20c
Category 20c - Swirlprisms
Above are sections of 4 of the swirlprisms, sisp - quite nice and simple, gisp - the most outragious looking polychoron, ditsop - one of the "middle" swirls, and the hybrid swirlprism spittid - which I sometimes refer to as the "ugliest uniform polychoron"
The swirlprisms were first discovered by George Olshevsky in 1999, he first found sisp and gisp, then later I found ditsop and tipsop, then George found the 6 hybrid swirls. They have a very unusual symmetry group (or a sub symmetry of this group). Sisp belongs to the ex regiment while gisp belongs to the gishi regiment, the others belong to the sishi regiment, all having 120 vertices. The hybrid swirls are formed by taking the small and great prismasauri and blending out a number of "swirlsets" of prisms (the cells of the small and great prismasauri). The swirlprism symmetry can be seen by taking a 120-cell and use 12 colors to color 10 dodecahedra each, the 10 dodecahedra form a ring (also called girdle), it has 5 girdles adjacent to it, that swirl around the first one (each girdle colored its own color), then 5 more swirling around those (these are orthogonal to the last five), and the final one which is orthogonal from the first - all 12 girdles swirl around each other. The swirlprisms later compelled me to find the polytwisters. The swirlprisms are as follows:
1129. Sisp - small swirlprism - has 120 paps, has swirlprism symmetry.
1130. Gisp - great swirlprism - has 120 starps, has swirlprism symmetry. Extremely wild looking sections.
1131. Ditsop - ditrigonary swirlprism - has 120 starps, 120 paps, and 600 tets. Has swirlprism symmetry.
1132. Tipsop - triangular prismattic swirlprism - has 120 starps, 120 paps, and 1200 trips. Has swirlprism symmetry.
Hybrid Swrilprisms:
1133. Sphix - swirlprismattic 120-600 - has 120 pips (pentagonal prism) and 600 stips (5/2 prism). Has swirlprism symmetry.
1134. Spiddit - swirlprismattic 240-480 - has 240 pips and 480 stips. Verf looks like a dodecahedron which got chewed up and spit back out! I also call this "the Clunker". Has a sub symmetry of the swirlprism (Due to the chaotic appearance of the sections, I sometimes call this symmetry the "clobbered" symmetry).
1135. Sispatit - small swirlprismattic 360-360 - has 360 pips and 360 stips. Has a sub symmetry of the swirlprism (a higher symmetry than the clobbered). Verf has hat like patterns on it.
1136. Gispatit - great swirlprismattic 360-360 - has 360 pips and 360 stips. Same symmetry as sispatit - uses different swirl sets than sispatit. Verf has fish like patterns on it.
1137. Spittid - swirlprismattic 480-240 - has 480 pips and 240 stips. Has clobbered symmetry - I also call this one "the Trash Compactor" and refer it as the "Ugliest Uniform Polychoron".
1138. Spaxhi - swirlprismattic 600-120 - has 600 pips and 120 stips. Has swirlprism symmetry, this one is quite intricate and attractive.
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