idcossids

Category 28 - Idcossids

        Above are vertex figures of 12 different idcossids, in various orientations, as you can see, these are no doubt - monstrosities.  These verfs have such strange and chaotic charictaristics, that I have nick named a few of them, like 1377 - I call "Fangs", I call 1042 "Darth Vader", and 1302 "Yoshimoto".

        From the looks of these vertex figures, polychora from previous categories dont have a chance to beat them in complexity, to make matters worse, an idcossid has 7200 vertices, with 16 edges coming off each vertex - therefore they have 57600 edges!  I discovered these monstrosities in 1997 while considering the compound of 5 and 10 padohis (padohi has a pentagonal antipodium verf, cat. 21 is the padohi regiment) - these compounds are both uniform.  The 5-padohi is a chiral compound, the 10-padohi is the compound of the right 5-padohi and left 5-padohi, vertices crash, so the verf of this compound is a compound of 2 pentagonal antipodiums, this compound verf blends on a rectangular face (the verf of the cuboctahedron) - which I call the blending face of the verf, the cuboctahedra that form by the blending face will form the compound of 5 cuboctahedra in the idcossid - if you take any padohi that has coes, ohoes, or choes (cuboctahedron regiment members) it can be one of 2 components of the idcossid.  Example, let padohi A be a padohi with coes, ohoes, or choes, let padohi B also be a padohi with coes, ohoes, or choes (they can be different), then the first component is the right handed compound of 5 padohi As, and the 2nd component is the left handed compound of 5 padohi Bs, since both of these have a cuboctahedron regiment member as cells, the 2 components will blend together to form not a compound, but a non compound figure, many of these turn out to be true polychora - these are the idcossids.  If A and B were different, then the idcossid will be chiral.  There are a whopping 2749 idcossids! - these are no doubt the monsters of the fourth dimension along with their conjugates the dircospids.  I would consider the idcossid (and dircospid) discovery, my biggest polychoron discovery ever, this discovery was literally an answer to prayer.

        How bad are these polychora? - they are all snubs, nearly all are chiral, some have as many as 5 different snub cells, even snub pseudocells (has the faces, but missing the cells).  Many of these have 10 different types of cells.  The list of possible cells are these:

600 sissids (left), 600 gikes (left), 600 gacids (left)

600 sissids (right), 600 gikes (right), 600 gacids (right)

600 coes (blend - as 120 "5-co"), 600 ohoes (blend - as 120 "5-oho"), 600 choes (blend - as 120 "5-cho")

2400 coes (left), 2400 ohoes (left), 2400 choes (left)  - snub cells

2400 coes (right), 2400 ohoes (right), 2400 choes (right)  - snub cells

600 srids (left), 600 saddids (left), 600 sirds (left)

600 srids (right), 600 saddids (right), 600 sirds (right)

600 radeds (left), 600 ideds (left), 600 ris (left)

600 radeds (right), 600 ideds (right), 600 ris (right)

600 siids (left), 600 sidditdids (left), 600 siddies (left)

600 siids (right), 600 sidditdids (right), 600 siddies (right)

600 tis (left)

600 tis (right)

600 tuts (left acts as 120 "5-tut")

600 tuts (right acts as 120 "5-tut")  - right and left makes the 10-tut

2400 tuts (left snub cells)

2400 tuts (right snub cells)

3600 stips (left snub cells - stip=5/2P)

3600 stips (right snub cells)

6000 trips (2400+3600 - left snub cells) 

6000 trips (2400+3600 - right snub cells)

YIKES!

        The term "idcossid" originated from the name "idcossid pidpippis tuxdasix" which was my original short name for idcossid 82 (the first idcossid I have studied) - it was short for inverted dicuboctisnub double pseudodiprismicpseudoprismisnub tetra600dispiro600 (I plan on revising these names to a more systemmatic scheme - however I plan on keeping the term "idcossid").  I usually refer the idcossids and the dircospids together as "the Monster Snubs".  They aren't ordinary snubs, they are all non-Wythoffian snubs, like gidrid (Miller's Monster).  I have built models of several idcossid vertex figures, and they usually have between 100 and 300 pieces (usually in a chaotic looking pattern) - These polychora would no doubt have millions if not tens or hundreds of millions of piecies, so far no idcossid has been sectioned - I do hope to have one done for the CD.  The first one planned to be sectioned will be sadohos daskydox - (small disoctahemioctisnub disnub deca120dis600) - cells are 4800 ohoes, 6000 tuts (1200 (120 "10-tut"s) + 4800 snub tuts), and 1200 gikes (as 600 "2-gike"s) - this one is not chiral (verf is pictured above).  Sadohos daskydox is the blended form of the compound of 10 sad phiddixes (padohi member with 120 gikes, 600 tuts, and 600 ohoes).

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