Category S4: Scaliform Swirlprisms


Like the uniform swirlprisms in polychoron category 20, these scaliforms have the same sort of swirling symmetries.

Sisp's Friends

Verfs of Sisp's Friends

These swirlprisms are in the ex regiment with sisp, they have 120 vertices.

Spysp - (SPISP / small pyramidic swirlprism) - cells are 240 peppies (pentagon pyramids). It almost belongs to the ex regiment (it's missing some of ex's edges). It's verf looks like a pentagon antiprism with five edges carved out in a chiral way. This polychoron has the strange property that it's entire surface is exposed, even though it is not convex - it is actually concave. This object was discovered by George Olshevsky in the early mid-2000's. It is tame and orientable.

Stodsap - (STOD sap / small toroidal digonal swirlprism) - cells are 240 'butterfly pentagonal wedge's. Stodsap is the result of blending two sisps. The cells can be generated by blending two paps within an ike - this is a strange shape with a hole in it - but this shape is exotic, however, it can actually be split where it is two cells connected by two edges - these cells look like some sort of butterfly wedge but with pentagons intersecting inside instead of triangles. This makes it ambigous and it could be considered as exotic celled or legit depending on how we look at it. It's verf is wacky looking - it looks like you took a hollow gad and blown off some of it's wedges, resulting in some sort of twisted toroid. Stodsap, which is hollow inside, is no doubt one of the most outlandish looking polychora due to the many twisted chasms swirling about each other. I found this oddball around 2004 and later built a model of it's verf. It is wild and orientable.

Sodasp - (SO dasp / small digonal swirlprism) - cells are 120 'spaceships'. It is the result of blending fix with stodsap. The cells look like two fused wedges with disphenoids dangling off the blended area, making it look like a winged spaceship. It's verf has 4 piscoids, 4 long isosceles and 4 small isosceles triangles. The piscoids look like fish swimming by each other. I found this one in summer 2005. It is orientable and tame.

Stasp - (STASP / small trigonal swirlprism) - cells are 120 'accordion's. To generate the accordion shaped cell, take a gad and stand it on a pseudo-triangle - remove the 6 equatorial pentagons (leaving the top three and bottom three), then add three triangles near the top pseudo-triangle, and do likewise to the bottom - this is the accordion. It has a spiky toroidal verf with chiral trigonal antiprism symmetry which has three butterflies and three crossed trapezoids. It is tame and non-orientable. I found it in summer 2005 also.

Sotatsop - (so TAT sop / small toroidal trigonal swirlprism) - cells are 120 'crazy-tube's. To find it's cells, consider the gad mentioned with stasp - this time keep the equatorial pentagons and remove the others - also keep the same set of triangles - the result is some sort of tube shape. Its verf has a chiral trigonal antiprism symmetry and has 6 isosceles triangles and 6 sombraroids. I found this in summer 2005. It is tame and non-orientable.


Sishi Swirls

Verfs of the Sishi Swirls

These swirlprisms are in the sishi regiment, they have 120 vertices.

Sispyphi - (sis PIFF fee / small swirlprismatic pyri-120) - cells are 120 paps and 240 stappies. Paps connect by pentagons, stappies connect by stars, while they connect to each other by triangles. The verf has a swirly appearance resembling a tall starp (5/3 AP) with disphenoids dangling off five of the edges. I discovered it in early 2005. It is tame and orientable.

Gispyphi - (giss PIFF fee / great swirlprismatic pyri-120) - cells are 120 starps and 240 peppies. Starps connect by stars, peppies connect by pentagons, while triangles connect them together. The verf has a swirly spiky appearance, almost looking like a sandwich with five spikes shooting off both sides. I also found this one in early 2005. It is tame and orientable.


Gisp's Friends

Verfs of Gisp's Friends

These swirlprisms are in the gishi regiment with gisp, they have 120 vertices.

Gypasp - (JI pasp / great pyramidic swirlprism) - cells are 240 stappies which are grouped in pairs. It almost belongs to the gishi regiment. It's verf looks like a twisted stap. It was also found by George Olshevsky during the spysp discovery. It is tame and orientable.

Gatodsap - (ga TODD sap / great toroidal digonal swirlprism) - cells are 240 'two-star thingy's. It is the result of blending two gisps. The cells can be found by blending two starps within a gike, which is splitable - split it into it's two parts, these parts are the cells. It's verf is the reslult of blending two gisp verfs. This polychoron will also be wacky looking and quite spiky. I found this one around 2004. It is wild and orientable. It looks fissary, but this is caused by the "two star thingy's" forming positive-negative pairs and thus removing their intersection areas out. Due to its ambiguous nature, we could consider this one and stodsap as exotic instead of legit polychora.

Godasp - (GO dasp / great digonal swirlprism) - cells are 120 'four-star thingy's. It is the result of blending gofix with gatodsap. It's cells will have four stars in it along with eight triangles. Its verf has a strange look, it reminds me of a Rubik's puzzle with partially twisted faces. The verf has 4 sombraroids, 4 long and 4 short isosceles triangles. I found this one in summer 2005. It is orientable and tame.

Gotasp - (GO tasp / great trigonal swirlprism) - cells are 120 'six-star thingy's. I found it in summer 2005 also. Its verf has 6 trapezoids and 6 butterflies and has chiral trigonal antiprism symmetry. It is tame and non-orientable.

Gotatsop - (go TAT sop / great toroidal trigonal swirlprism) - cells are 120 'six-star-thingamajigs'. I found it in summer 2005. Its toroidal verf has chiral trigonal antiprism symmetry and has 6 isosceles triangles and 6 piscoids. It is tame and non-orientable.


Rox Swirls

Verfs of the Rox Swirls

These swirlprisms are formed from rox and its conjugate raggix.

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.

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.


Conjugates

Below shows how these pair up as conjugates.

Conjugates

The following are conjugate pairs: spysp-gypasp, stodsap-gatodsap, sodasp-godasp, stasp-gotasp, sotatsop-gotatsop, sispyphi-gispyphi, spidrox-sporraggix.

Category S3: Special Scaliforms --- back to Polychoron Page --- Category S5: Ondip Family