Acronym | sidpith | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Name |
small disprismatotesseractihexadecachoron, runcinated tesseract, small prismated tesseract | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Cross sections |
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Circumradius | sqrt[(3+sqrt(2))/2] = 1.485633 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. tet | [1+2 sqrt(2)]/sqrt(8) = 1.353553 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. trip | [3+sqrt(2)]/sqrt(12) = 1.274274 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. cube | (1+sqrt(2))/2 = 1.207107 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Vertex figure |
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Vertex layers |
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Lace city in approx. ASCII-art |
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o3x o3x o3o o3o q3x q3x q3o q3o o3w o3w w3o w3o o3q o3q x3q x3q o3o o3o x3o x3o | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Coordinates | ((1+sqrt(2))/2, 1/2, 1/2, 1/2) & all permutations, all changes of sign | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Volume | [43+32 sqrt(2)]/6 = 14.709139 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Surface | [96+4 sqrt(2)+24 sqrt(3)]/3 = 47.742025 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
General of army | (is itself convex) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Colonel of regiment |
(is itself locally convex
– uniform polychoral members:
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Dihedral angles | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Face vector | 64, 192, 208, 80 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Dual | m3o3o4m | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Confer |
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External links |
As abstract polytope sidpith is isomorphic to quidpith, thereby replacing tet by inverted tet resp. an antipodium vertex figure by a frustrum one.
Note that sidpith can be thought of as the external blend of 1 hex + 16 tepes + 32 triddips + 24 squippyps + 8 cubpies. This decomposition is described as the degenerate segmentoteron xx3oo3oo4ox&#x.
Incidence matrix according to Dynkin symbol
x3o3o4x . . . . | 64 | 3 3 | 3 6 3 | 1 3 3 1 --------+----+-------+----------+----------- x . . . | 2 | 96 * | 2 2 0 | 1 2 1 0 . . . x | 2 | * 96 | 0 2 2 | 0 1 2 1 --------+----+-------+----------+----------- x3o . . | 3 | 3 0 | 64 * * | 1 1 0 0 x . . x | 4 | 2 2 | * 96 * | 0 1 1 0 . . o4x | 4 | 0 4 | * * 48 | 0 0 1 1 --------+----+-------+----------+----------- x3o3o . ♦ 4 | 6 0 | 4 0 0 | 16 * * * x3o . x ♦ 6 | 6 3 | 2 3 0 | * 32 * * x . o4x ♦ 8 | 4 8 | 0 4 2 | * * 24 * . o3o4x ♦ 8 | 0 12 | 0 0 6 | * * * 8 snubbed forms: β3o3o4x, x3o3o4s, β3o3o4β
x3o3/2o4/3x . . . . | 64 | 3 3 | 3 6 3 | 1 3 3 1 ------------+----+-------+----------+----------- x . . . | 2 | 96 * | 2 2 0 | 1 2 1 0 . . . x | 2 | * 96 | 0 2 2 | 0 1 2 1 ------------+----+-------+----------+----------- x3o . . | 3 | 3 0 | 64 * * | 1 1 0 0 x . . x | 4 | 2 2 | * 96 * | 0 1 1 0 . . o4/3x | 4 | 0 4 | * * 48 | 0 0 1 1 ------------+----+-------+----------+----------- x3o3/2o . ♦ 4 | 6 0 | 4 0 0 | 16 * * * x3o . x ♦ 6 | 6 3 | 2 3 0 | * 32 * * x . o4/3x ♦ 8 | 4 8 | 0 4 2 | * * 24 * . o3/2o4/3x ♦ 8 | 0 12 | 0 0 6 | * * * 8
x3/2o3o4/3x . . . . | 64 | 3 3 | 3 6 3 | 1 3 3 1 ------------+----+-------+----------+----------- x . . . | 2 | 96 * | 2 2 0 | 1 2 1 0 . . . x | 2 | * 96 | 0 2 2 | 0 1 2 1 ------------+----+-------+----------+----------- x3/2o . . | 3 | 3 0 | 64 * * | 1 1 0 0 x . . x | 4 | 2 2 | * 96 * | 0 1 1 0 . . o4/3x | 4 | 0 4 | * * 48 | 0 0 1 1 ------------+----+-------+----------+----------- x3/2o3o . ♦ 4 | 6 0 | 4 0 0 | 16 * * * x3/2o . x ♦ 6 | 6 3 | 2 3 0 | * 32 * * x . o4/3x ♦ 8 | 4 8 | 0 4 2 | * * 24 * . o3o4/3x ♦ 8 | 0 12 | 0 0 6 | * * * 8
x3/2o3/2o4x . . . . | 64 | 3 3 | 3 6 3 | 1 3 3 1 ------------+----+-------+----------+----------- x . . . | 2 | 96 * | 2 2 0 | 1 2 1 0 . . . x | 2 | * 96 | 0 2 2 | 0 1 2 1 ------------+----+-------+----------+----------- x3/2o . . | 3 | 3 0 | 64 * * | 1 1 0 0 x . . x | 4 | 2 2 | * 96 * | 0 1 1 0 . . o4x | 4 | 0 4 | * * 48 | 0 0 1 1 ------------+----+-------+----------+----------- x3/2o3/2o . ♦ 4 | 6 0 | 4 0 0 | 16 * * * x3/2o . x ♦ 6 | 6 3 | 2 3 0 | * 32 * * x . o4x ♦ 8 | 4 8 | 0 4 2 | * * 24 * . o3/2o4x ♦ 8 | 0 12 | 0 0 6 | * * * 8
oxxo3oooo4xxxx&#xt → outer heights = 1/sqrt(2) = 0.707107 inner height = 1 (cube || pseudo sirco || pseudo sirco || cube) o...3o...4o... | 8 * * * | 3 3 0 0 0 0 0 0 0 | 3 3 6 0 0 0 0 0 0 0 0 0 0 0 | 1 1 3 3 0 0 0 0 0 0 0 .o..3.o..4.o.. | * 24 * * | 0 1 2 2 1 0 0 0 0 | 0 2 2 1 2 1 2 2 0 0 0 0 0 0 | 0 1 2 1 1 2 1 0 0 0 0 ..o.3..o.4..o. | * * 24 * | 0 0 0 0 1 2 2 1 0 | 0 0 0 0 0 0 2 2 1 2 1 2 2 0 | 0 0 0 0 1 2 1 1 2 1 0 ...o3...o4...o | * * * 8 | 0 0 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 0 0 3 6 3 | 0 0 0 0 0 0 0 1 3 3 1 ------------------+-----------+----------------------------+-------------------------------------+------------------------- .... .... x... | 2 0 0 0 | 12 * * * * * * * * | 2 0 2 0 0 0 0 0 0 0 0 0 0 0 | 1 0 1 2 0 0 0 0 0 0 0 oo..3oo..4oo..&#x | 1 1 0 0 | * 24 * * * * * * * | 0 2 2 0 0 0 0 0 0 0 0 0 0 0 | 0 1 2 1 0 0 0 0 0 0 0 .x.. .... .... | 0 2 0 0 | * * 24 * * * * * * | 0 1 0 1 1 0 1 0 0 0 0 0 0 0 | 0 1 1 0 1 1 0 0 0 0 0 .... .... .x.. | 0 2 0 0 | * * * 24 * * * * * | 0 0 1 0 1 1 0 1 0 0 0 0 0 0 | 0 0 1 1 0 1 1 0 0 0 0 .oo.3.oo.4.oo.&#x | 0 1 1 0 | * * * * 24 * * * * | 0 0 0 0 0 0 2 2 0 0 0 0 0 0 | 0 0 0 0 1 2 1 0 0 0 0 ..x. .... .... | 0 0 2 0 | * * * * * 24 * * * | 0 0 0 0 0 0 1 0 1 1 0 1 0 0 | 0 0 0 0 1 1 0 1 1 0 0 .... .... ..x. | 0 0 2 0 | * * * * * * 24 * * | 0 0 0 0 0 0 0 1 0 1 1 0 1 0 | 0 0 0 0 0 1 1 0 1 1 0 ..oo3..oo4..oo&#x | 0 0 1 1 | * * * * * * * 24 * | 0 0 0 0 0 0 0 0 0 0 0 2 2 0 | 0 0 0 0 0 0 0 1 2 1 0 .... .... ...x | 0 0 0 2 | * * * * * * * * 12 | 0 0 0 0 0 0 0 0 0 0 0 0 2 2 | 0 0 0 0 0 0 0 0 1 2 1 ------------------+-----------+----------------------------+-------------------------------------+------------------------- .... o...4x... | 4 0 0 0 | 4 0 0 0 0 0 0 0 0 | 6 * * * * * * * * * * * * * | 1 0 0 1 0 0 0 0 0 0 0 ox.. .... ....&#x | 1 2 0 0 | 0 2 1 0 0 0 0 0 0 | * 24 * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 0 0 .... .... xx..&#x | 2 2 0 0 | 1 2 0 1 0 0 0 0 0 | * * 24 * * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 0 0 .x..3.o.. .... | 0 3 0 0 | 0 0 3 0 0 0 0 0 0 | * * * 8 * * * * * * * * * * | 0 1 0 0 1 0 0 0 0 0 0 .x.. .... .x.. | 0 4 0 0 | 0 0 2 2 0 0 0 0 0 | * * * * 12 * * * * * * * * * | 0 0 1 0 0 1 0 0 0 0 0 .... .o..4.x.. | 0 4 0 0 | 0 0 0 4 0 0 0 0 0 | * * * * * 6 * * * * * * * * | 0 0 0 1 0 0 1 0 0 0 0 .xx. .... ....&#x | 0 2 2 0 | 0 0 1 0 2 1 0 0 0 | * * * * * * 24 * * * * * * * | 0 0 0 0 1 1 0 0 0 0 0 .... .... .xx.&#x | 0 2 2 0 | 0 0 0 1 2 0 1 0 0 | * * * * * * * 24 * * * * * * | 0 0 0 0 0 1 1 0 0 0 0 ..x.3..o. .... | 0 0 3 0 | 0 0 0 0 0 3 0 0 0 | * * * * * * * * 8 * * * * * | 0 0 0 0 1 0 0 1 0 0 0 ..x. .... ..x. | 0 0 4 0 | 0 0 0 0 0 2 2 0 0 | * * * * * * * * * 12 * * * * | 0 0 0 0 0 1 0 0 1 0 0 .... ..o.4..x. | 0 0 4 0 | 0 0 0 0 0 0 4 0 0 | * * * * * * * * * * 6 * * * | 0 0 0 0 0 0 1 0 0 1 0 ..xo .... ....&#x | 0 0 2 1 | 0 0 0 0 0 1 0 2 0 | * * * * * * * * * * * 24 * * | 0 0 0 0 0 0 0 1 1 0 0 .... .... ..xx&#x | 0 0 2 2 | 0 0 0 0 0 0 1 2 1 | * * * * * * * * * * * * 24 * | 0 0 0 0 0 0 0 0 1 1 0 .... ...o4...x | 0 0 0 4 | 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * * * 6 | 0 0 0 0 0 0 0 0 0 1 1 ------------------+-----------+----------------------------+-------------------------------------+------------------------- o...3o...4x... ♦ 8 0 0 0 | 12 0 0 0 0 0 0 0 0 | 6 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * ox..3oo.. ....&#x ♦ 1 3 0 0 | 0 3 3 0 0 0 0 0 0 | 0 3 0 1 0 0 0 0 0 0 0 0 0 0 | * 8 * * * * * * * * * ox.. .... xx..&#x ♦ 2 4 0 0 | 1 4 2 2 0 0 0 0 0 | 0 2 2 0 1 0 0 0 0 0 0 0 0 0 | * * 12 * * * * * * * * .... oo..4xx..&#x ♦ 4 4 0 0 | 4 4 0 4 0 0 0 0 0 | 1 0 4 0 0 1 0 0 0 0 0 0 0 0 | * * * 6 * * * * * * * .xx.3.oo. ....&#x ♦ 0 3 3 0 | 0 0 3 0 3 3 0 0 0 | 0 0 0 1 0 0 3 0 1 0 0 0 0 0 | * * * * 8 * * * * * * .xx. .... .xx.&#x ♦ 0 4 4 0 | 0 0 2 2 4 2 2 0 0 | 0 0 0 0 1 0 2 2 0 1 0 0 0 0 | * * * * * 12 * * * * * .... .oo.4.xx.&#x ♦ 0 4 4 0 | 0 0 0 4 4 0 4 0 0 | 0 0 0 0 0 1 0 4 0 0 1 0 0 0 | * * * * * * 6 * * * * ..xo3..oo ....&#x ♦ 0 0 3 1 | 0 0 0 0 0 3 0 3 0 | 0 0 0 0 0 0 0 0 1 0 0 3 0 0 | * * * * * * * 8 * * * ..xo .... ..xx&#x ♦ 0 0 4 2 | 0 0 0 0 0 2 2 4 1 | 0 0 0 0 0 0 0 0 0 1 0 2 2 0 | * * * * * * * * 12 * * .... ..oo4..xx&#x ♦ 0 0 4 4 | 0 0 0 0 0 0 4 4 4 | 0 0 0 0 0 0 0 0 0 0 1 0 4 1 | * * * * * * * * * 6 * ...o3...o4...x ♦ 0 0 0 8 | 0 0 0 0 0 0 0 0 12 | 0 0 0 0 0 0 0 0 0 0 0 0 0 6 | * * * * * * * * * * 1
or o...3o...4o... & | 16 * | 3 3 0 0 0 | 3 3 6 0 0 0 0 0 | 1 1 3 3 0 0 0 .o..3.o..4.o.. & | * 48 | 0 1 2 2 1 | 0 2 2 1 2 1 2 2 | 0 1 2 1 1 2 1 --------------------+-------+----------------+-------------------------+------------------ .... .... x... & | 2 0 | 24 * * * * | 2 0 2 0 0 0 0 0 | 1 0 1 2 0 0 0 oo..3oo..4oo..&#x & | 1 1 | * 48 * * * | 0 2 2 0 0 0 0 0 | 0 1 2 1 0 0 0 .x.. .... .... & | 0 2 | * * 48 * * | 0 1 0 1 1 0 1 0 | 0 1 1 0 1 1 0 .... .... .x.. & | 0 2 | * * * 48 * | 0 0 1 0 1 1 0 1 | 0 0 1 1 0 1 1 .oo.3.oo.4.oo.&#x | 0 2 | * * * * 24 | 0 0 0 0 0 0 2 2 | 0 0 0 0 1 2 1 --------------------+-------+----------------+-------------------------+------------------ .... o...4x... & | 4 0 | 4 0 0 0 0 | 12 * * * * * * * | 1 0 0 1 0 0 0 ox.. .... ....&#x & | 1 2 | 0 2 1 0 0 | * 48 * * * * * * | 0 1 1 0 0 0 0 .... .... xx..&#x & | 2 2 | 1 2 0 1 0 | * * 48 * * * * * | 0 0 1 1 0 0 0 .x..3.o.. .... & | 0 3 | 0 0 3 0 0 | * * * 16 * * * * | 0 1 0 0 1 0 0 .x.. .... .x.. & | 0 4 | 0 0 2 2 0 | * * * * 24 * * * | 0 0 1 0 0 1 0 .... .o..4.x.. & | 0 4 | 0 0 0 4 0 | * * * * * 12 * * | 0 0 0 1 0 0 1 .xx. .... ....&#x | 0 4 | 0 0 2 0 2 | * * * * * * 24 * | 0 0 0 0 1 1 0 .... .... .xx.&#x | 0 4 | 0 0 0 2 2 | * * * * * * * 24 | 0 0 0 0 0 1 1 --------------------+-------+----------------+-------------------------+------------------ o...3o...4x... & ♦ 8 0 | 12 0 0 0 0 | 6 0 0 0 0 0 0 0 | 2 * * * * * * ox..3oo.. ....&#x & ♦ 1 3 | 0 3 3 0 0 | 0 3 0 1 0 0 0 0 | * 16 * * * * * ox.. .... xx..&#x & ♦ 2 4 | 1 4 2 2 0 | 0 2 2 0 1 0 0 0 | * * 24 * * * * .... oo..4xx..&#x & ♦ 4 4 | 4 4 0 4 0 | 1 0 4 0 0 1 0 0 | * * * 12 * * * .xx.3.oo. ....&#x ♦ 0 6 | 0 0 6 0 3 | 0 0 0 2 0 0 3 0 | * * * * 8 * * .xx. .... .xx.&#x ♦ 0 8 | 0 0 4 4 4 | 0 0 0 0 2 0 2 2 | * * * * * 12 * .... .oo.4.xx.&#x ♦ 0 8 | 0 0 0 8 4 | 0 0 0 0 0 2 0 4 | * * * * * * 6
xxxowoqo3ooqooqoo3oqowoxxx&#xt → height(1,2) = height(2,3) = height(6,7) = height(7,8) = 1/2 height(3,4) = height(5,6) = (sqrt(2)-1)/2 = 0.207107 height(4,5) = (2-sqrt(2))/2 = 0.292893 (tet || pseudo (x,q)-co || pseudo (x,q)-tut || pseudo inv w-tet || pseudo w-tet || pseudo inv (x,q)-tut || pseudo (q,x)-co || dual tet) o.......3o.......3o....... & | 8 * * * | 3 3 0 0 0 0 0 0 | 3 6 3 0 0 0 0 0 0 | 1 3 3 1 0 0 0 0 .o......3.o......3.o...... & | * 24 * * | 0 1 2 2 1 0 0 0 | 0 2 2 1 2 2 1 2 0 | 0 1 2 1 1 2 1 0 ..o.....3..o.....3..o..... & | * * 24 * | 0 0 0 2 0 1 1 2 | 0 0 1 0 2 0 2 4 3 | 0 0 1 1 0 3 2 1 ...o....3...o....3...o.... & | * * * 8 | 0 0 0 0 3 0 3 0 | 0 0 0 0 0 3 3 6 0 | 0 0 0 1 1 3 3 0 ----------------------------------+-----------+-------------------------+--------------------------+------------------- x....... ........ ........ & | 2 0 0 0 | 12 * * * * * * * | 2 2 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 0 oo......3oo......3oo......&#x & | 1 1 0 0 | * 24 * * * * * * | 0 2 2 0 0 0 0 0 0 | 0 1 2 1 0 0 0 0 .x...... ........ ........ & | 0 2 0 0 | * * 24 * * * * * | 0 1 0 1 1 1 0 0 0 | 0 1 1 0 1 1 0 0 .oo.....3.oo.....3.oo.....&#x & | 0 1 1 0 | * * * 48 * * * * | 0 0 1 0 1 0 1 1 0 | 0 0 1 1 0 1 1 0 .o.o....3.o.o....3.o.o....&#x & | 0 1 0 1 | * * * * 24 * * * | 0 0 0 0 0 2 0 2 0 | 0 0 0 0 1 2 1 0 ..x..... ........ ........ & | 0 0 2 0 | * * * * * 12 * * | 0 0 0 0 2 0 0 0 2 | 0 0 1 0 0 2 0 1 ..o.o...3..o.o...3..o.o...&#x & | 0 0 1 1 | * * * * * * 24 * | 0 0 0 0 0 0 2 2 0 | 0 0 0 1 0 1 2 0 ..o..o..3..o..o..3..o..o..&#x | 0 0 2 0 | * * * * * * * 24 | 0 0 0 0 0 0 0 2 2 | 0 0 0 0 0 2 1 1 ----------------------------------+-----------+-------------------------+--------------------------+------------------- x.......3o....... ........ & | 3 0 0 0 | 3 0 0 0 0 0 0 0 | 8 * * * * * * * * | 1 1 0 0 0 0 0 0 xx...... ........ ........&#x & | 2 2 0 0 | 1 2 1 0 0 0 0 0 | * 24 * * * * * * * | 0 1 1 0 0 0 0 0 ........ ........ oqo.....&#xt & | 1 2 1 0 | 0 2 0 2 0 0 0 0 | * * 24 * * * * * * | 0 0 1 1 0 0 0 0 .x......3.o...... ........ & | 0 3 0 0 | 0 0 3 0 0 0 0 0 | * * * 8 * * * * * | 0 1 0 0 1 0 0 0 .xx..... ........ ........&#x & | 0 2 2 0 | 0 0 1 2 0 1 0 0 | * * * * 24 * * * * | 0 0 1 0 0 1 0 0 .x.o.... ........ ........&#x & | 0 2 0 1 | 0 0 1 0 2 0 0 0 | * * * * * 24 * * * | 0 0 0 0 1 1 0 0 ........ .oq.o... ........&#xt & | 0 1 2 1 | 0 0 0 2 0 0 2 0 | * * * * * * 24 * * | 0 0 0 1 0 0 1 0 .ooo.o..3.ooo.o..3.ooo.o..&#xt & | 0 1 2 1 | 0 0 0 1 1 0 1 1 | * * * * * * * 48 * | 0 0 0 0 0 1 1 0 ..x..o.. ........ ........&#x & | 0 0 3 0 | 0 0 0 0 0 1 0 2 | * * * * * * * * 24 | 0 0 0 0 0 1 0 1 ----------------------------------+-----------+-------------------------+--------------------------+------------------- x.......3o.......3o....... & ♦ 4 0 0 0 | 6 0 0 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 | 2 * * * * * * * xx......3oo...... ........&#x & ♦ 3 3 0 0 | 3 3 3 0 0 0 0 0 | 1 3 0 1 0 0 0 0 0 | * 8 * * * * * * xxx..... ........ oqo.....&#xt & ♦ 2 4 2 0 | 1 4 2 4 0 1 0 0 | 0 2 2 0 2 0 0 0 0 | * * 12 * * * * * ........ ooq.o...3oqo.o...&#xt & ♦ 1 3 3 1 | 0 3 0 6 0 0 3 0 | 0 0 3 0 0 0 3 0 0 | * * * 8 * * * * .x.o....3.o.o.... ........&#x & ♦ 0 3 0 1 | 0 0 3 0 3 0 0 0 | 0 0 0 1 0 3 0 0 0 | * * * * 8 * * * .xxo.o.. ........ ........&#xt & ♦ 0 2 3 1 | 0 0 1 2 2 1 1 2 | 0 0 0 0 1 1 0 2 1 | * * * * * 24 * * ........ .oqooqo. ........&#xt ♦ 0 2 4 2 | 0 0 0 4 2 0 4 2 | 0 0 0 0 0 0 2 4 0 | * * * * * * 12 * ..x..o.. ........ ..o..x..&#x ♦ 0 0 4 0 | 0 0 0 0 0 2 0 4 | 0 0 0 0 0 0 0 0 4 | * * * * * * * 6
xowqwox xxxxxxx4oxoxoxox&#xt → height(1,2) = height(3,4) = height(4,5) = height(6,7) = 1/2 height(2,3) = height(5,6) = (sqrt(2)-1)/2 = 0.207107 (cube || pseudo {8} || pseudo (w,x,x)-cube || pseudo (q,x)-op || pseudo (w,x,x)-cube || pseudo {8} || cube) o...... o......4o...... & | 16 * * * | 1 2 2 1 0 0 0 0 0 0 0 0 | 2 1 2 2 1 2 2 0 0 0 0 0 0 0 0 | 1 2 1 1 2 1 0 0 0 0 0 .o..... .o.....4.o..... & | * 16 * * | 0 0 2 0 1 1 2 0 0 0 0 0 | 0 0 1 2 2 0 2 1 2 2 0 0 0 0 0 | 0 1 1 0 2 2 1 1 0 0 0 ..o.... ..o....4..o.... & | * * 16 * | 0 0 0 1 0 0 0 2 2 1 0 0 | 0 0 0 0 0 2 2 0 0 0 1 2 1 2 2 | 0 0 0 1 2 1 0 0 2 2 1 ...o... ...o...4...o... | * * * 16 | 0 0 0 0 0 0 2 0 2 0 1 1 | 0 0 0 0 0 0 2 1 2 2 0 2 2 0 1 | 0 0 0 0 2 2 1 1 0 1 1 -------------------------------+-------------+-------------------------------+-----------------------------------------+------------------------ x...... ....... ....... & | 2 0 0 0 | 8 * * * * * * * * * * * | 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 0 0 0 0 ....... x...... ....... & | 2 0 0 0 | * 16 * * * * * * * * * * | 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 | 1 1 0 1 1 0 0 0 0 0 0 oo..... oo.....4oo.....&#x & | 1 1 0 0 | * * 32 * * * * * * * * * | 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 | 0 1 1 0 1 1 0 0 0 0 0 o.o.... o.o....4o.o....&#x & | 1 0 1 0 | * * * 16 * * * * * * * * | 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 | 0 0 0 1 2 1 0 0 0 0 0 ....... .x..... ....... & | 0 2 0 0 | * * * * 8 * * * * * * * | 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 | 0 1 0 0 2 0 1 0 0 0 0 ....... ....... .x..... & | 0 2 0 0 | * * * * * 8 * * * * * * | 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 | 0 0 1 0 0 2 0 1 0 0 0 .o.o... .o.o...4.o.o...&#x & | 0 1 0 1 | * * * * * * 32 * * * * * | 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 | 0 0 0 0 1 1 1 1 0 0 0 ....... ..x.... ....... & | 0 0 2 0 | * * * * * * * 16 * * * * | 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 | 0 0 0 1 1 0 0 0 1 1 0 ..oo... ..oo...4..oo...&#x & | 0 0 1 1 | * * * * * * * * 32 * * * | 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 | 0 0 0 0 1 1 0 0 0 1 1 ..o.o.. ..o.o..4..o.o..&#x | 0 0 2 0 | * * * * * * * * * 8 * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 | 0 0 0 0 0 0 0 0 1 2 1 ....... ...x... ....... | 0 0 0 2 | * * * * * * * * * * 8 * | 0 0 0 0 0 0 0 0 2 0 0 2 0 0 0 | 0 0 0 0 2 0 1 0 0 1 0 ....... ....... ...x... | 0 0 0 2 | * * * * * * * * * * * 8 | 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 | 0 0 0 0 0 2 0 1 0 0 1 -------------------------------+-------------+-------------------------------+-----------------------------------------+------------------------ x...... x...... ....... & | 4 0 0 0 | 2 2 0 0 0 0 0 0 0 0 0 0 | 8 * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 0 0 ....... x......4o...... & | 4 0 0 0 | 0 4 0 0 0 0 0 0 0 0 0 0 | * 4 * * * * * * * * * * * * * | 1 0 0 1 0 0 0 0 0 0 0 xo..... ....... .......&#x & | 2 1 0 0 | 1 0 2 0 0 0 0 0 0 0 0 0 | * * 16 * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 0 0 ....... xx..... .......&#x & | 2 2 0 0 | 0 1 2 0 1 0 0 0 0 0 0 0 | * * * 16 * * * * * * * * * * * | 0 1 0 0 1 0 0 0 0 0 0 ....... ....... ox.....&#x & | 1 2 0 0 | 0 0 2 0 0 1 0 0 0 0 0 0 | * * * * 16 * * * * * * * * * * | 0 0 1 0 0 1 0 0 0 0 0 ....... x.x.... .......&#x & | 2 0 2 0 | 0 1 0 2 0 0 0 1 0 0 0 0 | * * * * * 16 * * * * * * * * * | 0 0 0 1 1 0 0 0 0 0 0 oooo... oooo...4oooo...&#xr & | 1 1 1 1 | 0 0 1 1 0 0 1 0 1 0 0 0 | * * * * * * 32 * * * * * * * * | 0 0 0 0 1 1 0 0 0 0 0 .o.q.o. ....... .......&#xt | 0 2 0 2 | 0 0 0 0 0 0 4 0 0 0 0 0 | * * * * * * * 8 * * * * * * * | 0 0 0 0 0 0 1 1 0 0 0 ....... .x.x... .......&#x & | 0 2 0 2 | 0 0 0 0 1 0 2 0 0 0 1 0 | * * * * * * * * 16 * * * * * * | 0 0 0 0 1 0 1 0 0 0 0 ....... ....... .x.x...&#x & | 0 2 0 2 | 0 0 0 0 0 1 2 0 0 0 0 1 | * * * * * * * * * 16 * * * * * | 0 0 0 0 0 1 0 1 0 0 0 ....... ..x....4..o.... & | 0 0 4 0 | 0 0 0 0 0 0 0 4 0 0 0 0 | * * * * * * * * * * 4 * * * * | 0 0 0 1 0 0 0 0 1 0 0 ....... ..xx... .......&#x & | 0 0 2 2 | 0 0 0 0 0 0 0 1 2 0 1 0 | * * * * * * * * * * * 16 * * * | 0 0 0 0 1 0 0 0 0 1 0 ....... ....... ..ox...&#x & | 0 0 1 2 | 0 0 0 0 0 0 0 0 2 0 0 1 | * * * * * * * * * * * * 16 * * | 0 0 0 0 0 1 0 0 0 0 1 ....... ..x.x.. .......&#x | 0 0 4 0 | 0 0 0 0 0 0 0 2 0 2 0 0 | * * * * * * * * * * * * * 8 * | 0 0 0 0 0 0 0 0 1 1 0 ..ooo.. ..ooo..4..ooo..&#x | 0 0 2 1 | 0 0 0 0 0 0 0 0 2 1 0 0 | * * * * * * * * * * * * * * 16 | 0 0 0 0 0 0 0 0 0 1 1 -------------------------------+-------------+-------------------------------+-----------------------------------------+------------------------ x...... x......4o...... & ♦ 8 0 0 0 | 4 8 0 0 0 0 0 0 0 0 0 0 | 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * * xo..... xx..... .......&#x & ♦ 4 2 0 0 | 2 2 4 0 1 0 0 0 0 0 0 0 | 1 0 2 2 0 0 0 0 0 0 0 0 0 0 0 | * 8 * * * * * * * * * xo..... ....... ox.....&#x & ♦ 2 2 0 0 | 1 0 4 0 0 1 0 0 0 0 0 0 | 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 | * * 8 * * * * * * * * ....... x.x....4o.o....&#x & ♦ 4 0 4 0 | 0 4 0 4 0 0 0 4 0 0 0 0 | 0 1 0 0 0 4 0 0 0 0 1 0 0 0 0 | * * * 4 * * * * * * * ....... xxxx... .......&#xr & ♦ 2 2 2 2 | 0 1 2 2 1 0 2 1 2 0 1 0 | 0 0 0 1 0 1 2 0 1 0 0 1 0 0 0 | * * * * 16 * * * * * * ....... ....... oxox...&#xr & ♦ 1 2 1 2 | 0 0 2 1 0 1 2 0 2 0 0 1 | 0 0 0 0 1 0 2 0 0 1 0 0 1 0 0 | * * * * * 16 * * * * * .o.q.o. .x.x.x. .......&#xt ♦ 0 4 0 4 | 0 0 0 0 2 0 8 0 0 0 2 0 | 0 0 0 0 0 0 0 2 4 0 0 0 0 0 0 | * * * * * * 4 * * * * .o.q.o. ....... .x.x.x.&#xt ♦ 0 4 0 4 | 0 0 0 0 0 2 8 0 0 0 0 2 | 0 0 0 0 0 0 0 2 0 4 0 0 0 0 0 | * * * * * * * 4 * * * ....... ..x.x..4..o.o..&#x ♦ 0 0 8 0 | 0 0 0 0 0 0 0 8 0 4 0 0 | 0 0 0 0 0 0 0 0 0 0 2 0 0 4 0 | * * * * * * * * 2 * * ....... ..xxx.. .......&#x ♦ 0 0 4 2 | 0 0 0 0 0 0 0 2 4 2 1 0 | 0 0 0 0 0 0 0 0 0 0 0 2 0 1 2 | * * * * * * * * * 8 * ....... ....... ..oxo..&#x ♦ 0 0 2 2 | 0 0 0 0 0 0 0 0 4 1 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 | * * * * * * * * * * 8
qo3oo3oq *b3xx&#zx → height = 0 (tegum sum of 2 mutually gyrated (x,q)-rits) o.3o.3o. *b3o. | 32 * | 3 3 0 | 3 3 6 0 | 1 1 3 3 0 .o3.o3.o *b3.o | * 32 | 0 3 3 | 0 3 6 3 | 0 1 3 3 1 -------------------+-------+----------+-------------+------------ .. .. .. x. | 2 0 | 48 * * | 2 0 2 0 | 1 0 1 2 0 oo3oo3oo *b3oo&#x | 1 1 | * 96 * | 0 2 2 0 | 0 1 2 1 0 .. .. .. .x | 0 2 | * * 48 | 0 0 2 2 | 0 0 1 2 1 -------------------+-------+----------+-------------+------------ .. o. .. *b3x. | 3 0 | 3 0 0 | 32 * * * | 1 0 0 1 0 qo .. oq ..&#zx | 2 2 | 0 4 0 | * 48 * * | 0 1 1 0 0 .. .. .. xx&#x | 2 2 | 1 2 1 | * * 96 * | 0 0 1 1 0 .. .o .. *b3.x | 0 3 | 0 0 3 | * * * 32 | 0 0 0 1 1 -------------------+-------+----------+-------------+------------ .. o.3o. *b3x. ♦ 4 0 | 6 0 0 | 4 0 0 0 | 8 * * * * qo3oo3oq ..&#zx ♦ 4 4 | 0 12 0 | 0 6 0 0 | * 8 * * * qo .. oq xx&#zx ♦ 4 4 | 2 8 2 | 0 2 4 0 | * * 24 * * .. oo .. *b3xx&#x ♦ 3 3 | 3 3 3 | 1 0 3 1 | * * * 32 * .o3.o .. *b3.x ♦ 0 4 | 0 0 6 | 0 0 0 4 | * * * * 8
wx ox3oo4xx&#zx → height = 0 (tegum sum of (w,x,x,x)-tes and sircope) o. o.3o.4o. | 16 * | 3 3 0 0 0 | 3 3 6 0 0 0 0 0 | 1 1 3 3 0 0 0 .o .o3.o4.o | * 48 | 0 1 1 2 2 | 0 2 2 2 2 1 2 1 | 0 1 2 1 1 2 1 ----------------+-------+----------------+-------------------------+------------------ .. .. .. x. | 2 0 | 24 * * * * | 2 0 2 0 0 0 0 0 | 1 0 1 2 0 0 0 oo oo3oo4oo&#x | 1 1 | * 48 * * * | 0 2 2 0 0 0 0 0 | 0 1 2 1 0 0 0 .x .. .. .. | 0 2 | * * 24 * * | 0 0 0 2 2 0 0 0 | 0 0 0 0 1 2 1 .. .x .. .. | 0 2 | * * * 48 * | 0 1 0 1 0 1 1 0 | 0 1 1 0 1 1 0 .. .. .. .x | 0 2 | * * * * 48 | 0 0 1 0 1 0 1 1 | 0 0 1 1 0 1 1 ----------------+-------+----------------+-------------------------+------------------ .. .. o.4x. | 4 0 | 4 0 0 0 0 | 12 * * * * * * * | 1 0 0 1 0 0 0 .. ox .. ..&#x | 1 2 | 0 2 0 1 0 | * 48 * * * * * * | 0 1 1 0 0 0 0 .. .. .. xx&#x | 2 2 | 1 2 0 0 1 | * * 48 * * * * * | 0 0 1 1 0 0 0 .x .x .. .. | 0 4 | 0 0 2 2 0 | * * * 24 * * * * | 0 0 0 0 1 1 0 .x .. .. .x | 0 4 | 0 0 2 0 2 | * * * * 24 * * * | 0 0 0 0 0 1 1 .. .x3.o .. | 0 3 | 0 0 0 3 0 | * * * * * 16 * * | 0 1 0 0 1 0 0 .. .x .. .x | 0 4 | 0 0 0 2 2 | * * * * * * 24 * | 0 0 1 0 0 1 0 .. .. .o4.x | 0 4 | 0 0 0 0 4 | * * * * * * * 12 | 0 0 0 1 0 0 1 ----------------+-------+----------------+-------------------------+------------------ .. o.3o.4x. ♦ 8 0 | 12 0 0 0 0 | 6 0 0 0 0 0 0 0 | 2 * * * * * * .. ox3oo ..&#x ♦ 1 3 | 0 3 0 3 0 | 0 3 0 0 0 1 0 0 | * 16 * * * * * .. ox .. xx&#x ♦ 2 4 | 1 4 0 2 2 | 0 2 2 0 0 0 1 0 | * * 24 * * * * .. .. oo4xx&#x ♦ 4 4 | 4 4 0 0 4 | 1 0 4 0 0 0 0 1 | * * * 12 * * * .x .x3.o .. ♦ 0 6 | 0 0 3 6 0 | 0 0 0 3 0 2 0 0 | * * * * 8 * * .x .x .. .x ♦ 0 8 | 0 0 4 4 4 | 0 0 0 2 2 0 2 0 | * * * * * 12 * .x .. .o4.x ♦ 0 8 | 0 0 4 0 8 | 0 0 0 0 4 0 0 2 | * * * * * * 6
xo4xx ox4xx&#zx → height = 0 (tegum sum of 2 interchanged sodips.) o.4o. o.4o. & | 64 | 1 1 2 2 | 2 2 1 3 4 | 1 1 1 3 2 ------------------+----+-------------+----------------+------------- x. .. .. .. & | 2 | 32 * * * | 2 0 0 2 0 | 1 0 1 2 0 .. x. .. .. & | 2 | * 32 * * | 0 2 0 0 2 | 0 1 0 1 2 .. .. .. x. & | 2 | * * 64 * | 1 1 1 0 1 | 1 1 0 1 1 oo4oo oo4oo&#x | 2 | * * * 64 | 0 0 0 2 2 | 0 0 1 2 1 ------------------+----+-------------+----------------+------------- x. .. .. x. & | 4 | 2 0 2 0 | 32 * * * * | 1 0 0 1 0 .. x. .. x. & | 4 | 0 2 2 0 | * 32 * * * | 0 1 0 0 1 .. .. o.4x. & | 4 | 0 0 4 0 | * * 16 * * | 1 1 0 0 0 xo .. .. ..&#x & | 3 | 1 0 0 2 | * * * 64 * | 0 0 1 1 0 .. xx .. ..&#x & | 4 | 0 1 1 2 | * * * * 64 | 0 0 0 1 1 ------------------+----+-------------+----------------+------------- x. .. o.4x. & ♦ 8 | 4 0 8 0 | 4 0 2 0 0 | 8 * * * * .. x. o.4x. & ♦ 8 | 0 4 8 0 | 0 4 2 0 0 | * 8 * * * xo .. ox ..&#x ♦ 4 | 2 0 0 4 | 0 0 0 4 0 | * * 16 * * xo .. .. xx&#x & ♦ 6 | 2 1 2 4 | 1 0 0 2 2 | * * * 32 * .. xx .. xx&#x ♦ 8 | 0 4 4 4 | 0 2 0 0 4 | * * * * 16
wxxx xwxx xxwx xxxw&#zx → height = 0 (tegum sum of 4 orthogonal (w,x,x,x)-teses.) o... o... o... o... & | 64 | 3 3 | 3 6 3 | 1 3 3 1 --------------------------+----+-------+----------+----------- .... x... .... .... & | 2 | 96 * | 2 2 0 | 1 1 2 0 oo.. oo.. oo.. oo..&#x & | 2 | * 96 | 0 2 2 | 0 2 1 1 --------------------------+----+-------+----------+----------- .... x... x... .... & | 4 | 4 0 | 48 * * | 1 0 1 0 .... x.x. .... ....&#x & | 4 | 2 2 | * 96 * | 0 1 1 0 ooo. ooo. ooo. ooo.&#x & | 3 | 0 3 | * * 64 | 0 1 0 1 --------------------------+----+-------+----------+----------- .... x... x... x... & ♦ 8 | 12 0 | 6 0 0 | 8 * * * .... x.xx .... ....&#x & ♦ 6 | 3 6 | 0 3 2 | * 32 * * .... x..x x..x ....&#x & ♦ 8 | 8 4 | 2 4 0 | * * 24 * oooo oooo oooo oooo&#x ♦ 4 | 0 6 | 0 0 4 | * * * 16
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