only one type. LOC = 28. It has swirlprism symmetry.

976. Gisp - (GISP) great swirlprism. Its cells are 120 starps that group in 12 girdles of ten (decagram style), these girdles swirl about each other. It is a noble swirlprism with a chiral verf which looks like a spindle with 5 disphenoids on it arranged like a crazy looking drill bit. It has swirlprism symmetry. It has 3600 pieces in only three types. LOC = 164. Gisp is probably the most dangerous looking polychoron, maybe we should of called it "Gasp"!

977. Sphix - (SFIKS) swirlprismattic 120-600. Its cells are 120 pips and 600 stips. Its verf looks like an inverted dodecahedron with a few edges missing. It has swirlprism symmetry. It has 8400 pieces with 7 types. LOC = 224.

978. Spiddit - (SPID it) swirlprismattic 240-480. Its cells are 240 pips and 480 stips. Its verf actually looks like a dodecahedron got chewed up and spit back out, making the name "spiddit" more appropriate. It has ionic swirlprism symmetry and has 10080 pieces in 21 types. LOC = 772.

979. Sispatit - (SIS pa tit) small swirlprismattic 360-360. Its cells are 360 pips and 360 stips. Its best to view the pic to understand how its verf looks. It appears to have tettic swirlprism symmetry with 18000 pieces in 25 types. LOC = 1120.

980. Gispatit - (GIS pa tit) great swirlprismattic 360-360. Its cells are 360 pips and 360 stips. Its best to view the pic to understand how its verf looks. It appears to have tettic swirlprism symmetry. It has 36720 pieces with 52 types. LOC = 2400.

981. Spittid - (SPIT id) swirlprismattic 480-240. Its cells are 480 pips and 240 stips. Its verf can be viewed in the pic. It appears to have ionic swirlprism symmetry. It has 99360 pieces with 207 types. LOC = 10,212. I like to call this one "the most ugliest polychoron".

982. Spaxhi - (SPAK she) swirlprismattic 600-120. Its cells are 600 pips and 120 stips. Its verf looks like paphackis, but with much of it covered by 5 pairs of isosceles triangles in a chiral arrangement. It has swirlprism symmetry. It has 353,640 pieces with 296 types. LOC = 14,304. Spaxhi has the highest LOC and number of types of pieces in this category.


Fissary and Compound Swirlprisms

Verfs of the Fissary and Compound Swirlprisms

Here's are a couple swirlprism compounds and a fissary. Spidy is tame, the others are wild.

C. Spidy - (SPI de) swirlprismattic dis120. Its cells are 120 pips and 120 stips. Its verf is a swirling compound of 5 disphenoids. It has swirlprism symmetry. This compound is in the sishi regiment.

C. Ditsop - (DIT sop) ditrigonary swirlprism. Its cells are 120 paps, 120 starps, and 600 tets. Its verf is a strange looking faceting of doe. It has swirlprism symmetry. It has 33840 pieces with 30 types. LOC = 1090. This one and the next one are also in the sishi regiment.

F23. Tipsop - (TIP sop) trigonal prismattoswirlprism. Its cells are 120 paps, 120 starps, and 1200 trips. Its verf is a strange looking faceting of doe. It has swirlprism symmetry. It has 137,640 pieces with 116 types. LOC = 3858.


Iquipadah Type

Verfs of Iquipadah and Gaquipadah

These two polychora have squared square symmetry, each with 64 verts. Every non-prime dimension has some of these. Iquipadah types are usually formed by blending an "octagon-like" polytope with various "octagon"-"square" duoprisms, where octagon can represent the octagon, sirco, sidpith, and so on - and the square represents hypercubes. And of course their octagram like conjugates. Both wild. I usually symbolize iquipadah as O4-2O2S2 where O4 represents the 4-D octagon "sidpith", O2 is the 2-D octagon "the true octagon" and S2 is the 2-D square, and "-" represents blending. In 6-D there are the following "iquipadahs": O6-2O3S3, O6-3O2S4, O6-3O4S2, O6-3O2S4-3O4S2, and 3O2S4-3O4S2

983. Iquipadah - (i QUIP uh dah) inverted quasiprismatodis16. It is the blend of a sidpith with the compound of 2 sodips (square octagon duoprism). It belongs to the sidpith regiment. Its cells are 16 tets, 16 cubes, 32 trips, and 8 ops. It has 80 pieces with 5 types. LOC = 30.

984. Gaquipadah - (ga QUIP uh dah) great quasiprismatodis16. Its the blend of quidpith with the compound of 2 sistodips (square octagram duoprism). It belongs to the gittith regiment. Its cells are 16 tets, 16 cubes, 32 trips, and 8 stops. It has 5560 pieces with 52 types. LOC = 1474.


Ondip Type

Verfs of Ondip and Friends

These four polychora were discovered on March 2, 2006, two by Mason Green (ondip and gondip), and two more by myself (sidtindip and gidtindip) after investigating Mason's polychora. Mason found his after learning of a scaliform polychoron that Andrew Weimholt found by blending 4 tats together. I later found two fissary cases, mentioned below as F31 and F32. These form two new regiments, the ondip and the gondip regiments. These figures all have 128 vertices. There are also 20 scaliforms (10 in each regiment) along with 16 fissary scaliforms (8 in each regiment). Ondip and gondip are tame, the others are wild.

1846. Ondip - (ON dip) octagonal spinoduoprism. This polychoron was discovered by Mason Green by blending 4 iquipadahs together, it can also be formed by blending 4 sidpiths together, it has squared octagon symmetry (octagon^2). Its cells are 64 tets, 128 trips, and 64 cubes. Its verf has a beak shape - formed by taking sidpith's verf (a triangle antipodium) and blending a flipped second on the base triangle and one adjacent triangle. This polychoron actually has chasms going through the center of it (chasms are planar holes), it is the only known uniform polychoron with chasms. It also begins a new regiment - It also appears that all even dimensions has these sort of figures. It has 1408 pieces with 8 types. LOC = 108.

1847. Sidtindip - (sid TIN dip) small ditetragonal spinoduoprism. This one is formed by blending 2 sidpiths and 2 sniptoes together, its verf is a blend of the sidpith verf with the snipto verf. This polychoron has anti-squared square symmetry. This one is a very wierd looking one with a strange topology. Its cells are 32 tets, 64 trips, 64 cubes, and 16 srohs. It belongs to the ondip regiment. It has atleast 2400 pieces with atleast 20 types. LOC > 456 (The Wikichoron article missed the pieces belonging to the center part of sroh - which actually dangle in the midst of the polychoron looking like a compound of two tesseracts, so its LOC, piece count and types are a bit off).

F31. Sidtafdip - (sid TAF dip) - small ditetragonal fissary duoprism. This fissary case is formed by blending 2 sidpiths with 2 steths. It has anti-squared square symmetry. Its verf is a blend of sidpith's verf with steths (which looks like an hourglass). Cells are 64 tets, 64 trips, 16 soccoes, and 48 cubes. It belongs to the ondip regiment.

1848. Gondip - (GON dip) great octagonal spinoduoprism. This polychoron is formed by blending four quidpiths together. It starts a new regiment. It's verf is a blend of two quidpith verfs, blending on two adjacent triangles and flipped. It has squared octagon symmetry. Its cells are 64 tets, 128 trips, and 64 cubes. It has 120,576 pieces with 257 types. LOC = 8746.

1849. Gidtindip - (gid TIN dip) great ditetragonal spinoduoprism. This one is a blend of two quidpiths and two gniptoes. Its verf is a blend of their two verfs. It has anti-squared square symmetry. Its cells are 32 tets, 64 trips, 64 cubes, and 16 grohs. It belongs to the gondip regiment. It has 40160 pieces with 174 types. LOC = 6920.

F32. Gidtafdip - (gid TAF dip) - great ditetragonal fissary duoprism. This fissary case is formed by blending 2 quidpiths with 2 gittiths. It has anti-squared square symmetry. Its verf is a blend of quidpith's verf with gittiths (which is a trigonal podium). Cells are 64 tets, 64 trips, 16 goccoes, and 48 cubes. It belongs to the gondip regiment.


Conjugates

Below shows how these pair up as conjugates.

Conjugates

The following are self conjugates: gudap, rappisdi, ditsop, and tipsop.

The following are conjugate pairs: gap-padiap, sadi-rasdi, sirhapsippady-girhapsippady, sisp-gisp, sphixhi-spaxhi, spiddit-spittid, sispatit-gispatit, iquipadah-gaquipadah, ondip-gondip, sidtindip-gidtindip, sidtafdip-gidtafdip.

The following have no true uniform conjugates: sidtidap, ditdidap, gidtidap, and rapsady.

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