Acronym | prit | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Name |
prismatorhombated tesseract, prismatotruncated hexadecachoron, runcitruncated hexadecachoron | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Net |
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Cross sections |
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Circumradius | sqrt[(7+3 sqrt(2))/2] = 2.370932 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Vertex layers |
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Vertex figure |
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Lace city in approx. ASCII-art |
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x3x x3x u3o u3o x3w x3w x3o x3o u3q u3q x3q u3w u3w x3q W3o W3o w3o W3x W3x w3o o3w x3W x3W o3w o3W o3W q3x w3u w3u q3x q3u q3u o3x o3x w3x w3x o3u o3u x3x x3x | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Coordinates | ((1+2 sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2) & all permutations, all changes of sign | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
General of army | (is itself convex) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Colonel of regiment |
(is itself locally convex
– uniform polychoral members:
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Dihedral angles | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Face vector | 192, 480, 368, 80 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Confer |
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External links |
As abstract polytope prit is isomorphic to paqrit, thereby replacing sirco by querco.
Note that prit can be thought of as the external blend of 1 thex + 16 tuttips + 32 thiddips + 24 squippyps + 8 octasircos. This decomposition is described as the degenerate segmentoteron xx3xx3oo4ox&#x. – Alternatively it could also be decomposed into 1 sidpith + 16 tetatuts + 32 tricupes + 24 teses + 8 cubasircoes, as described by xx3ox3oo4xx&#x. – Further, although subdimensioanlly degenerate, prit could also be decomposed into 1 tat + 16 tetaltuts + 32 hippyps + 24 squicufs + 8 sircoatics, as described by ox3ox3xo4xx&#x.
Incidence matrix according to Dynkin symbol
x3x3o4x . . . . | 192 | 1 2 2 | 2 2 1 2 1 | 1 2 1 1 --------+-----+------------+----------------+----------- x . . . | 2 | 96 * * | 2 2 0 0 0 | 1 2 1 0 . x . . | 2 | * 192 * | 1 0 1 1 0 | 1 1 0 1 . . . x | 2 | * * 192 | 0 1 0 1 1 | 0 1 1 1 --------+-----+------------+----------------+----------- x3x . . | 6 | 3 3 0 | 64 * * * * | 1 1 0 0 x . . x | 4 | 2 0 2 | * 96 * * * | 0 1 1 0 . x3o . | 3 | 0 3 0 | * * 64 * * | 1 0 0 1 . x . x | 4 | 0 2 2 | * * * 96 * | 0 1 0 1 . . o4x | 4 | 0 0 4 | * * * * 48 | 0 0 1 1 --------+-----+------------+----------------+----------- x3x3o . ♦ 12 | 6 12 0 | 4 0 4 0 0 | 16 * * * x3x . x ♦ 12 | 6 6 6 | 2 3 0 3 0 | * 32 * * x . o4x ♦ 8 | 4 0 8 | 0 4 0 0 2 | * * 24 * . x3o4x ♦ 24 | 0 24 24 | 0 0 8 12 6 | * * * 8 snubbed forms: β3x3o4x, x3β3o4x, x3x3o4s, β3β3o4x, β3x3o4β, x3β3o4β, β3β3o4β
x3x3/2o4/3x . . . . | 192 | 1 2 2 | 2 2 1 2 1 | 1 2 1 1 ------------+-----+------------+----------------+----------- x . . . | 2 | 96 * * | 2 2 0 0 0 | 1 2 1 0 . x . . | 2 | * 192 * | 1 0 1 1 0 | 1 1 0 1 . . . x | 2 | * * 192 | 0 1 0 1 1 | 0 1 1 1 ------------+-----+------------+----------------+----------- x3x . . | 6 | 3 3 0 | 64 * * * * | 1 1 0 0 x . . x | 4 | 2 0 2 | * 96 * * * | 0 1 1 0 . x3/2o . | 3 | 0 3 0 | * * 64 * * | 1 0 0 1 . x . x | 4 | 0 2 2 | * * * 96 * | 0 1 0 1 . . o4/3x | 4 | 0 0 4 | * * * * 48 | 0 0 1 1 ------------+-----+------------+----------------+----------- x3x3/2o . ♦ 12 | 6 12 0 | 4 0 4 0 0 | 16 * * * x3x . x ♦ 12 | 6 6 6 | 2 3 0 3 0 | * 32 * * x . o4/3x ♦ 8 | 4 0 8 | 0 4 0 0 2 | * * 24 * . x3/2o4/3x ♦ 24 | 0 24 24 | 0 0 8 12 6 | * * * 8
xuxxux3ooxxoo4xxxxxx&#xt → all non-central heights = 1/sqrt(2) = 0.707107 central height = 1 (sirco || pseudo (u,x)-sirco || pseudo girco || pseudo girco || pseudo (u,x)-sirco || sirco) o.....3o.....4o..... & | 48 * * | 2 2 1 0 0 0 0 0 0 | 1 2 1 2 2 0 0 0 0 0 0 0 0 | 1 1 1 2 0 0 0 .o....3.o....4.o.... & | * 48 * | 0 0 1 2 2 0 0 0 0 | 0 0 0 2 2 1 1 2 0 0 0 0 0 | 0 1 1 2 1 0 0 ..o...3..o...4..o... & | * * 96 | 0 0 0 0 1 1 1 1 1 | 0 0 0 0 1 0 1 1 1 1 1 1 1 | 0 0 1 1 1 1 1 ----------------------------+----------+----------------------------+----------------------------------------+------------------ x..... ...... ...... & | 2 0 0 | 48 * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0 0 ...... ...... x..... & | 2 0 0 | * 48 * * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0 0 oo....3oo....4oo....&#x & | 1 1 0 | * * 48 * * * * * * | 0 0 0 2 2 0 0 0 0 0 0 0 0 | 0 1 1 2 0 0 0 ...... ...... .x.... & | 0 2 0 | * * * 48 * * * * * | 0 0 0 1 0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0 0 .oo...3.oo...4.oo...&#x & | 0 1 1 | * * * * 96 * * * * | 0 0 0 0 1 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0 0 ..x... ...... ...... & | 0 0 2 | * * * * * 48 * * * | 0 0 0 0 1 0 0 0 1 1 1 0 0 | 0 0 1 1 0 1 1 ...... ..x... ...... & | 0 0 2 | * * * * * * 48 * * | 0 0 0 0 0 0 1 0 1 0 0 1 0 | 0 0 1 0 1 1 0 ...... ...... ..x... & | 0 0 2 | * * * * * * * 48 * | 0 0 0 0 0 0 0 1 0 1 0 0 1 | 0 0 0 1 1 0 1 ..oo..3..oo..4..oo..&#x | 0 0 2 | * * * * * * * * 48 | 0 0 0 0 0 0 0 0 0 0 1 1 1 | 0 0 0 0 1 1 1 ----------------------------+----------+----------------------------+----------------------------------------+------------------ x.....3o..... ...... & | 3 0 0 | 3 0 0 0 0 0 0 0 0 | 16 * * * * * * * * * * * * | 1 0 1 0 0 0 0 x..... ...... x..... & | 4 0 0 | 2 2 0 0 0 0 0 0 0 | * 24 * * * * * * * * * * * | 1 0 0 1 0 0 0 ...... o.....4x..... & | 4 0 0 | 0 4 0 0 0 0 0 0 0 | * * 12 * * * * * * * * * * | 1 1 0 0 0 0 0 ...... ...... xx....&#x & | 2 2 0 | 0 1 2 1 0 0 0 0 0 | * * * 48 * * * * * * * * * | 0 1 0 1 0 0 0 xux... ...... ......&#xt & | 2 2 2 | 1 0 2 0 2 1 0 0 0 | * * * * 48 * * * * * * * * | 0 0 1 1 0 0 0 ...... .o....4.x.... & | 0 4 0 | 0 0 0 4 0 0 0 0 0 | * * * * * 12 * * * * * * * | 0 1 0 0 1 0 0 ...... .ox... ......&#x & | 0 1 2 | 0 0 0 0 2 0 1 0 0 | * * * * * * 48 * * * * * * | 0 0 1 0 1 0 0 ...... ...... .xx...&#x & | 0 2 2 | 0 0 0 1 2 0 0 1 0 | * * * * * * * 48 * * * * * | 0 0 0 1 1 0 0 ..x...3..x... ...... & | 0 0 6 | 0 0 0 0 0 3 3 0 0 | * * * * * * * * 16 * * * * | 0 0 1 0 0 1 0 ..x... ...... ..x... & | 0 0 4 | 0 0 0 0 0 2 0 2 0 | * * * * * * * * * 24 * * * | 0 0 0 1 0 0 1 ..xx.. ...... ......&#x | 0 0 4 | 0 0 0 0 0 2 0 0 2 | * * * * * * * * * * 24 * * | 0 0 0 0 0 1 1 ...... ..xx.. ......&#x | 0 0 4 | 0 0 0 0 0 0 2 0 2 | * * * * * * * * * * * 24 * | 0 0 0 0 1 1 0 ...... ...... ..xx..&#x | 0 0 4 | 0 0 0 0 0 0 0 2 2 | * * * * * * * * * * * * 24 | 0 0 0 0 1 0 1 ----------------------------+----------+----------------------------+----------------------------------------+------------------ x.....3o.....4x..... & ♦ 24 0 0 | 24 24 0 0 0 0 0 0 0 | 8 12 6 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * ...... oo....4xx....&#x & ♦ 4 4 0 | 0 4 4 4 0 0 0 0 0 | 0 0 1 4 0 1 0 0 0 0 0 0 0 | * 12 * * * * * xux...3oox... ......&#xt & ♦ 3 3 6 | 3 0 3 0 6 3 3 0 0 | 1 0 0 0 3 0 3 0 1 0 0 0 0 | * * 16 * * * * xux... ...... xxx...&#xt & ♦ 4 4 4 | 2 2 4 2 4 2 0 2 0 | 0 1 0 2 2 0 0 2 0 1 0 0 0 | * * * 24 * * * ...... .oxxo.4.xxxx.&#xt ♦ 0 8 16 | 0 0 0 8 16 0 8 8 8 | 0 0 0 0 0 2 8 8 0 0 0 4 4 | * * * * 6 * * ..xx..3..xx.. ......&#x ♦ 0 0 12 | 0 0 0 0 0 6 6 0 6 | 0 0 0 0 0 0 0 0 2 0 3 3 0 | * * * * * 8 * ..xx.. ...... ..xx..&#x ♦ 0 0 8 | 0 0 0 0 0 4 0 4 4 | 0 0 0 0 0 0 0 0 0 2 2 0 2 | * * * * * * 12
qo3xx3oq *b3xx&#zx → height = 0 (tegum sum of 2 mutually gyrated (x,x,q)-tahs) o.3o.3o. *b3o. | 96 * | 2 1 2 0 0 | 1 2 1 2 2 0 0 | 1 1 1 2 0 .o3.o3.o *b3.o | * 96 | 0 0 2 2 1 | 0 0 1 2 2 1 2 | 0 1 1 2 1 -------------------+-------+-----------------+----------------------+------------ .. x. .. .. | 2 0 | 96 * * * * | 1 1 0 1 0 0 0 | 1 1 0 1 0 .. .. .. x. | 2 0 | * 48 * * * | 0 2 0 0 2 0 0 | 1 0 1 2 0 oo3oo3oo *b3oo&#x | 1 1 | * * 192 * * | 0 0 1 1 1 0 0 | 0 1 1 1 0 .. .x .. .. | 0 2 | * * * 96 * | 0 0 0 1 0 1 1 | 0 1 0 1 1 .. .. .. .x | 0 2 | * * * * 48 | 0 0 0 0 2 0 2 | 0 0 1 2 1 -------------------+-------+-----------------+----------------------+------------ .. x.3o. .. | 3 0 | 3 0 0 0 0 | 32 * * * * * * | 1 1 0 0 0 .. x. .. *b3x. | 6 0 | 3 3 0 0 0 | * 32 * * * * * | 1 0 0 1 0 qo .. oq ..&#zx | 2 2 | 0 0 4 0 0 | * * 48 * * * * | 0 1 1 0 0 .. xx .. ..&#x | 2 2 | 1 0 2 1 0 | * * * 96 * * * | 0 1 0 1 0 .. .. .. xx&#x | 2 2 | 0 1 2 0 1 | * * * * 96 * * | 0 0 1 1 0 .o3.x .. .. | 0 3 | 0 0 0 3 0 | * * * * * 32 * | 0 1 0 0 1 .. .x .. *b3.x | 0 6 | 0 0 0 3 3 | * * * * * * 32 | 0 0 0 1 1 -------------------+-------+-----------------+----------------------+------------ .. x.3o. *b3x. ♦ 12 0 | 12 6 0 0 0 | 4 4 0 0 0 0 0 | 8 * * * * qo3xx3oq ..&#zx ♦ 12 12 | 12 0 24 12 0 | 4 0 6 12 0 4 0 | * 8 * * * qo .. oq xx&#zx ♦ 4 4 | 0 2 8 0 2 | 0 0 2 0 4 0 0 | * * 24 * * .. xx .. *b3xx&#x ♦ 6 6 | 3 3 6 3 3 | 0 1 0 3 3 0 1 | * * * 32 * .o3.x .. *b3.x ♦ 0 12 | 0 0 0 12 6 | 0 0 0 0 0 4 4 | * * * * 8
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