Acronym | thex | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Name |
truncated hexadecachoron, cantic tesseract, equatorial cross-section of hex-first tot | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Cross sections |
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Circumradius | sqrt(5/2) = 1.581139 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. oct | sqrt(2) = 1.414214 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. tut | 3/sqrt(8) = 1.060660 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Vertex figure |
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Vertex layers |
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Lace city in approx. ASCII-art |
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x3o u3o x3x -- x3x3o (tut) o3x u3x u3o -- u3o3x ((u,x)-co) o3u x3u x3o -- x3o3u (inv. (u,x)-co) x3x o3u o3x -- o3x3x (inv. tut) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Coordinates |
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Volume | 77/6 = 12.833333 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Surface | 100 sqrt(2)/3 = 47.140452 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
General of army | (is itself convex) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Colonel of regiment |
(is itself locally convex
– uniform polychoral members:
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Dihedral angles | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Face vector | 48, 120, 96, 24 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Confer |
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External links |
Note that thex can be thought of as the external blend of 1 hex + 16 tetatuts + 8 octpies. This decomposition is described as the degenerate segmentoteron xx3ox3oo4oo&#x. – Alternatively it can be (subdimensioanlly degenerate) decomposed into 1 rit + 16 tetaltuts + 24 squascs + 8 octacoes according to ox3ox3xo4oo&#x.
Incidence matrix according to Dynkin symbol
x3x3o4o . . . . | 48 ♦ 1 4 | 4 4 | 4 1 --------+----+-------+-------+----- x . . . | 2 | 24 * | 4 0 | 4 0 . x . . | 2 | * 96 | 1 2 | 2 1 --------+----+-------+-------+----- x3x . . | 6 | 3 3 | 32 * | 2 0 . x3o . | 3 | 0 3 | * 64 | 1 1 --------+----+-------+-------+----- x3x3o . ♦ 12 | 6 12 | 4 4 | 16 * . x3o4o ♦ 6 | 0 12 | 0 8 | * 8 snubbed forms: β3x3o4o, x3β3o4o, β3β3o4o
x3x3o4/3o . . . . | 48 ♦ 1 4 | 4 4 | 4 1 ----------+----+-------+-------+----- x . . . | 2 | 24 * | 4 0 | 4 0 . x . . | 2 | * 96 | 1 2 | 2 1 ----------+----+-------+-------+----- x3x . . | 6 | 3 3 | 32 * | 2 0 . x3o . | 3 | 0 3 | * 64 | 1 1 ----------+----+-------+-------+----- x3x3o . ♦ 12 | 6 12 | 4 4 | 16 * . x3o4/3o ♦ 6 | 0 12 | 0 8 | * 8
x3x3/2o4o . . . . | 48 ♦ 1 4 | 4 4 | 4 1 ----------+----+-------+-------+----- x . . . | 2 | 24 * | 4 0 | 4 0 . x . . | 2 | * 96 | 1 2 | 2 1 ----------+----+-------+-------+----- x3x . . | 6 | 3 3 | 32 * | 2 0 . x3/2o . | 3 | 0 3 | * 64 | 1 1 ----------+----+-------+-------+----- x3x3/2o . ♦ 12 | 6 12 | 4 4 | 16 * . x3/2o4o ♦ 6 | 0 12 | 0 8 | * 8
x3x3/2o4/3o . . . . | 48 ♦ 1 4 | 4 4 | 4 1 ------------+----+-------+-------+----- x . . . | 2 | 24 * | 4 0 | 4 0 . x . . | 2 | * 96 | 1 2 | 2 1 ------------+----+-------+-------+----- x3x . . | 6 | 3 3 | 32 * | 2 0 . x3/2o . | 3 | 0 3 | * 64 | 1 1 ------------+----+-------+-------+----- x3x3/2o . ♦ 12 | 6 12 | 4 4 | 16 * . x3/2o4/3o ♦ 6 | 0 12 | 0 8 | * 8
x3x3o *b3o . . . . | 48 ♦ 1 4 | 4 2 2 | 2 2 1 -----------+----+-------+----------+------ x . . . | 2 | 24 * | 4 0 0 | 2 2 0 . x . . | 2 | * 96 | 1 1 1 | 1 1 1 -----------+----+-------+----------+------ x3x . . | 6 | 3 3 | 32 * * | 1 1 0 . x3o . | 3 | 0 3 | * 32 * | 1 0 1 . x . *b3o | 3 | 0 3 | * * 32 | 0 1 1 -----------+----+-------+----------+------ x3x3o . ♦ 12 | 6 12 | 4 4 0 | 8 * * x3x . *b3o ♦ 12 | 6 12 | 4 0 4 | * 8 * . x3o *b3o ♦ 6 | 0 12 | 0 4 4 | * * 8 snubbed forms: β3x3o *b3o, x3β3o *b3o, β3β3o *b3o
x3x3o *b3/2o . . . . | 48 ♦ 1 4 | 4 2 2 | 2 2 1 -------------+----+-------+----------+------ x . . . | 2 | 24 * | 4 0 0 | 2 2 0 . x . . | 2 | * 96 | 1 1 1 | 1 1 1 -------------+----+-------+----------+------ x3x . . | 6 | 3 3 | 32 * * | 1 1 0 . x3o . | 3 | 0 3 | * 32 * | 1 0 1 . x . *b3/2o | 3 | 0 3 | * * 32 | 0 1 1 -------------+----+-------+----------+------ x3x3o . ♦ 12 | 6 12 | 4 4 0 | 8 * * x3x . *b3/2o ♦ 12 | 6 12 | 4 0 4 | * 8 * . x3o *b3/2o ♦ 6 | 0 12 | 0 4 4 | * * 8
x3x3/2o *b3/2o . . . . | 48 ♦ 1 4 | 4 2 2 | 2 2 1 ---------------+----+-------+----------+------ x . . . | 2 | 24 * | 4 0 0 | 2 2 0 . x . . | 2 | * 96 | 1 1 1 | 1 1 1 ---------------+----+-------+----------+------ x3x . . | 6 | 3 3 | 32 * * | 1 1 0 . x3/2o . | 3 | 0 3 | * 32 * | 1 0 1 . x . *b3/2o | 3 | 0 3 | * * 32 | 0 1 1 ---------------+----+-------+----------+------ x3x3/2o . ♦ 12 | 6 12 | 4 4 0 | 8 * * x3x . *b3/2o ♦ 12 | 6 12 | 4 0 4 | * 8 * . x3/2o *b3/2o ♦ 6 | 0 12 | 0 4 4 | * * 8
s4o3x3o demi( . . . . ) | 48 ♦ 1 4 | 2 2 4 | 2 1 2 ----------------+----+-------+----------+------ s4o . . | 2 | 24 * | 0 0 4 | 2 0 2 demi( . . x . ) | 2 | * 96 | 1 1 1 | 1 1 1 ----------------+----+-------+----------+------ demi( . o3x . ) | 3 | 0 3 | 32 * * | 1 1 0 demi( . . x3o ) | 3 | 0 3 | * 32 * | 0 1 1 sefa( s4o3x . ) | 6 | 3 3 | * * 32 | 1 0 1 ----------------+----+-------+----------+------ s4o3x . ♦ 12 | 6 12 | 4 0 4 | 8 * * demi( . o3x3o ) ♦ 6 | 0 12 | 4 4 0 | * 8 * sefa( s4o3x3o ) ♦ 12 | 6 12 | 0 4 4 | * * 8 starting figure: x4o3x3o
xuxo3xoox3oxux&#xt → all heights = 1/sqrt(2) = 0.707107 (tut || pseudo (u,x)-co || pseudo inv (u,x)-co || inv tut) o...3o...3o... | 12 * * * ♦ 1 2 2 0 0 0 0 0 0 | 2 1 2 2 1 0 0 0 0 0 0 0 | 1 2 1 1 0 0 0 .o..3.o..3.o.. | * 12 * * ♦ 0 0 2 2 1 0 0 0 0 | 0 0 2 1 2 1 2 0 0 0 0 0 | 0 1 2 1 1 0 0 ..o.3..o.3..o. | * * 12 * ♦ 0 0 0 0 1 2 2 0 0 | 0 0 2 0 0 0 2 1 2 1 0 0 | 0 1 2 0 1 1 0 ...o3...o3...o | * * * 12 ♦ 0 0 0 0 0 0 2 2 1 | 0 0 0 0 0 0 2 0 1 2 1 2 | 0 0 1 0 2 1 1 -------------------+-------------+--------------------------+-------------------------------+-------------- x... .... .... | 2 0 0 0 | 6 * * * * * * * * | 2 0 2 0 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 .... x... .... | 2 0 0 0 | * 12 * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0 0 oo..3oo..3oo..&#x | 1 1 0 0 | * * 24 * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 .... .... .x.. | 0 2 0 0 | * * * 12 * * * * * | 0 0 0 0 1 1 1 0 0 0 0 0 | 0 0 1 1 1 0 0 .oo.3.oo.3.oo.&#x | 0 1 1 0 | * * * * 12 * * * * | 0 0 2 0 0 0 2 0 0 0 0 0 | 0 1 2 0 1 0 0 ..x. .... .... | 0 0 2 0 | * * * * * 12 * * * | 0 0 1 0 0 0 0 1 1 0 0 0 | 0 1 1 0 0 1 0 ..oo3..oo3..oo&#x | 0 0 1 1 | * * * * * * 24 * * | 0 0 0 0 0 0 1 0 1 1 0 0 | 0 0 1 0 1 1 0 .... ...x .... | 0 0 0 2 | * * * * * * * 12 * | 0 0 0 0 0 0 0 0 0 1 1 1 | 0 0 0 0 1 1 1 .... .... ...x | 0 0 0 2 | * * * * * * * * 6 | 0 0 0 0 0 0 2 0 0 0 0 2 | 0 0 1 0 2 0 1 -------------------+-------------+--------------------------+-------------------------------+-------------- x...3x... .... | 6 0 0 0 | 3 3 0 0 0 0 0 0 0 | 4 * * * * * * * * * * * | 1 1 0 0 0 0 0 .... x...3o... | 3 0 0 0 | 0 3 0 0 0 0 0 0 0 | * 4 * * * * * * * * * * | 1 0 0 1 0 0 0 xux. .... ....&#xt | 2 2 2 0 | 1 0 2 0 2 1 0 0 0 | * * 12 * * * * * * * * * | 0 1 1 0 0 0 0 .... xo.. ....&#x | 2 1 0 0 | 0 1 2 0 0 0 0 0 0 | * * * 12 * * * * * * * * | 0 1 0 1 0 0 0 .... .... ox..&#x | 1 2 0 0 | 0 0 2 1 0 0 0 0 0 | * * * * 12 * * * * * * * | 0 0 1 1 0 0 0 .... .o..3.x.. | 0 3 0 0 | 0 0 0 3 0 0 0 0 0 | * * * * * 4 * * * * * * | 0 0 0 1 1 0 0 .... .... .xux&#xt | 0 2 2 2 | 0 0 0 1 2 0 2 0 1 | * * * * * * 12 * * * * * | 0 0 1 0 1 0 0 ..x.3..o. .... | 0 0 3 0 | 0 0 0 0 0 3 0 0 0 | * * * * * * * 4 * * * * | 0 1 0 0 0 1 0 ..xo .... ....&#x | 0 0 2 1 | 0 0 0 0 0 1 2 0 0 | * * * * * * * * 12 * * * | 0 0 1 0 0 1 0 .... ..ox ....&#x | 0 0 1 2 | 0 0 0 0 0 0 2 1 0 | * * * * * * * * * 12 * * | 0 0 0 0 1 1 0 ...o3...x .... | 0 0 0 3 | 0 0 0 0 0 0 0 3 0 | * * * * * * * * * * 4 * | 0 0 0 0 0 1 1 .... ...x3...x | 0 0 0 6 | 0 0 0 0 0 0 0 3 3 | * * * * * * * * * * * 4 | 0 0 0 0 1 0 1 -------------------+-------------+--------------------------+-------------------------------+-------------- x...3x...3o... ♦ 12 0 0 0 | 6 12 0 0 0 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * xux.3xoo. ....&#xt ♦ 6 3 3 0 | 3 3 6 0 3 3 0 0 0 | 1 0 3 3 0 0 0 1 0 0 0 0 | * 4 * * * * * xuxo .... oxux&#xt ♦ 2 4 4 2 | 1 0 4 2 4 2 4 0 1 | 0 0 2 0 2 0 2 0 2 0 0 0 | * * 6 * * * * .... xo..3ox..&#x ♦ 3 3 0 0 | 0 3 6 3 0 0 0 0 0 | 0 1 0 3 3 1 0 0 0 0 0 0 | * * * 4 * * * .... .oox3.xux&#xt ♦ 0 3 3 6 | 0 0 0 3 3 0 6 3 3 | 0 0 0 0 0 1 3 0 0 3 0 1 | * * * * 4 * * ..xo3..ox ....&#x ♦ 0 0 3 3 | 0 0 0 0 0 3 6 3 0 | 0 0 0 0 0 0 0 1 3 3 1 0 | * * * * * 4 * ...o3...x3...x ♦ 0 0 0 12 | 0 0 0 0 0 0 0 12 6 | 0 0 0 0 0 0 0 0 0 0 4 4 | * * * * * * 1
or o...3o...3o... & | 24 * ♦ 1 2 2 0 0 | 2 1 2 2 1 0 | 1 2 1 1 .o..3.o..3.o.. & | * 24 ♦ 0 0 2 2 1 | 0 0 4 1 2 1 | 0 2 2 1 ----------------------+-------+----------------+----------------+-------- x... .... .... & | 2 0 | 12 * * * * | 2 0 2 0 0 0 | 1 2 1 0 .... x... .... & | 2 0 | * 24 * * * | 1 1 0 1 0 0 | 1 1 0 1 oo..3oo..3oo..&#x & | 1 1 | * * 48 * * | 0 0 1 1 1 0 | 0 1 1 1 .... .... .x.. & | 0 2 | * * * 24 * | 0 0 1 0 1 1 | 0 1 1 1 .oo.3.oo.3.oo.&#x | 0 2 | * * * * 12 | 0 0 4 0 0 0 | 0 2 2 0 ----------------------+-------+----------------+----------------+-------- x...3x... .... & | 6 0 | 3 3 0 0 0 | 8 * * * * * | 1 1 0 0 .... x...3o... & | 3 0 | 0 3 0 0 0 | * 8 * * * * | 1 0 0 1 xux. .... ....&#xt & | 2 4 | 1 0 2 1 2 | * * 24 * * * | 0 1 1 0 .... xo.. ....&#x & | 2 1 | 0 1 2 0 0 | * * * 24 * * | 0 1 0 1 .... .... ox..&#x & | 1 2 | 0 0 2 1 0 | * * * * 24 * | 0 0 1 1 .... .o..3.x.. & | 0 3 | 0 0 0 3 0 | * * * * * 8 | 0 1 0 1 ----------------------+-------+----------------+----------------+-------- x...3x...3o... & ♦ 12 0 | 6 12 0 0 0 | 4 4 0 0 0 0 | 2 * * * xux.3xoo. ....&#xt & ♦ 6 6 | 3 3 6 3 3 | 1 0 3 3 0 1 | * 8 * * xuxo .... oxux&#xt ♦ 4 8 | 2 0 8 4 4 | 0 0 4 0 4 0 | * * 6 * .... xo..3ox..&#x & ♦ 3 3 | 0 3 6 3 0 | 0 1 0 3 3 1 | * * * 8
xuxux3ooxoo4ooooo&#xt → all heights = 1/sqrt(2) = 0.707107 (oct || pseudo u-oct || pseudo toe || pseudo u-oct || oct) o....3o....4o.... | 6 * * * * ♦ 4 1 0 0 0 0 0 0 | 4 4 0 0 0 0 0 | 1 4 0 0 0 .o...3.o...4.o... | * 6 * * * ♦ 0 1 4 0 0 0 0 0 | 0 4 4 0 0 0 0 | 0 4 1 0 0 ..o..3..o..4..o.. | * * 24 * * ♦ 0 0 1 1 2 1 0 0 | 0 1 2 2 1 2 0 | 0 2 1 2 0 ...o.3...o.4...o. | * * * 6 * ♦ 0 0 0 0 0 4 1 0 | 0 0 0 0 4 4 0 | 0 0 1 4 0 ....o3....o4....o | * * * * 6 ♦ 0 0 0 0 0 0 1 4 | 0 0 0 0 4 0 4 | 0 0 0 4 1 ----------------------+------------+-----------------------+-------------------+---------- x.... ..... ..... | 2 0 0 0 0 | 12 * * * * * * * | 2 1 0 0 0 0 0 | 1 2 0 0 0 oo...3oo...4oo...&#x | 1 1 0 0 0 | * 6 * * * * * * | 0 4 0 0 0 0 0 | 0 4 0 0 0 .oo..3.oo..4.oo..&#x | 0 1 1 0 0 | * * 24 * * * * * | 0 1 2 0 0 0 0 | 0 2 1 0 0 ..x.. ..... ..... | 0 0 2 0 0 | * * * 12 * * * * | 0 1 0 2 1 0 0 | 0 2 0 2 0 ..... ..x.. ..... | 0 0 2 0 0 | * * * * 24 * * * | 0 0 1 1 0 1 0 | 0 1 1 1 0 ..oo.3..oo.4..oo.&#x | 0 0 1 1 0 | * * * * * 24 * * | 0 0 0 0 1 2 0 | 0 0 1 2 0 ...oo3...oo4...oo&#x | 0 0 0 1 1 | * * * * * * 6 * | 0 0 0 0 4 0 0 | 0 0 0 4 0 ....x ..... ..... | 0 0 0 0 2 | * * * * * * * 12 | 0 0 0 0 1 0 2 | 0 0 0 2 1 ----------------------+------------+-----------------------+-------------------+---------- x....3o.... ..... | 3 0 0 0 0 | 3 0 0 0 0 0 0 0 | 8 * * * * * * | 1 1 0 0 0 xux.. ..... .....&#xt | 2 2 2 0 0 | 1 2 2 1 0 0 0 0 | * 12 * * * * * | 0 2 0 0 0 ..... .ox.. .....&#x | 0 1 2 0 0 | 0 0 2 0 1 0 0 0 | * * 24 * * * * | 0 1 1 0 0 ..x..3..x.. ..... | 0 0 6 0 0 | 0 0 0 3 3 0 0 0 | * * * 8 * * * | 0 1 0 1 0 ..xux ..... .....&#xt | 0 0 2 2 2 | 0 0 0 1 0 2 2 1 | * * * * 12 * * | 0 0 0 2 0 ..... ..xo. .....&#x | 0 0 2 1 0 | 0 0 0 0 1 2 0 0 | * * * * * 24 * | 0 0 1 1 0 ....x3....o ..... | 0 0 0 0 3 | 0 0 0 0 0 0 0 3 | * * * * * * 8 | 0 0 0 1 1 ----------------------+------------+-----------------------+-------------------+---------- x....3o....4o.... ♦ 6 0 0 0 0 | 12 0 0 0 0 0 0 0 | 8 0 0 0 0 0 0 | 1 * * * * xux..3oox.. .....&#xt ♦ 3 3 6 0 0 | 3 3 6 3 3 0 0 0 | 1 3 3 1 0 0 0 | * 8 * * * ..... .oxo.4.ooo.&#xt ♦ 0 1 4 1 0 | 0 0 4 0 4 4 0 0 | 0 0 4 0 0 4 0 | * * 6 * * ..xux3..xoo .....&#xt ♦ 0 0 6 3 3 | 0 0 0 3 3 6 3 3 | 0 0 0 1 3 3 1 | * * * 8 * ....x3....o4....o ♦ 0 0 0 0 6 | 0 0 0 0 0 0 0 12 | 0 0 0 0 0 0 8 | * * * * 1
or o....3o....4o.... & | 12 * * ♦ 4 1 0 0 0 | 4 4 0 0 | 1 4 0 .o...3.o...4.o... & | * 12 * ♦ 0 1 4 0 0 | 0 4 4 0 | 0 4 1 ..o..3..o..4..o.. | * * 24 ♦ 0 0 2 1 2 | 0 2 4 2 | 0 4 1 -------------------------+----------+----------------+------------+------- x.... ..... ..... & | 2 0 0 | 24 * * * * | 2 1 0 0 | 1 2 0 oo...3oo...4oo...&#x & | 1 1 0 | * 12 * * * | 0 4 0 0 | 0 4 0 .oo..3.oo..4.oo..&#x & | 0 1 1 | * * 48 * * | 0 1 2 0 | 0 2 1 ..x.. ..... ..... | 0 0 2 | * * * 12 * | 0 2 0 2 | 0 4 0 ..... ..x.. ..... | 0 0 2 | * * * * 24 | 0 0 2 1 | 0 2 1 -------------------------+----------+----------------+------------+------- x....3o.... ..... & | 3 0 0 | 3 0 0 0 0 | 16 * * * | 1 1 0 xux.. ..... .....&#xt & | 2 2 2 | 1 2 2 1 0 | * 24 * * | 0 2 0 ..... .ox.. .....&#x & | 0 1 2 | 0 0 2 0 1 | * * 48 * | 0 1 1 ..x..3..x.. ..... | 0 0 6 | 0 0 0 3 3 | * * * 8 | 0 2 0 -------------------------+----------+----------------+------------+------- x....3o....4o.... & ♦ 6 0 0 | 12 0 0 0 0 | 8 0 0 0 | 2 * * xux..3oox.. .....&#xt & ♦ 3 3 6 | 3 3 6 3 3 | 1 3 3 1 | * 16 * ..... .oxo.4.ooo.&#xt ♦ 0 2 4 | 0 0 8 0 4 | 0 0 8 0 | * * 6
ooxoo3xuxux3ooxoo&#xt → all heights = 1/sqrt(2) = 0.707107 (oct || pseudo u-oct || pseudo toe || pseudo u-oct || oct) o....3o....3o.... | 6 * * * * ♦ 4 1 0 0 0 0 0 0 0 | 2 2 4 0 0 0 0 0 0 0 0 0 | 1 2 2 0 0 0 0 .o...3.o...3.o... | * 6 * * * ♦ 0 1 4 0 0 0 0 0 0 | 0 0 4 2 2 0 0 0 0 0 0 0 | 0 2 2 1 0 0 0 ..o..3..o..3..o.. | * * 24 * * ♦ 0 0 1 1 1 1 1 0 0 | 0 0 1 1 1 1 1 1 1 1 0 0 | 0 1 1 1 1 1 0 ...o.3...o.3...o. | * * * 6 * ♦ 0 0 0 0 0 0 4 1 0 | 0 0 0 0 0 0 0 2 4 2 0 0 | 0 0 0 1 2 2 0 ....o3....o3....o | * * * * 6 ♦ 0 0 0 0 0 0 0 1 4 | 0 0 0 0 0 0 0 0 4 0 2 2 | 0 0 0 0 2 2 1 ----------------------+------------+--------------------------+-------------------------------+-------------- ..... x.... ..... | 2 0 0 0 0 | 12 * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 oo...3oo...3oo...&#x | 1 1 0 0 0 | * 6 * * * * * * * | 0 0 4 0 0 0 0 0 0 0 0 0 | 0 2 2 0 0 0 0 .oo..3.oo..3.oo..&#x | 0 1 1 0 0 | * * 24 * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 ..x.. ..... ..... | 0 0 2 0 0 | * * * 12 * * * * * | 0 0 0 1 0 1 0 1 0 0 0 0 | 0 1 0 1 1 0 0 ..... ..x.. ..... | 0 0 2 0 0 | * * * * 12 * * * * | 0 0 1 0 0 1 1 0 1 0 0 0 | 0 1 1 0 1 1 0 ..... ..... ..x.. | 0 0 2 0 0 | * * * * * 12 * * * | 0 0 0 0 1 0 1 0 0 1 0 0 | 0 0 1 1 0 1 0 ..oo.3..oo.3..oo.&#x | 0 0 1 1 0 | * * * * * * 24 * * | 0 0 0 0 0 0 0 1 1 1 0 0 | 0 0 0 1 1 1 0 ...oo3...oo3...oo&#x | 0 0 0 1 1 | * * * * * * * 6 * | 0 0 0 0 0 0 0 0 4 0 0 0 | 0 0 0 0 2 2 0 ..... ....x ..... | 0 0 0 0 2 | * * * * * * * * 12 | 0 0 0 0 0 0 0 0 1 0 1 1 | 0 0 0 0 1 1 1 ----------------------+------------+--------------------------+-------------------------------+-------------- o....3x.... ..... | 3 0 0 0 0 | 3 0 0 0 0 0 0 0 0 | 4 * * * * * * * * * * * | 1 1 0 0 0 0 0 ..... x....3o.... | 3 0 0 0 0 | 3 0 0 0 0 0 0 0 0 | * 4 * * * * * * * * * * | 1 0 1 0 0 0 0 ..... xux.. .....&#xt | 2 2 2 0 0 | 1 2 2 0 1 0 0 0 0 | * * 12 * * * * * * * * * | 0 1 1 0 0 0 0 .ox.. ..... .....&#x | 0 1 2 0 0 | 0 0 2 1 0 0 0 0 0 | * * * 12 * * * * * * * * | 0 1 0 1 0 0 0 ..... ..... .ox..&#x | 0 1 2 0 0 | 0 0 2 0 0 1 0 0 0 | * * * * 12 * * * * * * * | 0 0 1 1 0 0 0 ..x..3..x.. ..... | 0 0 6 0 0 | 0 0 0 3 3 0 0 0 0 | * * * * * 4 * * * * * * | 0 1 0 0 1 0 0 ..... ..x..3..x.. | 0 0 6 0 0 | 0 0 0 0 3 3 0 0 0 | * * * * * * 4 * * * * * | 0 0 1 0 0 1 0 ..xo. ..... .....&#x | 0 0 2 1 0 | 0 0 0 1 0 0 2 0 0 | * * * * * * * 12 * * * * | 0 0 0 1 1 0 0 ..... ..xux .....&#xt | 0 0 2 2 2 | 0 0 0 0 1 0 2 2 1 | * * * * * * * * 12 * * * | 0 0 0 0 1 1 0 ..... ..... ..xo.&#x | 0 0 2 1 0 | 0 0 0 0 0 1 2 0 0 | * * * * * * * * * 12 * * | 0 0 0 1 0 1 0 ....o3....x ..... | 0 0 0 0 3 | 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * 4 * | 0 0 0 0 1 0 1 ..... ....x3....o | 0 0 0 0 3 | 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * * 4 | 0 0 0 0 0 1 1 ----------------------+------------+--------------------------+-------------------------------+-------------- o....3x....3o.... ♦ 6 0 0 0 0 | 12 0 0 0 0 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * oox..3xux.. .....&#xt ♦ 3 3 6 0 0 | 3 3 6 3 3 0 0 0 0 | 1 0 3 3 0 1 0 0 0 0 0 0 | * 4 * * * * * ..... xux..3oox..&#xt ♦ 3 3 6 0 0 | 3 3 6 0 3 3 0 0 0 | 0 1 3 0 3 0 1 0 0 0 0 0 | * * 4 * * * * .oxo. ..... .oxo.&#xt ♦ 0 1 4 1 0 | 0 0 4 2 0 2 4 0 0 | 0 0 0 2 2 0 0 2 0 2 0 0 | * * * 6 * * * ..xoo3..xux .....&#xt ♦ 0 0 6 3 3 | 0 0 0 3 3 0 6 3 3 | 0 0 0 0 0 1 0 3 3 0 1 0 | * * * * 4 * * ..... ..xux3..xoo&#xt ♦ 0 0 6 3 3 | 0 0 0 0 3 3 6 3 3 | 0 0 0 0 0 0 1 0 3 3 0 1 | * * * * * 4 * ....o3....x3....o ♦ 0 0 0 0 6 | 0 0 0 0 0 0 0 0 12 | 0 0 0 0 0 0 0 0 0 0 4 4 | * * * * * * 1
or o....3o....3o.... & | 12 * * ♦ 4 1 0 0 0 0 | 2 2 4 0 0 0 0 | 1 2 2 0 .o...3.o...3.o... & | * 12 * ♦ 0 1 4 0 0 0 | 0 0 4 2 2 0 0 | 0 2 2 1 ..o..3..o..3..o.. | * * 24 ♦ 0 0 2 1 1 1 | 0 0 2 2 2 1 1 | 0 2 2 1 -------------------------+----------+-------------------+------------------+-------- ..... x.... ..... & | 2 0 0 | 24 * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0 oo...3oo...3oo...&#x & | 1 1 0 | * 12 * * * * | 0 0 4 0 0 0 0 | 0 2 2 0 .oo..3.oo..3.oo..&#x & | 0 1 1 | * * 48 * * * | 0 0 1 1 1 0 0 | 0 1 1 1 ..x.. ..... ..... | 0 0 2 | * * * 12 * * | 0 0 0 2 0 1 0 | 0 2 0 1 ..... ..x.. ..... | 0 0 2 | * * * * 12 * | 0 0 2 0 0 1 1 | 0 2 2 0 ..... ..... ..x.. | 0 0 2 | * * * * * 12 | 0 0 0 0 2 0 1 | 0 0 2 1 -------------------------+----------+-------------------+------------------+-------- o....3x.... ..... & | 3 0 0 | 3 0 0 0 0 0 | 8 * * * * * * | 1 1 0 0 ..... x....3o.... & | 3 0 0 | 3 0 0 0 0 0 | * 8 * * * * * | 1 0 1 0 ..... xux.. .....&#xt & | 2 2 2 | 1 2 2 0 1 0 | * * 24 * * * * | 0 1 1 0 .ox.. ..... .....&#x & | 0 1 2 | 0 0 2 1 0 0 | * * * 24 * * * | 0 1 0 1 ..... ..... .ox..&#x & | 0 1 2 | 0 0 2 0 0 1 | * * * * 24 * * | 0 0 1 1 ..x..3..x.. ..... | 0 0 6 | 0 0 0 3 3 0 | * * * * * 4 * | 0 2 0 0 ..... ..x..3..x.. | 0 0 6 | 0 0 0 0 3 3 | * * * * * * 4 | 0 0 2 0 -------------------------+----------+-------------------+------------------+-------- o....3x....3o.... & ♦ 6 0 0 | 12 0 0 0 0 0 | 4 4 0 0 0 0 0 | 2 * * * oox..3xux.. .....&#xt & ♦ 3 3 6 | 3 3 6 3 3 0 | 1 0 3 3 0 1 0 | * 8 * * ..... xux..3oox..&#xt & ♦ 3 3 6 | 3 3 6 0 3 3 | 0 1 3 0 3 0 1 | * * 8 * .oxo. ..... .oxo.&#xt ♦ 0 2 4 | 0 0 8 2 0 2 | 0 0 0 4 4 0 0 | * * * 6
Qqo xux3oox4ooo&#zxt (where Q=2q) o.. o..3o..4o.. | 12 * * ♦ 4 1 0 0 0 | 4 4 0 0 | 1 4 0 .o. .o.3.o.4.o. | * 12 * ♦ 0 1 4 0 0 | 0 4 4 0 | 0 4 1 ..o ..o3..o4..o | * * 24 ♦ 0 0 2 1 2 | 0 2 4 2 | 0 4 1 --------------------+----------+----------------+------------+------- ... x.. ... ... | 2 0 0 | 24 * * * * | 2 1 0 0 | 1 2 0 oo. oo.3oo.4oo.&#x | 1 1 0 | * 12 * * * | 0 4 0 0 | 0 4 0 .oo .oo3.oo4.oo&#x | 0 1 1 | * * 48 * * | 0 1 2 0 | 0 2 1 ... ..x ... ... | 0 0 2 | * * * 12 * | 0 2 0 2 | 0 4 0 ... ... ..x ... | 0 0 2 | * * * * 24 | 0 0 2 1 | 0 2 1 --------------------+----------+----------------+------------+------- ... x..3o.. ... | 3 0 0 | 3 0 0 0 0 | 16 * * * | 1 1 0 ... xux ... ...&#xt | 2 2 2 | 1 2 2 1 0 | * 24 * * | 0 2 0 ... ... .ox ...&#x | 0 1 2 | 0 0 2 0 1 | * * 48 * | 0 1 1 ... ..x3..x ... | 0 0 6 | 0 0 0 3 3 | * * * 8 | 0 2 0 --------------------+----------+----------------+------------+------- ... x..3o..4o.. ♦ 6 0 0 | 12 0 0 0 0 | 8 0 0 0 | 2 * * ... xux3oox ...&#xt ♦ 3 3 6 | 3 3 6 3 3 | 1 3 3 1 | * 16 * .qo ... .ox4.oo&#zx ♦ 0 2 4 | 0 0 8 0 4 | 0 0 8 0 | * * 6
ooxxuuxd ooxxuudx QqQoqooo qQoQoqoo &#zx (where Q=2q, d=3x) o....... o....... o....... o....... | 4 * * * * * * * ♦ 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4 2 2 0 0 0 0 0 0 0 0 | 2 2 1 0 0 .o...... .o...... .o...... .o...... | * 4 * * * * * * ♦ 1 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4 0 0 2 2 0 0 0 0 0 0 | 2 2 0 1 0 ..o..... ..o..... ..o..... ..o..... | * * 8 * * * * * ♦ 0 2 0 1 1 1 0 0 0 0 0 0 0 0 0 0 | 2 2 2 0 0 1 1 0 0 0 0 | 2 2 1 0 0 ...o.... ...o.... ...o.... ...o.... | * * * 8 * * * * ♦ 0 0 2 0 0 0 1 1 1 0 0 0 0 0 0 0 | 2 0 0 2 2 0 0 1 1 0 0 | 2 2 0 1 0 ....o... ....o... ....o... ....o... | * * * * 8 * * * ♦ 0 0 0 0 0 1 0 0 0 2 1 1 0 0 0 0 | 2 0 0 0 0 1 1 0 0 2 2 | 2 2 0 0 1 .....o.. .....o.. .....o.. .....o.. | * * * * * 8 * * ♦ 0 0 0 0 0 0 0 0 1 2 0 0 1 1 0 0 | 2 0 0 0 0 0 0 1 1 2 2 | 2 2 0 0 1 ......o. ......o. ......o. ......o. | * * * * * * 4 * ♦ 0 0 0 0 0 0 0 0 0 0 2 0 2 0 1 0 | 0 0 0 0 0 2 0 2 0 4 0 | 4 0 0 0 1 .......o .......o .......o .......o | * * * * * * * 4 ♦ 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 1 | 0 0 0 0 0 0 2 0 2 0 4 | 0 4 0 0 1 -----------------------------------------+-----------------+------------------------------------+--------------------------+---------- oo...... oo...... oo...... oo...... &#x | 1 1 0 0 0 0 0 0 | 4 * * * * * * * * * * * * * * * | 4 0 0 0 0 0 0 0 0 0 0 | 2 2 0 0 0 o.o..... o.o..... o.o..... o.o..... &#x | 1 0 1 0 0 0 0 0 | * 16 * * * * * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 | 1 1 1 0 0 .o.o.... .o.o.... .o.o.... .o.o.... &#x | 0 1 0 1 0 0 0 0 | * * 16 * * * * * * * * * * * * * | 1 0 0 1 1 0 0 0 0 0 0 | 1 1 0 1 0 ..x..... ........ ........ ........ | 0 0 2 0 0 0 0 0 | * * * 4 * * * * * * * * * * * * | 0 2 0 0 0 1 0 0 0 0 0 | 2 0 1 0 0 ........ ..x..... ........ ........ | 0 0 2 0 0 0 0 0 | * * * * 4 * * * * * * * * * * * | 0 0 2 0 0 0 1 0 0 0 0 | 0 2 1 0 0 ..o.o... ..o.o... ..o.o... ..o.o... &#x | 0 0 1 0 1 0 0 0 | * * * * * 8 * * * * * * * * * * | 2 0 0 0 0 1 1 0 0 0 0 | 2 2 0 0 0 ...x.... ........ ........ ........ | 0 0 0 2 0 0 0 0 | * * * * * * 4 * * * * * * * * * | 0 0 0 2 0 0 0 1 0 0 0 | 2 0 0 1 0 ........ ...x.... ........ ........ | 0 0 0 2 0 0 0 0 | * * * * * * * 4 * * * * * * * * | 0 0 0 0 2 0 0 0 1 0 0 | 0 2 0 1 0 ...o.o.. ...o.o.. ...o.o.. ...o.o.. &#x | 0 0 0 1 0 1 0 0 | * * * * * * * * 8 * * * * * * * | 2 0 0 0 0 0 0 1 1 0 0 | 2 2 0 0 0 ....oo.. ....oo.. ....oo.. ....oo.. &#x | 0 0 0 0 1 1 0 0 | * * * * * * * * * 16 * * * * * * | 1 0 0 0 0 0 0 0 0 1 1 | 1 1 0 0 1 ....o.o. ....o.o. ....o.o. ....o.o. &#x | 0 0 0 0 1 0 1 0 | * * * * * * * * * * 8 * * * * * | 0 0 0 0 0 1 0 0 0 2 0 | 2 0 0 0 1 ....o..o ....o..o ....o..o ....o..o &#x | 0 0 0 0 1 0 0 1 | * * * * * * * * * * * 8 * * * * | 0 0 0 0 0 0 1 0 0 0 2 | 0 2 0 0 1 .....oo. .....oo. .....oo. .....oo. &#x | 0 0 0 0 0 1 1 0 | * * * * * * * * * * * * 8 * * * | 0 0 0 0 0 0 0 1 0 2 0 | 2 0 0 0 1 .....o.o .....o.o .....o.o .....o.o &#x | 0 0 0 0 0 1 0 1 | * * * * * * * * * * * * * 8 * * | 0 0 0 0 0 0 0 0 1 0 2 | 0 2 0 0 1 ......x. ........ ........ ........ | 0 0 0 0 0 0 2 0 | * * * * * * * * * * * * * * 2 * | 0 0 0 0 0 2 0 2 0 0 0 | 4 0 0 0 0 ........ .......x ........ ........ | 0 0 0 0 0 0 0 2 | * * * * * * * * * * * * * * * 2 | 0 0 0 0 0 0 2 0 2 0 0 | 0 4 0 0 0 -----------------------------------------+-----------------+------------------------------------+--------------------------+---------- oooooo.. oooooo.. oooooo.. oooooo.. &#x | 1 1 1 1 1 1 0 0 | 1 1 1 0 0 1 0 0 1 1 0 0 0 0 0 0 | 16 * * * * * * * * * * | 1 1 0 0 0 o.x..... ........ ........ ........ &#x | 1 0 2 0 0 0 0 0 | 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | * 8 * * * * * * * * * | 1 0 1 0 0 ........ o.x..... ........ ........ &#x | 1 0 2 0 0 0 0 0 | 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | * * 8 * * * * * * * * | 0 1 1 0 0 .o.x.... ........ ........ ........ &#x | 0 1 0 2 0 0 0 0 | 0 0 2 0 0 0 1 0 0 0 0 0 0 0 0 0 | * * * 8 * * * * * * * | 1 0 0 1 0 ........ .o.x.... ........ ........ &#x | 0 1 0 2 0 0 0 0 | 0 0 2 0 0 0 0 1 0 0 0 0 0 0 0 0 | * * * * 8 * * * * * * | 0 1 0 1 0 ..x.u.x. ........ ........ ........ &#xt | 0 0 2 0 2 0 2 0 | 0 0 0 1 0 2 0 0 0 0 2 0 0 0 1 0 | * * * * * 4 * * * * * | 2 0 0 0 0 ........ ..x.u..x ........ ........ &#xt | 0 0 2 0 2 0 0 2 | 0 0 0 0 1 2 0 0 0 0 0 2 0 0 0 1 | * * * * * * 4 * * * * | 0 2 0 0 0 ...x.ux. ........ ........ ........ &#xt | 0 0 0 2 0 2 2 0 | 0 0 0 0 0 0 1 0 2 0 0 0 2 0 1 0 | * * * * * * * 4 * * * | 2 0 0 0 0 ........ ...x.u.x ........ ........ &#xt | 0 0 0 2 0 2 0 2 | 0 0 0 0 0 0 0 1 2 0 0 0 0 2 0 1 | * * * * * * * * 4 * * | 0 2 0 0 0 ....ooo. ....ooo. ....ooo. ....ooo. &#x | 0 0 0 0 1 1 1 0 | 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 | * * * * * * * * * 16 * | 1 0 0 0 1 ....oo.o ....oo.o ....oo.o ....oo.o &#x | 0 0 0 0 1 1 0 1 | 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 | * * * * * * * * * * 16 | 0 1 0 0 1 -----------------------------------------+-----------------+------------------------------------+--------------------------+---------- ooxxuux. ........ ........ ........ &#xr ♦ 1 1 2 2 2 2 2 0 | 1 2 2 1 0 2 1 0 2 2 2 0 2 0 1 0 | 2 1 0 1 0 1 0 1 0 2 0 | 8 * * * * ........ ooxxuu.x ........ ........ &#xr ♦ 1 1 2 2 2 2 0 2 | 1 2 2 0 1 2 0 1 2 2 0 2 0 2 0 1 | 2 0 1 0 1 0 1 0 1 0 2 | * 8 * * * o.x..... o.x..... ........ q.o..... &#zx ♦ 2 0 4 0 0 0 0 0 | 0 8 0 2 2 0 0 0 0 0 0 0 0 0 0 0 | 0 4 4 0 0 0 0 0 0 0 0 | * * 2 * * .o.x.... .o.x.... .q.o.... ........ &#zx ♦ 0 2 0 4 0 0 0 0 | 0 0 8 0 0 0 2 2 0 0 0 0 0 0 0 0 | 0 0 0 4 4 0 0 0 0 0 0 | * * * 2 * ........ ........ ....qooo ....oqoo &#xt ♦ 0 0 0 0 2 2 1 1 | 0 0 0 0 0 0 0 0 0 4 2 2 2 2 0 0 | 0 0 0 0 0 0 0 0 0 4 4 | * * * * 4
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