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Polychoron News
Feb. 2002 - I discovered 2 new polychora, both with square duoprism symmetry - the first (iquipadah) is a blend of sidpith (small disprismatotesseractihexadecachoron) with a compound of 2 orthogonal 4,8-duoprisms. Gaquipadah is the conjugate. I included these with cat. 20 - the miscelaneous ones. This brings the count to 8188. See pics.
April 2002 - Recently Hironori Sakamoto has been corresponding with me by e-mail. He started to search out the sidtaps (one of the baby monster snub regiments) - and found only 15, after mentioning this to me, I looked over this regiment again and found that I had included 2 degenerate ones by mistake - so this regiment looses 2 polychora, as well as the conjugate regiment (gidtaps) - so there are now 30 polychora in category 27 instead of 34. Later He searched out the affixthi regiment and discovered 4 new polychora in this regiment which was overlooked in my count - bringing the affixthi regiment to 100 (it was 96). The afdec regiment has similar vertex figures, and it increased by 2. Now there are 54 afdecs (was 52). The polychoron count first went down to 8184, then back up to 8190.
May 2002 - The number of uniform polychora to have some cross sections rendered has reached 1000, (3 years ago there were only around 20 or so). These 1000+ polychora are all planned to be on my upcoming polychoron CD, complete with sections and vertex figures. The monster pictured on the right is the .35 section of the 1000th polychoron to be rendered - giddip pixhihy - it belongs to the gidipthi regiment and has a spiky vertex figure, its cells are 120 gacids (great complex icosidodecahedra), 120 tiggies, 600 choes, and 1200 trips (triangular prisms). Since this polychoron has exotic cells (gacids), some polychoron definitions would exclude it, however I include this one (and similar ones) since each face joins exactly two cells (even though some cells are exotic).
July 2002 - Lately I've been studying higher dimensional polytopes and found a very interesting polyhexon (7-D polytope). This polyhexon is uniform and I call it "sidhotif" short for small duohedratotetratotetradecahexon - it is a non-convex polyhexon belonging to the runcinated hepteract regiment - and it has one very interesting property - the universe could go right through the center of it without touching anything! as a matter of fact, 35 universes at right angles to each other all meeting at the center could stick through sidhotif without any one part of it being touched! - I call these sort of realmic holes "gulleys". I call a planar hole - a "chasm". The hexons (6-D facets) of sidhotif are the following: 14 scadifdixed (see below), 560 tetcubes (tetrahedron x cube duoprism), and 448 hixips (hix prism = 5-D simplex prism). Scadifdix is a polypenton (6-D) with chasms in it, it has the following pentons (5-D facets) - 12 stans (see below), 160 tracubes (triangle x cube duoprism), 240 squatets (square x tet duoprism), 192 penps (pentachoron prism), and 64 hixes (hix = 5-D simplex). Stan is a polytetron with holes going through the center, it belongs to the shanit regiment (5-D version of sirco) - its tetrons are these: 10 sniptoes (see below) and 40 tesseracts (as cube prisms). I have also recently rendered "poke" sections (cross sections of cross sections) of stan as well as other polytetra in this regiment. Snipto is a polychoron of the sidpith regiment (in cat 11, sidpith is the 4-D version of sirco) - snipto's cells are 8 srohs, 8 cubes, and 24 cubes (as square prisms) - I recently discovered that snipto will actually have a hollow center, making it possible for the higher dimensional figures to have holes, chasms, and gulleys.
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