Lately, I've been rendering 2-D fields of 3-D sections of many of the uniform polytera (5-D versions of polyhedra). I recently hit an interesting milestone - all of the main regiments (those with hexateric (hixic), penteractic (pentic), and demipenteractic (hinnic) symmetry) has at least one member rendered in sections - I've also rendered all known uniform polytera in regiments with hixic and hinnic symmetries. That means it's time to reveal the uniform polytera in cross sections, so I decided to make a polyteron of the day website. Pictured will be the verf and a field of cross sections of each polyteron. Click on the field of sections for a much larger picture with many more sections rendered at a much larger size. Polytera released in September has been moved to here.
Oct. 1, 2013 - Gancpan - Aka - great spinocelliprismated penteract. It is a non-orientable member of the seven membered getitdin regiment, getitdin has the symbol o(o'x"x)x = oGx. Its facets are 10 girpdohs (yellow), 10 gnappoths (cyan), 32 tips (red), and 80 tuttips (blue). Gancpan looks "gancsta"!
Oct. 3, 2013 - Skatbacadint - Aka - small skewtrigonary biprismatocellidispenteracti32. It has the symbol xo(o'x"x) = xoG. It has the second largest known regiment amongst the non-prismattic uniform polytera, second only to nit. The regiment contains 133 members. It can be considered as the 5-D version of skiviphado. Its facets are 10 gittiths (lavender), 10 sidpiths (green), 32 spids (red), 40 goccopes (yellow), and 80 tistodips (blue).
Oct. 4, 2013 - Rawcax - Aka - retrosphenary cellihexateron. It belongs to the 15 member sarx regiment, which has the symbol ooxox. Its facets are 6 raps (blue), 6 rawvtips (red), 15 tepes (magenta), 15 tuttips (brown), and 20 thiddips (green).
Oct. 5, 2013 part 1 - Rin - Aka - rectified penteract. It has the symbol ooox'o = oo6x. Its regiment contains 11 members, which includes tin from Sept 25. Its facets are 10 rits (red) and 32 pens (blue).
Oct. 5, 2013 part 2 - Rat - Aka - rectified triacontaditeron or rectified pentacross. It has the symbol oxoo'o = ox8o. Its regiment contains 44 members, which includes ratchet from Sept 29. Its facets are 10 hexes (brownish) and 32 raps (magenta).
Oct. 8, 2013 part 1 - Garcornit - Aka - great retrocellirhombated penteracti32. It is in the wacbinant regiment which also contains gadencorm from Sept. 27. Garcornit's symbol is (o'x"(x)o,x). Its facets are 10 wavitoths (light magenta), 32 rawvtips (blue), 10 giphadoes (cyan), 10 gichadoes (red), and 80 tisdips (wood).
Oct. 8, 2013 part 2 - Wacbinant - Aka - Sphenary cellibiprimatopenteractipenteracti32. Wacbinant's symbol is (o'x"x)ox = Gox. It's regiment has 27 members. Its facets are 10 wavitoths (red-orange), 32 srips (yellow), 10 quiprohs (purple), 40 goccopes (aqua), and 80 tisdips (blue).
Oct. 9, 2013 part 1 - Quittin - Aka - quasitruncated penteract or stellatruncated penteract. It is a lone operative with the symbol ooox"x. It is the 5-D version of quith. An interesting thing occurs here, quittin has holes in it due to density zero regions in the quitit shaped facets. Its facets are 10 quitits (lavender) and 32 pens (aqua).
Oct. 9, 2013 part 2 - Gaqrin - Aka - great quasirhombated penteract. It is a lone operative with the symbol ooxx"x. Its facets are 10 gaqrits (blue), 32 tips (golden), and 80 tepes (red).
Oct. 10, 2013 part 1 - Hin - Aka - demipenteract, also known as 121. Its symbol is oo8x. The hin regiment has 6 members in it, including one that is noble. Its facets are 10 hexes (green) and 16 pens (yellow). Its verf is also uniform and shaped like a rap (rectified pentachoron).
Oct. 10, 2013 part 2 - Girn - Aka - cantitruncated penteract or great rhombated penteract. It is a lone operative with the symbol ooxx'x. Its facets are 10 grits (red), 32 tips (wud), and 80 tepes (cyan).
Oct. 11, 2013 part 1 - Dah - Aka - dishexadecateron. It belongs to the hin regiment and its verf is a firp. Its facets are 16 raps (pink) and 16 pens (blue).
Oct. 11, 2013 part 2 - Han - Aka - hexadecapenteract. It belongs to the hin regiment and its verf is a pinnip. Its facets are 10 hexes (yellow) and 16 raps (blue gray).
Oct. 11, 2013 part 3 - Hit - Aka - hexadecateron. It is a noble member of the hin regiment, hin's symbol being oo8x = ooos's. Its facets are 16 pinnips (wood).
Oct. 13, 2013 part 1 - Radah - Aka - retrodishexadecateron. It is a spiky member of the hin regiment. Its facets are 16 pens (cyan) and 16 firps (lavender).
Oct. 13, 2013 part 2 - Rinah - Aka - retropenteractihexadecateron. It belongs to the hin regiment and it is a copycat of han (looks just like it on the outside), only the internal structure looks different - so I rendered the hexes as transparent to see the inside. Its facets are 10 hexes (transparent red) and 16 firps (green).
Oct. 15, 2013 part 1 - Irl - Aka - invertiretrolepidoteron. It is a member of the nit regiment. Its facets are 16 pinnips (red), 16 rawvtips (purple), and 16 sirdops (cyan).
Oct. 15, 2013 part 2 - Raccoth - Aka - retrocelli32-16teron. This strange polyteron belongs to the nit regiment. Its facets are 32 firps (purple and green), 16 garpops (yellow), and 40 ohopes (red).
Oct. 19, 2013 part 1 - Scad - Aka - small cellated dodecateron. Its symbol is xooox and its regiment contains 11 members. Its facets are 12 pens (yellow and magenta), 30 tepes(blue and red), and 20 triddips (green).
Oct. 19, 2013 part 2 - Dibhid - Aka - dodecabiprismatohemidodecateron. This one belongs to the scad regiment. Its facets are 12 pens (red and green), 20 triddips (yellow), and 6 spids (blue). Dibhid is pronounced like (DIV vid).
Oct. 19, 2013 part 3 - Chad - Aka - cellihemidodecateron. This one belongs to the scad regiment. Its facets are 30 tepes (cyan and yellow) and 6 spids (red).
