Acronym | grip | |||||||||||||||||||||||||||||||||||||||||||||
Name |
great rhombated pentachoron, cantitruncated pentachoron | |||||||||||||||||||||||||||||||||||||||||||||
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Cross sections |
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Circumradius | sqrt(17/5) = 1.843909 | |||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. trip | 13/sqrt(60) = 1.678293 | |||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. tut | 9/sqrt(40) = 1.423025 | |||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. toe | 3/sqrt(10) = 0.948683 | |||||||||||||||||||||||||||||||||||||||||||||
Vertex figure |
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Vertex layers |
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Lace city in approx. ASCII-art |
x3x u3o x3o -- x3x3o (tut) u3x H3o x3o -- u3x3o ((u,x)-tut) x3u H3o u3o -- x3u3o ((x,u)-tut) x3x x3u u3x x3x -- x3x3x (toe) | |||||||||||||||||||||||||||||||||||||||||||||
x o u x x u o x -- x3x3o (tut) u o w x x w o u -- u3x3o ((u,x)-tut) x o w u u w o x -- x3u3o ((x,u)-tut) x x u u xw wx u u x x -- x3x3x (toe) | ||||||||||||||||||||||||||||||||||||||||||||||
Volume | 287 sqrt(5)/32 = 20.054735 | |||||||||||||||||||||||||||||||||||||||||||||
Surface | [595 sqrt(2)+30 sqrt(3)]/12 = 74.451549 | |||||||||||||||||||||||||||||||||||||||||||||
General of army | (is itself convex) | |||||||||||||||||||||||||||||||||||||||||||||
Colonel of regiment |
(is itself locally convex
– uniform polychoral members:
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Dihedral angles | ||||||||||||||||||||||||||||||||||||||||||||||
Face vector | 60, 120, 80, 20 | |||||||||||||||||||||||||||||||||||||||||||||
Confer |
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External links |
Note that grip can be thought of as the external blend of 1 srip + 5 coatuts + 10 trafs + 10 tricufs + 5 oct || toe. This decomposition is described as the (also subdimensioanlly) degenerate segmentoteron xo3ox3xx3ox&#x.
Incidence matrix according to Dynkin symbol
x3x3x3o . . . . | 60 | 1 1 2 | 1 2 2 1 | 2 1 1 --------+----+----------+-------------+------- x . . . | 2 | 30 * * | 1 2 0 0 | 2 1 0 . x . . | 2 | * 30 * | 1 0 2 0 | 2 0 1 . . x . | 2 | * * 60 | 0 1 1 1 | 1 1 1 --------+----+----------+-------------+------- x3x . . | 6 | 3 3 0 | 10 * * * | 2 0 0 x . x . | 4 | 2 0 2 | * 30 * * | 1 1 0 . x3x . | 6 | 0 3 3 | * * 20 * | 1 0 1 . . x3o | 3 | 0 0 3 | * * * 20 | 0 1 1 --------+----+----------+-------------+------- x3x3x . ♦ 24 | 12 12 12 | 4 6 4 0 | 5 * * x . x3o ♦ 6 | 3 0 6 | 0 3 0 2 | * 10 * . x3x3o ♦ 12 | 0 6 12 | 0 0 4 4 | * * 5 snubbed forms: β3x3x3o, x3β3x3o, x3x3β3o, β3β3x3o, β3x3β3o, x3β3β3o, β3β3β3o
x3x3x3/2o . . . . | 60 | 1 1 2 | 1 2 2 1 | 2 1 1 ----------+----+----------+-------------+------- x . . . | 2 | 30 * * | 1 2 0 0 | 2 1 0 . x . . | 2 | * 30 * | 1 0 2 0 | 2 0 1 . . x . | 2 | * * 60 | 0 1 1 1 | 1 1 1 ----------+----+----------+-------------+------- x3x . . | 6 | 3 3 0 | 10 * * * | 2 0 0 x . x . | 4 | 2 0 2 | * 30 * * | 1 1 0 . x3x . | 6 | 0 3 3 | * * 20 * | 1 0 1 . . x3/2o | 3 | 0 0 3 | * * * 20 | 0 1 1 ----------+----+----------+-------------+------- x3x3x . ♦ 24 | 12 12 12 | 4 6 4 0 | 5 * * x . x3/2o ♦ 6 | 3 0 6 | 0 3 0 2 | * 10 * . x3x3/2o ♦ 12 | 0 6 12 | 0 0 4 4 | * * 5
xuxx3xxux3ooox&#xt → all heights = sqrt(5/8) = 0.790569 (tut || pseudo (u,x)-tut || pseudo (x,u)-tut || toe) o...3o...3o... | 12 * * * | 1 2 1 0 0 0 0 0 0 0 | 2 1 2 1 0 0 0 0 0 0 0 | 1 1 2 0 0 0 .o..3.o..3.o.. | * 12 * * | 0 0 1 2 1 0 0 0 0 0 | 0 0 2 1 1 2 0 0 0 0 0 | 0 1 2 1 0 0 ..o.3..o.3..o. | * * 12 * | 0 0 0 0 1 1 2 0 0 0 | 0 0 0 1 0 2 2 1 0 0 0 | 0 0 2 1 1 0 ...o3...o3...o | * * * 24 | 0 0 0 0 0 0 1 1 1 1 | 0 0 0 0 0 1 1 1 1 1 1 | 0 0 1 1 1 1 -------------------+-------------+-----------------------------+---------------------------+------------ x... .... .... | 2 0 0 0 | 6 * * * * * * * * * | 2 0 0 1 0 0 0 0 0 0 0 | 1 0 2 0 0 0 .... x... .... | 2 0 0 0 | * 12 * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 oo..3oo..3oo..&#x | 1 1 0 0 | * * 12 * * * * * * * | 0 0 2 1 0 0 0 0 0 0 0 | 0 1 2 0 0 0 .... .x.. .... | 0 2 0 0 | * * * 12 * * * * * * | 0 0 1 0 1 1 0 0 0 0 0 | 0 1 1 1 0 0 .oo.3.oo.3.oo.&#x | 0 1 1 0 | * * * * 12 * * * * * | 0 0 0 1 0 2 0 0 0 0 0 | 0 0 2 1 0 0 ..x. .... .... | 0 0 2 0 | * * * * * 6 * * * * | 0 0 0 1 0 0 2 0 0 0 0 | 0 0 2 0 1 0 ..oo3..oo3..oo&#x | 0 0 1 1 | * * * * * * 24 * * * | 0 0 0 0 0 1 1 1 0 0 0 | 0 0 1 1 1 0 ...x .... .... | 0 0 0 2 | * * * * * * * 12 * * | 0 0 0 0 0 0 1 0 1 1 0 | 0 0 1 0 1 1 .... ...x .... | 0 0 0 2 | * * * * * * * * 12 * | 0 0 0 0 0 1 0 0 1 0 1 | 0 0 1 1 0 1 .... .... ...x | 0 0 0 2 | * * * * * * * * * 12 | 0 0 0 0 0 0 0 1 0 1 1 | 0 0 0 1 1 1 -------------------+-------------+-----------------------------+---------------------------+------------ x...3x... .... | 6 0 0 0 | 3 3 0 0 0 0 0 0 0 0 | 4 * * * * * * * * * * | 1 0 1 0 0 0 .... x...3o... | 3 0 0 0 | 0 3 0 0 0 0 0 0 0 0 | * 4 * * * * * * * * * | 1 1 0 0 0 0 .... xx.. ....&#x | 2 2 0 0 | 0 1 2 1 0 0 0 0 0 0 | * * 12 * * * * * * * * | 0 1 1 0 0 0 xux. .... ....&#xt | 2 2 2 0 | 1 0 2 0 2 1 0 0 0 0 | * * * 6 * * * * * * * | 0 0 2 0 0 0 .... .x..3.o.. | 0 3 0 0 | 0 0 0 3 0 0 0 0 0 0 | * * * * 4 * * * * * * | 0 1 0 1 0 0 .... .xux ....&#xt | 0 2 2 2 | 0 0 0 1 2 0 2 0 1 0 | * * * * * 12 * * * * * | 0 0 1 1 0 0 ..xx .... ....&#x | 0 0 2 2 | 0 0 0 0 0 1 2 1 0 0 | * * * * * * 12 * * * * | 0 0 1 0 1 0 .... .... ..ox&#x | 0 0 1 2 | 0 0 0 0 0 0 2 0 0 1 | * * * * * * * 12 * * * | 0 0 0 1 1 0 ...x3...x .... | 0 0 0 6 | 0 0 0 0 0 0 0 3 3 0 | * * * * * * * * 4 * * | 0 0 1 0 0 1 ...x .... ...x | 0 0 0 4 | 0 0 0 0 0 0 0 2 0 2 | * * * * * * * * * 6 * | 0 0 0 0 1 1 .... ...x3...x | 0 0 0 6 | 0 0 0 0 0 0 0 0 3 3 | * * * * * * * * * * 4 | 0 0 0 1 0 1 -------------------+-------------+-----------------------------+---------------------------+------------ x...3x...3o... ♦ 12 0 0 0 | 6 12 0 0 0 0 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 | 1 * * * * * .... xx..3oo..&#x ♦ 3 3 0 0 | 0 3 3 3 0 0 0 0 0 0 | 0 1 3 0 1 0 0 0 0 0 0 | * 4 * * * * xuxx3xxux ....&#xt ♦ 6 6 6 6 | 3 3 6 3 6 3 6 3 3 0 | 1 0 3 3 0 3 3 0 1 0 0 | * * 4 * * * .... .xux3.oox&#xt ♦ 0 3 3 6 | 0 0 0 3 3 0 6 0 3 3 | 0 0 0 0 1 3 0 3 0 0 1 | * * * 4 * * ..xx .... ..ox&#x ♦ 0 0 2 4 | 0 0 0 0 0 1 4 2 0 2 | 0 0 0 0 0 0 2 2 0 1 0 | * * * * 6 * ...x3...x3...x ♦ 0 0 0 24 | 0 0 0 0 0 0 0 12 12 12 | 0 0 0 0 0 0 0 0 4 6 4 | * * * * * 1
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