Category S3: Special Scaliforms


Like the miscellaneous uniform polychoron category (Cat 20), it consist of several small mini-categories. So far there are sixteen mini-categories here: Noble diminishings, snub containing, ike snubs, decasishis, duoprismatic blends, truncate blends, blended tessic snubs, ico scaliforms, gudap scaliforms, gap scaliforms, padiap scaliforms, ipe blends, greater ipe blends, ixitic ipe blends, tesapdid regiment, and diminishings and friends. Several new additions here.

Noble Diminishings

Verfs of the Noble Diminishings

These scaliforms start with a uniform polychoron and then chop off some of their vertices and they're noble (one type of cell and vertex).

S22. Bidex - (BI dex / bi24 diminished 600) - cells are 48 teddis, teddi is the tridiminished icosahedron. This object is convex and has directional tetrahedral swirlprism symmetry - its an unusual shaped dice! Bidex was discovered by Andrew Weimholt in 2004 and it got a bit of attention amongst the polychoronist. It's verf is a 6 sided chiral faceting of ike with 4 isosceles triangles and 2 trapezoids. Bidex has 72 vertices and it is orientable.

S23. Birgax - (BIR gax / bi24 replinished grand 600) - cells are 48 targis, targi is the trireplinished gike, the conjugate of teddi (looks quite stellar). This object hasn't gotten as much attention as bidex. It has 72 vertices, and it's verf is a chiral object with 4 flat isosceles triangles and 2 crossed trapezoids. It is orientable.


Snub Containing Scaliforms

Verfs of the Snub Containing Scaliforms

These are the snubs that contain snub polyhedra for cells. All are tame and the last four are new.

S24. Shi - (SHE / snub 120-cell) - cells are 120 sesides and 1440 stappies (star pyramids), it has 1440 vertices. The verf is a lampshade shaped object consisting of a star at the top, 5 isosceles hexagons joining the star and each other in a star fashion, then finally 5 triangles to fill the voids - it has a pentagonal shaped opening at the bottom which represent 120 pseudo-sissids. Shi was co-discovered by Mason Green and myself in summer 2005. It is non-orientable and only a shell of it exists in neo-filling.

S25. Rashi - (RASH shee / retrosnub 120-cell) - cells are 120 sirsids and 1440 stappies, it has 1440 vertices as well as 120 pseudo-sissids. This is none other than the 4-D version of sirsid (yog-sothoth). The verf is a spike-festival resembling a squashed gissid - actually it only has 10 spikes with a hollow pentagonal base acting like a stubby pedistal - the verf would make a great Christmas tree ornament. Rashi is a horrendously spiky object and is non-orientable, it likely has a hollow center. It was co-discovered by Mason Green and myself in summer 2005.

S26. Prishi - (PRIH she / prismatorhombisnub 120-cell) - cells are 120 sesides, 2400 trips, and 1440 stiscus, it has 3600 vertices. The verf looks like a mouth. Prishi was found by Planet N9ne on October 22, 2021. It is non-orientable and only a shell of it exists in neo-filling.

S27. Prarshi - (PRAR she / prismatorhombiretrosnub 120-cell) - cells are 120 sirsids, 2400 trips, and 1440 stiscus, it has 3600 vertices. The verf is a stretched spiky wedge thing with two sirsid verfs on the ends. It was found by Planet N9ne on October 22, 2021. It is non-orientable.

S28. Raprishi - (ra PRIH she / retroprismatorhombisnub 120-cell) - cells are 120 sesides, 2400 trips, and 1440 rastacus, it has 3600 vertices and 120 pseduo-gidhids. The verf is a strange shaped 'duck-beak' thing. It was found by _Geometer on October 24, 2021. It is orientable.

S29. Raprarshi - (ra PRAR she / retroprismatorhombiretrosnub 120-cell) - cells are 120 sirsids, 2400 trips, and 1440 rastacus, it has 3600 vertices and 120 pseudo-gidhids. The verf is a spiky wedge like shape with two sirsid verfs. It was discovered by _Geometer on October 24, 2021. It is orientable and quite complicated looking.


Ike Snubs

Verfs of the Ike Snubs

Here are some snubs which contain atleast one of the following: ike, gad, sissid, or gike.

S30. Prissi - (PRISS see / prismatorhombisnub 24) - cells are 24 ikes, 96 trips, 24 tuts, and 96 tricus. It has 288 vertices. The verf is a sort of pentagonal wedge which is actually hiding inside padohi's verf. Prissi is convex and can be found by chopping all but 288 vertices off of padohi. Richard Klitzing discovered it in September 2005, while Wendy Kreiger verified it's scaliformity. It has the symbol ss'ox. It is orientable.

S31. Prarsi - (PRAHR see / prismatorhombiretrosnub 24) - cells are 24 gikes, 96 trips, 24 tuts, and 96 tricus. It has 288 vertices and has the symbol ss"ox. The verf is a sort of crossed up star wedge which can be found inside gidipthi's verf. I found this one after investigating Klitzing's prissi in October 2005. It is orientable.

S32. Disdi - (DIS dee / disnub dis24) - cells are 24 sissids, 24 gads, 96 scuffis, and 96 scufgis. Scuffi and scufgi are trigonal Klitzing facetings of ike and sissid respectively, both containing 7 triangles, scuffi has 3 pentagons, scufgi has 3 pentagrams. Verf has 3 of each of the following faces: sombraroids (hat like pentagon), long isosceles triangles, small butterflies, pentagons, piscoids (fish like pentagon), fat isosceles triangles, large butterflies, and pentagrams. Disdi is in the sadi army with same symmetry, it was found by Mason Green in January 2006. It has 96 vertices.

S33. Mesdi - (MESS dee / medial snub dis24) - cells are 24 gads, 24 sissids, and 96 dritits (rappisdi verf shape). Verf is the alternated sipstar. It is in the rappisdi regiment with sadi symmetry and has 96 vertices. It was found by Mason Green in January 2006.

SF1. Fits - (FITS / fissary trisnubchoron) - cells are 96 dritits, 96 scuffis, and 96 scufgis. This is a wild non-orientable fissary which blends disdi and mesdi together. It is in the disdi regiment and has the same symetry as sadi. _Geometer has found this one late 2020. It has 96 vertices. Previously called fesdi by mistake.

Dhahic - (THA hik / dis16hemi48) - cells are 16 gads, 16 sissids, and 48 sipters - a did facetings with brick symmetry (4 stars, 4 pentagons, 4 hexagons). Verf is a strange irregular spiky thing with two pentagons and two large stars. It is in the disdi regiment with tessipyritic symmetry and has 96 vertices, but not all of disdi's edges. It was found by _Geometer on February 4, 2022. It is orientable and tame.

Dodihec - (doe DI hek / dis8dis24hemi48) - cells are 8 sissids, 8 gads, 24 scuffis, 24 scufgis, and 48 sipters. It is the blend of dhahic and disdi and is likely in _Geometer's finds. It is wild and non-orientable and has tessipyritic symmetry.

Fisdohec - (FISS do hek / fissary snub dis8hemi48) - cells are 8 gads, 8 sissids, 96 dritits, and 48 sipters. It is the blend of dhahic and mesdi and is fissary and is likely in _Geometer's finds. It is wild and non-orientable and has tessipyritic symmetry.


Decasishis

Verfs of the Decasishis

Here are some finds among the compound of ten sishis.

SF2. Sistakix - (SIS ta kix / small snub 3600) - cells are 3600 'two-stip blend's. The two-stip-blend is a blend of two star prisms - it resembles gadsadox's verf (gadsadox is the leader of the gidtaps). Sistakix has 600 vertices (same as hi). The verf is a blended compound of two paphicki verfs (paphicki is the small prismasaurus). This object might be excluded by some polychoron definitions since it is fissary. I found this one in late October 2005.

SF3. Gastakix - (GAS ta kix / great snub 3600) - cells are 3600 'two-pip blend's. The two-pip-blend is a blend of two pips and resembles sadsadox's verf (sadsadox is the leader of the sidtaps). Gastakix has 600 vertices. The verf is a blended compound of two paphacki verfs (paphacki is the great prismasaurus). This object is also fissary. I found it in late October 2005. Very similar to sistakix and gastakix are the compounds of 10 paphickis and 10 paphackis, I noticed these compounds several years before but didn't consider the blended versions (these two scaliforms) until 2005.


Duoprismatic Blends

Verfs of the Duoprismatic Blends

These are formed by blending 4 of the same tessic polychora together to get something with octagon^2 symmetry.

S34. Otbott - (OT bot / octagonnally tetrablended truncated tesseract) - cells are 64 tets and 16 tutics (TOO tic - the blend of 2 tics) - this is the blend of 4 tats. It has 128 vertices, it's verf is a butterfly wedge. It was discoverd by Andrew Weimholt in early March 2006.

S35. Otbaquitit - (ot BACK wit it / octagonnally tetrablended quasitruncated tesseract) - cells are 64 tets and 16 tuquiths (blend of two quiths) - this is the blend of 4 quitits. It has 128 vertices, its verf is a butterfly wedge. It was found by Mason Green after otbott was found.


Truncate Blends

Verfs of the Truncate Blends

The first four are formed by blending 24 or 18 tats or quitits together, I found these first four in 2019 during the PDW, the next two were found by _Geometer on December 13, 2021, and the last two were found by _Geometer on November 24, 2022. They are orientable and tame, the first four have 384 vertices each and the last four have 1152 vertices. They have contic symmetry except for the 18-blended ones which have 4-scubic (swirl cubic) symmetry. The first four have a core 6 tats / quitits and either 12 or 18 more that blends with them. If we tried to make a 12 blend, it generates compounds of three otbotts and three otbaquittits. The next two blends 24 thatoths or thaquitoths, the last two are related to the hexasidpiths.

S36. Becsadic - (bek SAY dic / blended 48snub dis48) - cells are 48 soes (stella octangula), 288 tets, and 48 fortics (FOR tic - three tics blended off a core tic) - this is the blend of 24 tats.

S37. Sebicsadic - (seh BIC sa dic / swirlblended 48snub dis48) - cells are 48 soes, 192 tets, and 48 thretics (THREE tic - two tics blended off a core tic) - this is the blend of 18 tats.

S38. Quabcasdic - (quab CAS dic / quasiblended 48snub dis48) - cells are 48 soes, 288 tets, and 48 forquiths (FOR quith - three quiths blended off a core quith) - this is the blend of 24 quitits.

S39. Squabcasdic - (squab CAS dic / swirlquasiblended 48snub dis48) - cells are 48 soes, 192 tets, and 48 threquiths (THREE quith - two quiths blended off a core quith) - this is the blend of 18 quitits.

S40. Sesdicabdic - (SES dih CAB dic / small snub dis48blendic dis48) - cells are 48 fortics, 48 forcotcoes, and 384 tuts - this is the blend of 24 thatoths. It has a crazy irregular verf.

S41. Gesdicabdic - (GES dih CAB dic / great snub dis48blendic dis48) - cells are 48 forquiths, 48 forcotcoes, and 384 tuts - this is the blend of 24 thaquitoths. Is it a bird, is it a wood plane tool, is it an alien space ship - no, it's the verf of this crazy thang!

S148. Bafdistuf - (BAF diss tuf / blended 144disnub tetris144) - cells are 144 4tets (actually 8/4 antiprisms giving 576 tets), 576 2tets (X antiprism giving 1152 tets), and 144 sixtics (SIX tic - a squippic symmetric blend of six tics) - this is the blend of 36+72 tats.

S149. Quibfedstuf - (quib FED stuf / quasiblended 144disnub tetris144) - cells are 144 4tets, 576 2tets, and 144 sixquiths (SIX quith - a squippic symmetric blend of six quiths) - this is the blend of 36+72 quitits.


Blended Tessic Snubs

Verfs of the Blended Tessic Snubs

These are the result of blending normal tessic polychora to get snub tessic polychora. These were originally mistaken for swirlprisms, so I recently updated their names on March 10, 2012. Another recent find is that scabtitho and stuthit aren't truely scaliform, even though they have only one type of vertex figure. What happens with those two is that half of their vertices are above one or two triangular pseudo-faces and the other half are only above triangular faces.

S42. Sobthex - (SOB thex / snub blended truncated 16) - cells are 64 tututs (TOO tut - the blend of two tuts) and 64 octs (which double up in a positive-negative pair). It has 192 vertices and has tessic symmetry. Its verf is a blend of two square pyramids, which looks similar to a butterfly wedge. It is tame and orientable. Discovered in mid-2006 by Mason Green, previously called spobthex for swirlprismatic blended thex.

S43. Sobtitho - (sob TITH tho / snub blended truncated tesseractihemioctachoron) - cells are 64 tuts, 64 thahs, and 16 tutoes (TOO toe - blend of two toes). It has 192 vertices and belongs to the sobthex regiment, it has an ionic tesseract symmetry. Discovered in mid-2006 by Mason Green, previously called spobtitho, also mistaken as a swirlprism blend. This one is wild and non-orientable.

SPs1. Stuthit - (STOO thit / snub tetrakis 32 hemi 32) - cells are 32 tututs, 32 tuts, 32 octs, 32 thahs, and 16 toes. It has 192 vertices and belongs to the sobthex regiment. It has chiral demi-tessic symmetry. I found this one on Feb. 8, 2007, it was originally named sputihi (sp for swirlprism, i's for 24 (now 32) - had the wrong count). This one is wild and non-orientable and is pseudo-scaliform.

SPs2. Scabtitho - (SCAB tith tho / snub cisblended truncated tesseractihemioctachoron) - cells are 32 tututs, 64 thahs, and 16 tutoes. It has 192 vertices and belongs to the sobthex regiment. This one was suspected to exist back in 2006, but we weren't sure at the time. I took a closer look at it and noticed that even though their vertices have the same shape, they come in two sorts, so this shape is pseudo-scaliform. It has demi-tessic symmetry and is tame and non-orientable.


Ico Scaliforms

Verfs of the Ico Scaliforms

These are in the ico regiment, the first two were found by the Polytope Discord team on the last week of March 2022 and the last one was found by the p o kekodjek in February 2023. They have 24 vertices and are wild and orientable.

S44. Kihi - (KI hi / skew 24hemi24) - cells are 24 bobipyrs and 12 bocucoes (bowtie cut co). Its verf is an essic symmetric faceting of the cube. I suspect it has 3-swirldappic symmetry.

S45. Pihi - (PI hi / pyri24hemi24) - cells are 24 squippies and 12 ebots (extended bowtie tegum). Its verf is a spiky faceting of the cube with no symmetry. I suspect it has 3-skibrick symmetry.

S150. Apihi - (AP a hi / alternate pyri24hemi24) - cells are 24 squippies and 12 ebots but in a different orientaion. Its verf is a spiky faceting of the cube with no symmetry. I suspect it has 3-skibrick symmetry.


Gudap Scaliforms

Verfs of the Gudap Scaliforms

These two are in the gudap regiment and were found by _Geometer in August 2019. They were planned to go in category S22, but would have got lost in the massive pecuexdap regiment, so I put them here. They have 50 vertices and are tame and orientable and has the same symmetry as gudap.

S46. Tocap - (TOE cap / toroidal cycloantiprism) - cells are 10 stips, 50 tets, and 50 squippies. Its verf looks like a claw, this one has a chasm.

S47. Gocap - (GO cap / great cycloantiprism) - cells are 10 pips, 50 tets, and 50 squippies. Its verf is a decked out wedge.


Gap Scaliforms

Verfs of the Gap Scaliforms

These are in the gap regiment and were found by H A M on April 6, 2022. They have 100 vertices, the first has 5-exdappic (gap) symmetry, the rest have 5-iodappic symmetry which is an ionic quarter of gap's symmetry.

S48. Dexdap - (DEX dap / dodecahedral extended double antiprism) - cells are 20 does, 100 tets, and 100 ifbahs (ike faceting 2-6 - two pentagons, 6 trigons). This one is non-orientable and wild.

S49. Sespex Dohap - (SES pex DOE hap / small snub pyriextended double hemiantiprism) - cells are 10 paps, 10 does, 25+25+100 tets, and 100 peppies. This one is non-orientable and wild.

S50. Spex Dohap - (SPEX doe hap / small pyriextended double hemiantiprism) - cells are 10 paps, 10 does, 25+25 tets, and 100 peppies. This one is orientable and wild.

S51. Spasex Dohap - (SPASE ex DOE hap / small pyrisnub extended double hemiantiprism) - cells are 10 paps, 10 does, 50+100 tets, and 100 peppies. This one is non-orientable and wild.

S52. Sassex Dohap - (SAS ex DOE hap / small snub extended double hemiantiprism) - cells are 10 paps, 10 does, 50 tets, and 100 ifthes (ike faceting 3-7). This one is non-orientable and wild.

SF4. Safex Dohap - (SAY fex DOE hap / small fissary extended double hemiantiprism) - cells are 100 tets and 100 scuffis. This one is fissary, non-orientable and wild. It also has chasms.


Padiap Scaliforms

Verfs of the Padiap Scaliforms

These are in the padiap regiment and were found by H A M on April 6, 2022. They have 100 vertices, the first has 5-exdappic symmetry, the others have 5-iodappic symmetry.

S53. Gasdexdap - (GAS dex dap / great stellated dodecahedral extended double antiprism) - cells are 20 gissids, 100 tets, and 100 gifbahs (gike faceting 2-6). This one is non-orientable and wild.

S54. Gespex Dohap - (GES pex DOE hap / great snub pyriextended double hemiantiprism) - cells are 10 starps, 10 gissids, 25+25+100 tets, and 100 stappies. This one is non-orientable and wild.

S55. Gopex Dohap - (GO pex DOE hap / great pyriextended double hemiantiprism) - cells are 10 starps, 10 gissids, 25+25 tets, and 100 stappies. This one is orientable and wild.

S56. Gapsex Dohap - (GAP sex DOE hap / great pyrisnub extended double hemiantiprism) - cells are 10 starps, 10 gissids, 50+100 tets, and 100 stappies. This one is non-orientable and wild.

S57. Gassex Dohap - (GAS ex DOE hap / great snub extended double hemiantiprism) - cells are 10 starps, 10 gissids, 50 tets, and 100 gifthes (gike faceting 3-7). This one is non-orientable and wild.

SF5. Gafex Dohap - (GAY fex DOE hap / great fissary extended double hemiantiprism) - cells are 100 tets and 100 scufgis. This one is fissary, non-orientable and wild.


Ipe Blends

Verfs of the Ipe Blends

These are the result of blending 8 ipes, gaddips, sissiddips, or gipes. These were found by a polytope Discorder going by H A M on February 28, 2022. They are tame and orientable with 96 vertices and have tessic symmetry.

S58. Prisdit - (PRISS dit / prismatorhombisnub distesseract) - cells are 16 ikes as 8 siddoes (but with a positive and a negative ike), 64 trips as 32 6/2 prisms (positive-negative pair), and 48 tutrips.

S59. Safdit - (SAF dit / small fusidistesseract) - cells are 16 gads as 8 presipsidoes (positive-negative pair) and 48 tupips.

S60. Gafdit - (GAF dit / great fusidistesseract) - cells are 16 sissids as 8 passipsidoes (positive-negative pair) and 48 tustips.

S61. Prarsdit - (PRARS dit / prismatorhombiretrosnub distesseract) - cells are 16 gikes as 8 sirsidoes (positive-negative paired), 64 trips as 32 6/2 prisms (positive-negative paired), and 48 tutrips.


Greater Ipe Blends

Verfs of the Greater Ipe Blends

These are the result of blending 360 ipes, gaddips, sissiddips, or gipes. These were found by H A M in March, 2022. They are tame and orientable with 1440 vertices and have hyic symmetry.

S62. Prishahi - (PRISH a hi / prismatorhombisnub hexa120) - cells are 120+600 ikes as 120 ike+snes, 2400 trips as 1200 6/2 prism, and 1200 fortrips (trip blended with 3 more). The trips and fortrips form combos of one fortrip and two trips.

S63. Safhiphehi - (saf HIF e hi / small fusihexiprismatohexa120) - cells are 120+600 gads as 120 gad+presipsis and 720 sixpips (pip blended with 5 more).

S64. Gafhiphehi - (gaf HIF e hi / great fusihexiprismatohexa120) - cells are 720 sissids as 120 sissid+passipsis and 720 sixstips (stip blended with 5 more).

S65. Prarshahi - (PRARSH a hi / prismatorhombiretrosnub hexa120) - cells are 120+600 gikes as 120 gike+sirseis, 2400 trips as 1200 6/2 prisms, and 1200 fortrips. The trips and fortrips form combos of one fortrip and two trips.


Ixitic Ipe Blends

Verfs of the Ixitic Ipe Blends

These are in the two regiments of the greater ipe blends but have ixitic symmetry. There are four in each regiment. These were found by the polytope Discorders in Mid March, 2022. They have 1440 vertices.

S66. Safpipsaphi - (saf PIPS a fee / small fusipentiprismatosnub penta120) - cells are 120 gads, 480 gads (as 120 4-gad compound), and 720 fivpips (a pip with for more pips blended on squares) - the first two cell types are co-realmic. This one is orientable and tame.

S67. Prisphi - (PRIS fee / prismatorhombisnub penta120) - cells are 120 ikes, 480 ikes (120 4-ike compound) which are corealmic with the 120 ikes, 480 trips, 480 fortrips which are corealmic to the 480 trips which are chirally positioned, 1440 trips as 720 6/2 prisms, and 720 fortrips which are corealmic with the 1440 trips. Say wuuuut! - I said this one is orientable and tame.

S68. Stis Fipaphi - (stis FIP a fee / small trisnub fusiprismatopenta120) - cells are 120 ikes, 480 tigdafs (accordions) as 120 4-tigdaf compounds which are corealmic to the ikes, 480 fortrips, 720 trips, and 1440 pips as 720 2-pip compounds which are slanted to each other. This one in wild and non-orientable.

S69. Stisp Fuphehi - (STISP foo FEE hee / small trisnub prismatofusiprismatohexi120) - cells are 120+120 ikes (120 siddos), 480 tigdafs (120 4-tigdaf compound) which are corealmic with the ikes, 480 trips, 480 fortrips which are corealmic to the trips, 720 tutrips, and 1440 pips as 720 compounds of two pips in slanted positions to each other. This one in wild and non-orientable.

S70. Gafpipsaphi - (gaf PIPS a fee / great fusipentiprismatosnub penta120) - cells are cells are 120 sissids, 480 sissids (as 120 4-sissid compound), and 720 fivstips (a stip with for more stips blended on squares) - the first two cell types are co-realmic. This one is orientable and tame.

S71. Prarsphi - (PRARS fee / prismatorhombiretrosnub penta120) - cells are 120 gikes, 480 gikes (120 4-gike compound) which are corealmic with the 120 gikes, 480 trips, 480 fortrips which are corealmic to the 480 trips which are chirally positioned, 1440 trips as 720 6/2 prisms, and 720 fortrips which are corealmic with the 1440 trips. This one is orientable and tame.

S72. Gets Fipaphi - (gets FIP a fee / great trisnub fusiprismatopenta120) - cells are 120 gikes, 480 tissidaf (six star thingies) as 120 4-tissidaf compounds which are corealmic to the gikes, 480 fortrips, 720 trips, and 1440 stips as 720 2-stip compounds which are slanted to each other. This one in wild and non-orientable.

S73. Getsip Fuphehi - (GET sip foo FEE hee / great trisnub prismatofusiprismatohexi120) - cells are 120+120 gikes (120 sirsidos), 480 tissidafs (120 4-tissidaf compound) which are corealmic with the gikes, 480 trips, 480 fortrips which are corealmic to the trips, 720 tutrips, and 1440 stips as 720 compounds of two stips in slanted positions to each other. This one in wild and non-orientable.


Tesapdid Regiment

Verfs of the Tesapdid Regiment

There are six scaliforms found in the tesapdid regiment plus two fissary ones. Tesapdid is the 2189th uniform polychoron found. These have iodecaic symmetry and were found by Galoomba not long after he found tesapdid. Info for this regiment came from the Scaliform Bananza spreadsheet. These are all non-orientable except for the first two.

S74. Sitsapsdid - (sit SAPS did / small tetrasnub prismatosnub disdecachoron) - cells are 10 ikes, 10 sissids, 40b trips, 60a+120c tets, 120 stappies, and 120c squippies. This one is wild.

S75. Gitsapsdid - (git SAPS did / great tetrasnub prismatosnub disdecachoron) - cells are 10 gikes, 10 gads, 40a trips, 60a+120b tets, 120 peppies, and 120d squippies. This one is wild.

S76. Pesdippisdid - (pes DIP pis did / pentasnub disprismatosnub disdecachoron) - cells are 10 gads, 10 sissids, 40 octs, 60a tets, 80(a+b) trips, 120a bobipyrs, 120 peppies, and 120 stappies. This one is wild.

S77. Sapshap - (SAP shap / small pentasnub hemiantipodichoron) - cells are 20 octs, 40a thahs, 40b+120c trips, 120c tets, and 120b bobipyrs. This one is wild.

S78. Gapshap - (GAP shap / great pentasnub hemiantipodichoron) - cells are 20 octs, 40b thahs, 40a+120c trips, 120b tets, and 120c bobipyrs. This one is wild.

S79. Tesap - (TEE sap / tetrasnub antipodichoron) - cells are 40 octs, 40a+40b trips, 120b+120c tets, and 120a bobipyrs. This one is tame.

SF6. Sifpisapdid - (SIF pis AP did / small fissary pentasnub antiprismatodisdecachoron) - cells are 10 ikes, 10 sissids, 20 octs, 40a thahs, 60a tets, 120c trips, 120 stappies, and 120a squippies. This one is fissary and wild.

SF7. Gifpisapdid - (GIF pis AP did / great fissary pentasnub antiprismatodisdecachoron) - cells are 10 gads, 10 gikes, 20 octs, 40b thahs, 60a tets, 120c trips, 120 peppies, and 120b squippies. This one is fissary and wild.


Diminishings and Friends

Verfs of the Diminishings and Friends

There are eight scaliforms that fit here so far, it was originally planned for cat. S28, but due to its small size, I added it here, I also moved spidrox and sporaggix from cat S4 to here. The others were found in 2021 by the polytope discord team. They are diminishings of rox, raggix, padohi, gidipthi, sidtaxhi, and gadtaxady as well as blends of the padohi and gidipthi ones. The first six are orientable and the last two are non-orientable, all are tame.

S80. Spidrox - (SPID drox / swirlprismatodiminished rox) - cells are 120 paps, 120 pips, and 600 squappies (square pyramids). This is the result of chopping off 120 vertices of rox, leaving pips behind. It is convex and has 600 vertices. It's verf looks like you took a pip and chose two corners which were as far as possible from each other and then chopped them off. In otherwords, all of rox's ikes turned into paps, while it's octs turned into squappies will produce this object. George Olshevsky found spidrox in the early mid-2000's. It is tame and orientable.

S81. Sporraggix - (spore RAG gix / swirlprismatoreplenished raggix) - cells are 120 starps, 120 stips, and 600 squappies. This is the conjugate of spidrox, so it is related to raggix in the same way spidrox is related to rox. It has 600 vertices. The verf is a strange looking thing with two crossed trapezoids as bases, twisted in relation to each other, a square, 4 right triangles, and two long isosceles triangles. Turn raggix's gikes into starps and it's octs into squappies, then fill in the blanks with stips and you'll get sporraggix. George Olshevsky has found this one when he found spidrox. It is tame and orientable.

S82. Sispaxthiccudy - (SIS pax thih COO dee / small swirlprismatic 600tris120cupolidis120) - cells are 120 stips, 120 starps, 120 paps, 600 trips, and 240 pecus (paring up). It is a padohi diminishing with 1200 vertices. It has sispic symmetry.

S83. Gispaxthiccudy - (SID pax thih COO dee / great swirlprismatic 600tris120cupolidis120) - cells are 120 pips, 120 starps, 120 paps, 600 trips, and 240 rastacus (pairing up). It is a gidipthi diminishing with 1200 vertices. It has sispic symmetry.

S84. Siddapsiddip Sidducstwy - (sid DAP sid dip sid DUCKS twee / small disdiakisantiprismatosnub disprismatosnub dicupolisnub 12kis120) - cells are 1440 stips as 120 giddirds, 1440 starps (pairs up as 720 10/4 aps), 1440 paps (pairs up as 720 10/2 aps), 7200 trips (pairs up as 3600 'X atop 8/2's), and 1440 tupecus (pairs up). It has hyic symmetry. It is formed by blending 12 sispaxthiccudies and has 7200 vertices.

S85. Giddapsiddip Sidducstwy - (gid DAP sid dip sid DUCKS twee / great disdiakisantiprismatosnub disprismatosnub dicupolisnub 12kis120) - cells are 1440 pips as 120 dirds, 1440 starps (pairs up as 720 10/4 aps), 1440 paps (pairs up as 720 10/2 aps), 7200 trips (pairs up as 3600 'X atop 8/2's), and 1440 turastacus (pairs up). It has hyic symmetry. It is formed by blending 12 gispaxthiccudies and has 7200 vertices.

S86. Squidditshi - (squid DIT she / small quadratitetrahedrosnub 120) - cells are 120 quistets and 480 trips. It is a diminishing of sidtaxhi and has 480 vertices. It has ixitic symmetry.

S87. Gaquidditshi - (GAH quid DIT she / great quadratitetrahedrosnub 120) - cells are 120 quistets and 480 trips. It is a diminishing of gadtaxady and has 480 vertices. It has ixitic symmetry.


Tispy Regiment

Verfs of the Tispy Regiment

There are four scaliforms that belong here plus two fissaries, it was originally planned for cat. S25 and were called 'bidex sishi derivatives', but due to its small size, they went here. These were first found by _Geometer in 2021 and later by the polytope discord team in 2022 to get the count using Miratope. They have the same 72 vertices as bidex and therefore have 3-spyritic symmetry. The first two are orientable and tame, the last four are non-orientable and wild. The last two are fissary.

S88. Tispy - (TIS pee / trigonal swirlpyritochoron) - cells are 48 octs and 72 stoppers (this is a sidtid faceting with 2 stars, 2 pentagons, 4 trigons, and 4 squares which has rectpyric symmetry which I named star pentagonal rhombihedron).

S89. Ritspy - (RIT spee / retrotrigonal swirlpyritochoron) - cells are 48 octs and 72 stappers (this is an inflected sidtid faceting with 2 stars, 2 pentagons, 4 trigons, and 2 squares which has rectpyric symmetry which I named star pentagonal retrohedron).

S90. Shitspy - (SHIT spee / small hemitrigonal swirlpyritochoron) - cells are 72 scufgis, 48b thahs, 72a squippies, 72 trips, and 144a tets. Pardon the really tounge in cheek short name, originally I had the swirl and pyrito part of the long name swapped and it would have been called shitpiss :P What fun we have with short names.

S91. Gohtspy - (GOTE spee / great hemitrigonal swirlpyritochoron) - cells are 72 scuffis, 48a thahs, 72b squippies, 72 trips, and 144b tets.

SF8. Sefohtspy - (see FOTE spee / small fissary hemitrigonal swirlpyritochoron) - cells are 72 scufgis, 48a thahs, 72a squippies, 72 trips, and 144a tets.

SF9. Gefohtspy - (gee FOTE spee / great fissary hemitrigonal swirlpyritochoron) - cells are 72 scuffis, 48b thahs, 72b squippies, 72 trips, and 144b tets.


Dope and Gissidip Blends

Verfs of the Dope Blends

These are the result of blending 360 dopes or 360 gissiddips. These were found by the p o kekodjek in November, 2022. They are fissary, tame and orientable with 96 vertices and have hyic symmetry. They are vertex fissary and might be considered as biform, but both types of vertices compound together with 2400 of these compound vertices, they are therefore 'combo-scaliform' and counted here.

SF10. Fuhiphehi - (FOO he FEE he / fusihexiprismatohexa120) - cells are 720 does as 120 sixdoes (compound of doe and dual of sne) and 720 sixpips.

SF11. Stuf Hephehi - (stuff HEF e he / stellar fusihexiprismatohexa120) - cells are 720 gissids as 120 sixgissids (compound of gissid and dual of sirseis) and 720 sixstips.


Conjugates

Below shows how these pair up as conjugates.

Conjugates

The following are self-conjugate: disdi, mesdi, dhahic, sobthex, sobtitho, stuthit, scabtitho.

The following are conjugate pairs: bidex-birgax, prissi-prarsi, sistakix-gastakix, otbott-otbaquitit, becsadic-quabcasdic, sebicsadic-squabcasdic, sesdicabdic-gesdicabdic, tocap-gocap, prisdit-prarsdit, safdit-gafdit.

The following are quasi-conjugate pairs: shi-rashi, prishi-prarshi, raprishi-raprarshi.

Category S2: Podary Scaliforms --- back to Polychoron Page --- Category S4: Ex and Gishi Scaliforms