Acronym | srit | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Name |
small rhombated tesseract, cantellated tesseract | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Cross sections |
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Circumradius | sqrt[2+sqrt(2)] = 1.847759 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. oct | 1+1/sqrt(2) = 1.707107 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. trip | sqrt[(17+12 sqrt(2))/12] = 1.682522 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. sirco | (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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x3o x3q w3o o3w q3x o3x o3x o3w x3w w3x w3o x3o o3x o3w x3w w3x w3o x3o x3o x3q w3o o3w q3x o3x | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Coordinates | ((1+sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2) & all permutations, all changes of sign | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Volume | [45+32 sqrt(2)]/3 = 30.084945 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Surface | 8[4+4 sqrt(2)+sqrt(3)] = 91.111240 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
General of army | (is itself convex) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Colonel of regiment |
(is itself locally convex
– uniform polychoral members:
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Dihedral angles | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Pattern (parts of total size: 8x8 squares) |
A---1---A---2---A---1---A---2---A-... | \ : / | | \ : / | | 1==B,B==1===3===1==B,B==1===3===1= | / : \ | | / : \ | | A---1---A---2---A---1---A---2---A-... | : | | : | | 2 3 2 2 3 2 2 | : | | : | | A---1---A---2---A---1---A---2---A-... | \ : / | | \ : / | | 1==B,B==1===3===1==B,B==1===3===1= | / : \ | | / : \ | | A---1---A---2---A---1---A---2---A-... | : | | : | | 2 3 2 2 3 2 2 | : | | : | | A---1---A---2---A---1---A---2---A-... | \ : / | | \ : / | | | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Face vector | 96, 288, 248, 56 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Confer |
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External links |
As abstract polytope srit is isomorphic to qrit, thereby replacing sirco by querco.
Augmenting octasircoes onto the sirco would lead to the spic (which would have an even larger symmetry)! Augmenting only a cycle of 4 of those results in cyted spic.
Just as tes can variously be seen as having full tessic symmetry or as having only a subsymmetric 4-duoprismatic one (fixing the 4-prism axis in each cube) here correspondingly the sircoes could be aligned into 2 great circles of 4 each. Moreover, the connecting squares are incident to 2 sircoes (face), 4 trips (sides), and 4 octs (vertices). The sectioning facet underneath those squares therfore is an op, i.e. cutting off a squipuf each. These 2 duoprismatic great circles thus show that srit can be further diminished by 4 of those within each ring, then resulting finally in an odip!
Note that srit can be thought of as the external blend of 1 ico + 16 opes + 32 triddips + 8 octasircoes. This decomposition is described as the degenerate segmentoteron oo3xx3oo4ox&#x. – Alternatively srit can be decomposed into 1 tes + 16 octpies + 32 tepes + 8 cubasircoes according to oo3ox3oo4xx&#x.
Incidence matrix according to Dynkin symbol
o3x3o4x . . . . | 96 | 4 2 | 2 2 4 1 | 1 2 2 (A),(B) --------+----+--------+-------------+-------- . x . . | 2 | 192 * | 1 1 1 0 | 1 1 1 (1),(/),(\) . . . x | 2 | * 96 | 0 0 2 1 | 0 1 2 (2),(3) --------+----+--------+-------------+-------- o3x . . | 3 | 3 0 | 64 * * * | 1 1 0 . x3o . | 3 | 3 0 | * 64 * * | 1 0 1 . x . x | 4 | 2 2 | * * 96 * | 0 1 1 . . o4x | 4 | 0 4 | * * * 24 | 0 0 2 --------+----+--------+-------------+-------- o3x3o . ♦ 6 | 12 0 | 4 4 0 0 | 16 * * o3x . x ♦ 6 | 6 3 | 2 0 3 0 | * 32 * . x3o4x ♦ 24 | 24 24 | 0 8 12 6 | * * 8 snubbed forms: o3β3o4x, o3x3o4s, o3β3o4β
o3x3/2o4/3x . . . . | 96 | 4 2 | 2 2 4 1 | 1 2 2 ------------+----+--------+-------------+-------- . x . . | 2 | 192 * | 1 1 1 0 | 1 1 1 . . . x | 2 | * 96 | 0 0 2 1 | 0 1 2 ------------+----+--------+-------------+-------- o3x . . | 3 | 3 0 | 64 * * * | 1 1 0 . x3/2o . | 3 | 3 0 | * 64 * * | 1 0 1 . x . x | 4 | 2 2 | * * 96 * | 0 1 1 . . o4/3x | 4 | 0 4 | * * * 24 | 0 0 2 ------------+----+--------+-------------+-------- o3x3/2o . ♦ 6 | 12 0 | 4 4 0 0 | 16 * * o3x . x ♦ 6 | 6 3 | 2 0 3 0 | * 32 * . x3/2o4/3x ♦ 24 | 24 24 | 0 8 12 6 | * * 8
o3/2x3o4x . . . . | 96 | 4 2 | 2 2 4 1 | 1 2 2 ----------+----+--------+-------------+-------- . x . . | 2 | 192 * | 1 1 1 0 | 1 1 1 . . . x | 2 | * 96 | 0 0 2 1 | 0 1 2 ----------+----+--------+-------------+-------- o3/2x . . | 3 | 3 0 | 64 * * * | 1 1 0 . x3o . | 3 | 3 0 | * 64 * * | 1 0 1 . x . x | 4 | 2 2 | * * 96 * | 0 1 1 . . o4x | 4 | 0 4 | * * * 24 | 0 0 2 ----------+----+--------+-------------+-------- o3/2x3o . ♦ 6 | 12 0 | 4 4 0 0 | 16 * * o3/2x . x ♦ 6 | 6 3 | 2 0 3 0 | * 32 * . x3o4x ♦ 24 | 24 24 | 0 8 12 6 | * * 8
o3/2x3/2o4/3x . . . . | 96 | 4 2 | 2 2 4 1 | 1 2 2 --------------+----+--------+-------------+-------- . x . . | 2 | 192 * | 1 1 1 0 | 1 1 1 . . . x | 2 | * 96 | 0 0 2 1 | 0 1 2 --------------+----+--------+-------------+-------- o3/2x . . | 3 | 3 0 | 64 * * * | 1 1 0 . x3/2o . | 3 | 3 0 | * 64 * * | 1 0 1 . x . x | 4 | 2 2 | * * 96 * | 0 1 1 . . o4/3x | 4 | 0 4 | * * * 24 | 0 0 2 --------------+----+--------+-------------+-------- o3/2x3/2o . ♦ 6 | 12 0 | 4 4 0 0 | 16 * * o3/2x . x ♦ 6 | 6 3 | 2 0 3 0 | * 32 * . x3/2o4/3x ♦ 24 | 24 24 | 0 8 12 6 | * * 8
xoox3oxxo4xxxx&#xt → outer heights = 1/sqrt(2) = 0.707107 inner height = 1 (sirco || pseudo tic || pseudo tic || sirco) o...3o...4o... | 24 * * * | 2 2 2 0 0 0 0 0 0 0 0 | 1 2 1 2 1 2 0 0 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0 0 0 .o..3.o..4.o.. | * 24 * * | 0 0 2 2 1 1 0 0 0 0 0 | 0 0 0 1 2 2 1 2 1 0 0 0 0 0 0 0 | 0 1 1 2 1 0 0 0 ..o.3..o.4..o. | * * 24 * | 0 0 0 0 0 1 2 1 2 0 0 | 0 0 0 0 0 0 0 2 1 1 1 2 2 0 0 0 | 0 0 0 2 1 1 1 0 ...o3...o4...o | * * * 24 | 0 0 0 0 0 0 0 0 2 2 2 | 0 0 0 0 0 0 0 0 0 0 2 1 2 1 2 1 | 0 0 0 1 0 1 2 1 -------------------+-------------+----------------------------------+-------------------------------------------+------------------ x... .... .... | 2 0 0 0 | 24 * * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0 .... .... x... | 2 0 0 0 | * 24 * * * * * * * * * | 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0 0 0 oo..3oo..4oo..&#x | 1 1 0 0 | * * 48 * * * * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0 .... .x.. .... | 0 2 0 0 | * * * 24 * * * * * * * | 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 | 0 1 0 1 1 0 0 0 .... .... .x.. | 0 2 0 0 | * * * * 12 * * * * * * | 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 0 | 0 0 1 2 0 0 0 0 .oo.3.oo.4.oo.&#x | 0 1 1 0 | * * * * * 24 * * * * * | 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 | 0 0 0 2 1 0 0 0 .... ..x. .... | 0 0 2 0 | * * * * * * 24 * * * * | 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 | 0 0 0 1 1 1 0 0 .... .... ..x. | 0 0 2 0 | * * * * * * * 12 * * * | 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 0 | 0 0 0 2 0 0 1 0 ..oo3..oo4..oo&#x | 0 0 1 1 | * * * * * * * * 48 * * | 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 | 0 0 0 1 0 1 1 0 ...x .... .... | 0 0 0 2 | * * * * * * * * * 24 * | 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 | 0 0 0 0 0 1 1 1 .... .... ...x | 0 0 0 2 | * * * * * * * * * * 24 | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 | 0 0 0 1 0 0 1 1 -------------------+-------------+----------------------------------+-------------------------------------------+------------------ x...3o... .... | 3 0 0 0 | 3 0 0 0 0 0 0 0 0 0 0 | 8 * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 x... .... x... | 4 0 0 0 | 2 2 0 0 0 0 0 0 0 0 0 | * 12 * * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 .... o...4x... | 4 0 0 0 | 0 4 0 0 0 0 0 0 0 0 0 | * * 6 * * * * * * * * * * * * * | 1 0 0 1 0 0 0 0 xo.. .... ....&#x | 2 1 0 0 | 1 0 2 0 0 0 0 0 0 0 0 | * * * 24 * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 .... ox.. ....&#x | 1 2 0 0 | 0 0 2 1 0 0 0 0 0 0 0 | * * * * 24 * * * * * * * * * * * | 0 1 0 1 0 0 0 0 .... .... xx..&#x | 2 2 0 0 | 0 1 2 0 1 0 0 0 0 0 0 | * * * * * 24 * * * * * * * * * * | 0 0 1 1 0 0 0 0 .o..3.x.. .... | 0 3 0 0 | 0 0 0 3 0 0 0 0 0 0 0 | * * * * * * 8 * * * * * * * * * | 0 1 0 0 1 0 0 0 .... .xx. ....&#x | 0 2 2 0 | 0 0 0 1 0 2 1 0 0 0 0 | * * * * * * * 24 * * * * * * * * | 0 0 0 1 1 0 0 0 .... .... .xx.&#x | 0 2 2 0 | 0 0 0 0 1 2 0 1 0 0 0 | * * * * * * * * 12 * * * * * * * | 0 0 0 2 0 0 0 0 ..o.3..x. .... | 0 0 3 0 | 0 0 0 0 0 0 3 0 0 0 0 | * * * * * * * * * 8 * * * * * * | 0 0 0 0 1 1 0 0 ..ox .... ....&#x | 0 0 1 2 | 0 0 0 0 0 0 0 0 2 1 0 | * * * * * * * * * * 24 * * * * * | 0 0 0 0 0 1 1 0 .... ..xo ....&#x | 0 0 2 1 | 0 0 0 0 0 0 1 0 2 0 0 | * * * * * * * * * * * 24 * * * * | 0 0 0 1 0 1 0 0 .... .... ..xx&#x | 0 0 2 2 | 0 0 0 0 0 0 0 1 2 0 1 | * * * * * * * * * * * * 24 * * * | 0 0 0 1 0 0 1 0 ...x3...o .... | 0 0 0 3 | 0 0 0 0 0 0 0 0 0 3 0 | * * * * * * * * * * * * * 8 * * | 0 0 0 0 0 1 0 1 ...x .... ...x | 0 0 0 4 | 0 0 0 0 0 0 0 0 0 2 2 | * * * * * * * * * * * * * * 12 * | 0 0 0 0 0 0 1 1 .... ...o4...x | 0 0 0 4 | 0 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * * * * * 6 | 0 0 0 1 0 0 0 1 -------------------+-------------+----------------------------------+-------------------------------------------+------------------ x...3o...4x... ♦ 24 0 0 0 | 24 24 0 0 0 0 0 0 0 0 0 | 8 12 6 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * xo..3ox.. ....&#x ♦ 3 3 0 0 | 3 0 6 3 0 0 0 0 0 0 0 | 1 0 0 3 3 0 1 0 0 0 0 0 0 0 0 0 | * 8 * * * * * * xo.. .... xx..&#x ♦ 4 2 0 0 | 2 2 4 0 1 0 0 0 0 0 0 | 0 1 0 2 0 2 0 0 0 0 0 0 0 0 0 0 | * * 12 * * * * * .... oxxo4xxxx&#xt ♦ 4 8 8 4 | 0 4 8 4 4 8 4 4 8 0 4 | 0 0 1 0 4 4 0 4 4 0 0 4 4 0 0 1 | * * * 6 * * * * .oo.3.xx. ....&#x ♦ 0 3 3 0 | 0 0 0 3 0 3 3 0 0 0 0 | 0 0 0 0 0 0 1 3 0 1 0 0 0 0 0 0 | * * * * 8 * * * ..ox3..xo ....&#x ♦ 0 0 3 3 | 0 0 0 0 0 0 3 0 6 3 0 | 0 0 0 0 0 0 0 0 0 1 3 3 0 1 0 0 | * * * * * 8 * * ..ox .... ..xx&#x ♦ 0 0 2 4 | 0 0 0 0 0 0 0 1 4 2 2 | 0 0 0 0 0 0 0 0 0 0 2 0 2 0 1 0 | * * * * * * 12 * ...x3...o4...x ♦ 0 0 0 24 | 0 0 0 0 0 0 0 0 0 24 24 | 0 0 0 0 0 0 0 0 0 0 0 0 0 8 12 6 | * * * * * * * 1
or o...3o...4o... & | 48 * | 2 2 2 0 0 0 | 1 2 1 2 1 2 0 0 0 | 1 1 2 1 0 .o..3.o..4.o.. & | * 48 | 0 0 2 2 1 1 | 0 0 0 1 2 2 1 2 1 | 0 1 1 2 1 ---------------------+-------+-------------------+----------------------------+------------ x... .... .... & | 2 0 | 48 * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0 .... .... x... & | 2 0 | * 48 * * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0 oo..3oo..4oo..&#x & | 1 1 | * * 96 * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0 .... .x.. .... & | 0 2 | * * * 48 * * | 0 0 0 0 1 0 1 1 0 | 0 1 0 1 1 .... .... .x.. & | 0 2 | * * * * 24 * | 0 0 0 0 0 2 0 0 1 | 0 0 1 2 0 .oo.3.oo.4.oo.&#x | 0 2 | * * * * * 24 | 0 0 0 0 0 0 0 2 1 | 0 0 0 2 1 ---------------------+-------+-------------------+----------------------------+------------ x...3o... .... & | 3 0 | 3 0 0 0 0 0 | 16 * * * * * * * * | 1 1 0 0 0 x... .... x... & | 4 0 | 2 2 0 0 0 0 | * 24 * * * * * * * | 1 0 1 0 0 .... o...4x... & | 4 0 | 0 4 0 0 0 0 | * * 12 * * * * * * | 1 0 0 1 0 xo.. .... ....&#x & | 2 1 | 1 0 2 0 0 0 | * * * 48 * * * * * | 0 1 1 0 0 .... ox.. ....&#x & | 1 2 | 0 0 2 1 0 0 | * * * * 48 * * * * | 0 1 0 1 0 .... .... xx..&#x & | 2 2 | 0 1 2 0 1 0 | * * * * * 48 * * * | 0 0 1 1 0 .o..3.x.. .... & | 0 3 | 0 0 0 3 0 0 | * * * * * * 16 * * | 0 1 0 0 1 .... .xx. ....&#x | 0 4 | 0 0 0 2 0 2 | * * * * * * * 24 * | 0 0 0 1 1 .... .... .xx.&#x | 0 4 | 0 0 0 0 2 2 | * * * * * * * * 12 | 0 0 0 2 0 ---------------------+-------+-------------------+----------------------------+------------ x...3o...4x... & ♦ 24 0 | 24 24 0 0 0 0 | 8 12 6 0 0 0 0 0 0 | 2 * * * * xo..3ox.. ....&#x & ♦ 3 3 | 3 0 6 3 0 0 | 1 0 0 3 3 0 1 0 0 | * 16 * * * xo.. .... xx..&#x & ♦ 4 2 | 2 2 4 0 1 0 | 0 1 0 2 0 2 0 0 0 | * * 24 * * .... oxxo4xxxx&#xt ♦ 8 16 | 0 8 16 8 8 8 | 0 0 2 0 8 8 0 4 4 | * * * 6 * .oo.3.xx. ....&#x ♦ 0 6 | 0 0 0 6 0 3 | 0 0 0 0 0 0 2 3 0 | * * * * 8
oqowxxooo3xxwoqowxx3oooxxwoqo&#xt → height(1,2) = height(2,3) = height(4,5) = height(5,6) = height(7,8) = height(8,9) = 1/2 height(3,4) = height(6,7) = [sqrt(2)-1]/2 = 0.207107 (oct || (q,x)-tut || w-oct || (w,x)-co || (x,q,x)-toe || (x,w)-co || w-oct || inv (q,x)-tut || oct) o........3o........3o........ | 6 * * * * * * * * | 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 2 0 0 0 0 0 0 0 0 .o.......3.o.......3.o....... | * 12 * * * * * * * | 0 1 2 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 2 1 1 2 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 2 1 1 0 0 0 0 0 0 ..o......3..o......3..o...... | * * 6 * * * * * * | 0 0 0 2 0 4 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 1 0 0 0 4 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 2 0 2 1 0 0 0 0 0 ...o.....3...o.....3...o..... | * * * 12 * * * * * | 0 0 0 0 2 0 2 2 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 1 2 2 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 1 2 0 1 0 0 0 0 ....o....3....o....3....o.... | * * * * 24 * * * * | 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 0 | 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 | 0 0 1 0 1 1 1 1 0 0 0 .....o...3.....o...3.....o... | * * * * * 12 * * * | 0 0 0 0 0 0 0 0 0 0 2 0 2 2 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 2 1 2 1 0 0 0 0 0 | 0 0 1 0 0 0 1 2 1 0 0 ......o..3......o..3......o.. | * * * * * * 6 * * | 0 0 0 0 0 0 0 0 0 0 0 4 0 0 2 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 4 0 0 0 1 0 0 0 0 | 0 0 0 0 0 1 2 2 0 0 0 .......o.3.......o.3.......o. | * * * * * * * 12 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 2 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 2 1 1 2 0 0 | 0 0 0 0 0 0 2 1 1 1 0 ........o3........o3........o | * * * * * * * * 6 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 4 2 2 | 0 0 0 0 0 0 2 0 0 2 1 ----------------------------------+------------------------+-------------------------------------------------------+------------------------------------------------------------------+------------------------ ......... x........ ......... | 2 0 0 0 0 0 0 0 0 | 12 * * * * * * * * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0 0 0 0 oo.......3oo.......3oo.......&#x | 1 1 0 0 0 0 0 0 0 | * 12 * * * * * * * * * * * * * * * * | 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 2 0 0 0 0 0 0 0 0 ......... .x....... ......... | 0 2 0 0 0 0 0 0 0 | * * 12 * * * * * * * * * * * * * * * | 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0 0 0 0 .oo......3.oo......3.oo......&#x | 0 1 1 0 0 0 0 0 0 | * * * 12 * * * * * * * * * * * * * * | 0 0 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 2 0 1 0 0 0 0 0 0 .o.o.....3.o.o.....3.o.o.....&#x | 0 1 0 1 0 0 0 0 0 | * * * * 24 * * * * * * * * * * * * * | 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 1 1 0 0 0 0 0 0 ..o.o....3..o.o....3..o.o....&#x | 0 0 1 0 1 0 0 0 0 | * * * * * 24 * * * * * * * * * * * * | 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 0 1 1 0 0 0 0 0 ......... ......... ...x..... | 0 0 0 2 0 0 0 0 0 | * * * * * * 12 * * * * * * * * * * * | 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 1 1 0 1 0 0 0 0 ...oo....3...oo....3...oo....&#x | 0 0 0 1 1 0 0 0 0 | * * * * * * * 24 * * * * * * * * * * | 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 0 1 0 1 0 0 0 0 ....x.... ......... ......... | 0 0 0 0 2 0 0 0 0 | * * * * * * * * 12 * * * * * * * * * | 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 | 0 0 1 0 0 1 0 1 0 0 0 ......... ......... ....x.... | 0 0 0 0 2 0 0 0 0 | * * * * * * * * * 12 * * * * * * * * | 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 | 0 0 0 0 1 1 1 0 0 0 0 ....oo...3....oo...3....oo...&#x | 0 0 0 0 1 1 0 0 0 | * * * * * * * * * * 24 * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 | 0 0 1 0 0 0 1 1 0 0 0 ....o.o..3....o.o..3....o.o..&#x | 0 0 0 0 1 0 1 0 0 | * * * * * * * * * * * 24 * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 | 0 0 0 0 0 1 1 1 0 0 0 .....x... ......... ......... | 0 0 0 0 0 2 0 0 0 | * * * * * * * * * * * * 12 * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 | 0 0 1 0 0 0 0 1 1 0 0 .....o.o.3.....o.o.3.....o.o.&#x | 0 0 0 0 0 1 0 1 0 | * * * * * * * * * * * * * 24 * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 | 0 0 0 0 0 0 1 1 1 0 0 ......oo.3......oo.3......oo.&#x | 0 0 0 0 0 0 1 1 0 | * * * * * * * * * * * * * * 12 * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 1 0 0 0 0 | 0 0 0 0 0 0 2 1 0 0 0 ......... .......x. ......... | 0 0 0 0 0 0 0 2 0 | * * * * * * * * * * * * * * * 12 * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 | 0 0 0 0 0 0 1 0 1 1 0 .......oo3.......oo3.......oo&#x | 0 0 0 0 0 0 0 1 1 | * * * * * * * * * * * * * * * * 12 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 | 0 0 0 0 0 0 2 0 0 1 0 ......... ........x ......... | 0 0 0 0 0 0 0 0 2 | * * * * * * * * * * * * * * * * * 12 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 | 0 0 0 0 0 0 1 0 0 1 1 ----------------------------------+------------------------+-------------------------------------------------------+------------------------------------------------------------------+------------------------ o........3x........ ......... | 3 0 0 0 0 0 0 0 0 | 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4 * * * * * * * * * * * * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 0 0 0 ......... x........3o........ | 3 0 0 0 0 0 0 0 0 | 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 4 * * * * * * * * * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 0 0 ......... xx....... .........&#x | 2 2 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * 12 * * * * * * * * * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 0 0 oqo...... ......... .........&#xt | 1 2 1 0 0 0 0 0 0 | 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 6 * * * * * * * * * * * * * * * * * * * * * | 0 0 2 0 0 0 0 0 0 0 0 ......... .x.......3.o....... | 0 3 0 0 0 0 0 0 0 | 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * 4 * * * * * * * * * * * * * * * * * * * * | 0 1 0 1 0 0 0 0 0 0 0 ......... .x.o..... .........&#x | 0 2 0 1 0 0 0 0 0 | 0 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * 12 * * * * * * * * * * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 0 0 ......... ......... .o.x.....&#x | 0 1 0 2 0 0 0 0 0 | 0 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * 12 * * * * * * * * * * * * * * * * * * | 0 0 0 1 1 0 0 0 0 0 0 .oooo....3.oooo....3.oooo....&#xr | 0 1 1 1 1 0 0 0 0 | 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 | * * * * * * * 24 * * * * * * * * * * * * * * * * * | 0 0 1 0 1 0 0 0 0 0 0 ..o.x.... ......... .........&#x | 0 0 1 0 2 0 0 0 0 | 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 | * * * * * * * * 12 * * * * * * * * * * * * * * * * | 0 0 1 0 0 1 0 0 0 0 0 ......... ......... ..o.x....&#x | 0 0 1 0 2 0 0 0 0 | 0 0 0 0 0 2 0 0 0 1 0 0 0 0 0 0 0 0 | * * * * * * * * * 12 * * * * * * * * * * * * * * * | 0 0 0 0 1 1 0 0 0 0 0 ......... ...o.....3...x..... | 0 0 0 3 0 0 0 0 0 | 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * 4 * * * * * * * * * * * * * * | 0 0 0 1 0 0 1 0 0 0 0 ......... ......... ...xx....&#x | 0 0 0 2 2 0 0 0 0 | 0 0 0 0 0 0 1 2 0 1 0 0 0 0 0 0 0 0 | * * * * * * * * * * * 12 * * * * * * * * * * * * * | 0 0 0 0 1 0 1 0 0 0 0 ......... ...oqo... .........&#xt | 0 0 0 1 2 1 0 0 0 | 0 0 0 0 0 0 0 2 0 0 2 0 0 0 0 0 0 0 | * * * * * * * * * * * * 12 * * * * * * * * * * * * | 0 0 1 0 0 0 1 0 0 0 0 ....xx... ......... .........&#x | 0 0 0 0 2 2 0 0 0 | 0 0 0 0 0 0 0 0 1 0 2 0 1 0 0 0 0 0 | * * * * * * * * * * * * * 12 * * * * * * * * * * * | 0 0 1 0 0 0 0 1 0 0 0 ....x.o.. ......... .........&#x | 0 0 0 0 2 0 1 0 0 | 0 0 0 0 0 0 0 0 1 0 0 2 0 0 0 0 0 0 | * * * * * * * * * * * * * * 12 * * * * * * * * * * | 0 0 0 0 0 1 0 1 0 0 0 ......... ......... ....x.o..&#x | 0 0 0 0 2 0 1 0 0 | 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0 0 0 0 | * * * * * * * * * * * * * * * 12 * * * * * * * * * | 0 0 0 0 0 1 1 0 0 0 0 ....oooo.3....oooo.3....oooo.&#xr | 0 0 0 0 1 1 1 1 0 | 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 | * * * * * * * * * * * * * * * * 24 * * * * * * * * | 0 0 0 0 0 0 1 1 0 0 0 .....x...3....o.... ......... | 0 0 0 0 0 3 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 | * * * * * * * * * * * * * * * * * 4 * * * * * * * | 0 0 1 0 0 0 0 0 1 0 0 .....x.o. ......... .........&#x | 0 0 0 0 0 2 0 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 | * * * * * * * * * * * * * * * * * * 12 * * * * * * | 0 0 0 0 0 0 0 1 1 0 0 ......... .....o.x. .........&#x | 0 0 0 0 0 1 0 2 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 | * * * * * * * * * * * * * * * * * * * 12 * * * * * | 0 0 0 0 0 0 1 0 1 0 0 ......... ......... ......oqo&#xt | 0 0 0 0 0 0 1 2 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 | * * * * * * * * * * * * * * * * * * * * 6 * * * * | 0 0 0 0 0 0 2 0 0 0 0 .......o.3.......x. ......... | 0 0 0 0 0 0 0 3 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 | * * * * * * * * * * * * * * * * * * * * * 4 * * * | 0 0 0 0 0 0 0 0 1 1 0 ......... .......xx .........&#x | 0 0 0 0 0 0 0 2 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 | * * * * * * * * * * * * * * * * * * * * * * 12 * * | 0 0 0 0 0 0 1 0 0 1 0 ........o3........x ......... | 0 0 0 0 0 0 0 0 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * * * * * * * * * * * * * * 4 * | 0 0 0 0 0 0 0 0 0 1 1 ......... ........x3........o | 0 0 0 0 0 0 0 0 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * * * * * * * * * * * * * * * 4 | 0 0 0 0 0 0 1 0 0 0 1 ----------------------------------+------------------------+-------------------------------------------------------+------------------------------------------------------------------+------------------------ o........3x........3o........ ♦ 6 0 0 0 0 0 0 0 0 | 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * ......... xx.......3oo.......&#x ♦ 3 3 0 0 0 0 0 0 0 | 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 3 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 4 * * * * * * * * * oqowxx...3xxwoqo... .........&#xt ♦ 3 6 3 3 6 3 0 0 0 | 3 6 3 6 6 6 0 6 3 0 6 0 3 0 0 0 0 0 | 1 0 3 3 0 3 0 6 3 0 0 0 3 3 0 0 0 1 0 0 0 0 0 0 0 | * * 4 * * * * * * * * ......... .x.o.....3.o.x.....&#x ♦ 0 3 0 3 0 0 0 0 0 | 0 0 3 0 6 0 3 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 1 3 3 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 4 * * * * * * * ......... ......... .ooxx....&#xr ♦ 0 1 1 2 2 0 0 0 0 | 0 0 0 1 2 2 1 2 0 1 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 1 2 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * 12 * * * * * * ..o.x.o.. ......... ..o.x.o..&#xt ♦ 0 0 1 0 4 0 1 0 0 | 0 0 0 0 0 4 0 0 2 2 0 4 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 2 2 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 | * * * * * 6 * * * * * ......... ...oqowxx3...xxwoqo&#xt ♦ 0 0 0 3 6 3 3 6 3 | 0 0 0 0 0 0 3 6 0 3 6 6 0 6 6 3 6 3 | 0 0 0 0 0 0 0 0 0 0 1 3 3 0 0 3 6 0 0 3 3 0 3 0 1 | * * * * * * 4 * * * * ....xxoo. ......... .........&#xr ♦ 0 0 0 0 2 2 1 1 0 | 0 0 0 0 0 0 0 0 1 0 2 2 1 2 1 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 2 0 1 0 0 0 0 0 0 | * * * * * * * 12 * * * .....x.o.3.....o.x. .........&#x ♦ 0 0 0 0 0 3 0 3 0 | 0 0 0 0 0 0 0 0 0 0 0 0 3 6 0 3 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 3 0 1 0 0 0 | * * * * * * * * 4 * * .......oo3.......xx .........&#x ♦ 0 0 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 1 0 | * * * * * * * * * 4 * ........o3........x3........o ♦ 0 0 0 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 | * * * * * * * * * * 1
qo3xx3oq *b3oo&#zx → height = 0 (tegum sum of 2 mutually gyrated (q,x)-thexes) o.3o.3o. *b3o. | 48 * | 4 2 0 | 2 2 1 4 0 0 | 1 2 2 0 .o3.o3.o *b3.o | * 48 | 0 2 4 | 0 0 1 4 2 2 | 0 2 2 1 -------------------+-------+----------+-------------------+--------- .. x. .. .. | 2 0 | 96 * * | 1 1 0 1 0 0 | 1 1 1 0 oo3oo3oo *b3oo&#x | 1 1 | * 96 * | 0 0 1 2 0 0 | 0 2 1 0 .. .x .. .. | 0 2 | * * 96 | 0 0 0 1 1 1 | 0 1 1 1 -------------------+-------+----------+-------------------+--------- .. x.3o. .. | 3 0 | 3 0 0 | 32 * * * * * | 1 1 0 0 .. x. .. *b3o. | 3 0 | 3 0 0 | * 32 * * * * | 1 0 1 0 qo .. oq ..&#zx | 2 2 | 0 4 0 | * * 24 * * * | 0 2 0 0 .. xx .. ..&#x | 2 2 | 1 2 1 | * * * 96 * * | 0 1 1 0 .o3.x .. .. | 0 3 | 0 0 3 | * * * * 32 * | 0 1 0 1 .. .x .. *b3.o | 0 3 | 0 0 3 | * * * * * 32 | 0 0 1 1 -------------------+-------+----------+-------------------+--------- .. x.3o. *b3.o ♦ 6 0 | 12 0 0 | 4 4 0 0 0 0 | 8 * * * qo3xx3oq ..&#zx ♦ 12 12 | 12 24 12 | 4 0 6 12 4 0 | * 8 * * .. xx .. *b3oo&#x ♦ 3 3 | 3 3 3 | 0 1 0 3 0 1 | * * 32 * .o3.x .. *b3.o ♦ 0 6 | 0 0 12 | 0 0 0 0 4 4 | * * * 8
wx xo3ox4xx&#zx → height = 0 (tegum sum of (w,x,x)-sircope and ticcup) o. o.3o.4o. | 48 * | 2 2 2 0 0 0 | 1 2 1 2 1 2 0 0 0 | 1 1 1 2 0 .o .o3.o4.o | * 48 | 0 0 2 1 2 1 | 0 0 0 1 2 2 2 1 1 | 0 2 1 1 1 ----------------+-------+-------------------+----------------------------+------------ .. x. .. .. | 2 0 | 48 * * * * * | 1 1 0 1 0 0 0 0 0 | 1 0 1 1 0 .. .. .. x. | 2 0 | * 48 * * * * | 0 1 1 0 0 1 0 0 0 | 1 1 0 1 0 oo oo3oo4oo&#x | 1 1 | * * 96 * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0 .x .. .. .. | 0 2 | * * * 24 * * | 0 0 0 0 0 0 2 1 0 | 0 2 0 0 1 .. .. .x .. | 0 2 | * * * * 48 * | 0 0 0 0 1 0 1 0 1 | 0 1 1 0 1 .. .. .. .x | 0 2 | * * * * * 24 | 0 0 0 0 0 2 0 1 0 | 0 2 0 1 0 ----------------+-------+-------------------+----------------------------+------------ .. x.3o. .. | 3 0 | 3 0 0 0 0 0 | 16 * * * * * * * * | 1 0 1 0 0 .. x. .. x. | 4 0 | 2 2 0 0 0 0 | * 24 * * * * * * * | 1 0 0 1 0 .. .. o.4x. | 4 0 | 0 4 0 0 0 0 | * * 12 * * * * * * | 1 1 0 0 0 .. xo .. ..&#x | 2 1 | 1 0 2 0 0 0 | * * * 48 * * * * * | 0 0 1 1 0 .. .. ox ..&#x | 1 2 | 0 0 2 0 1 0 | * * * * 48 * * * * | 0 1 1 0 0 .. .. .. xx&#x | 2 2 | 0 1 2 0 0 1 | * * * * * 48 * * * | 0 1 0 1 0 .x .. .x .. | 0 4 | 0 0 0 2 2 0 | * * * * * * 24 * * | 0 1 0 0 1 .x .. .. .x | 0 4 | 0 0 0 2 0 2 | * * * * * * * 12 * | 0 2 0 0 0 .. .o3.x .. | 0 3 | 0 0 0 0 3 0 | * * * * * * * * 16 | 0 0 1 0 1 ----------------+-------+-------------------+----------------------------+------------ .. x.3o.4x. ♦ 24 0 | 24 24 0 0 0 0 | 8 12 6 0 0 0 0 0 0 | 2 * * * * wx .. ox4xx&#zx ♦ 8 16 | 0 8 16 8 8 8 | 0 0 2 0 8 8 4 4 0 | * 6 * * * .. xo3ox ..&#x ♦ 3 3 | 3 0 6 0 3 0 | 1 0 0 3 3 0 0 0 1 | * * 16 * * .. xo .. xx&#x ♦ 4 2 | 2 2 4 0 0 1 | 0 1 0 2 0 2 0 0 0 | * * * 24 * .x .o3.x .. ♦ 0 6 | 0 0 0 3 6 0 | 0 0 0 0 0 0 3 0 2 | * * * * 8
oxo4xxw oxo4wxx&#zxt → height = 0 (tegum sum of 2 (x,w)-tes and odip) o..4o.. o..4o.. & | 32 * | 2 4 0 0 | 1 2 2 4 0 0 | 1 2 2 .o.4.o. .o.4.o. | * 64 | 0 2 2 2 | 0 2 2 2 2 1 | 1 2 2 ----------------------+-------+--------------+------------------+-------- ... x.. ... ... & | 2 0 | 32 * * * | 1 0 0 2 0 0 | 0 2 1 oo.4oo. oo.4oo.&#x & | 1 1 | * 128 * * | 0 1 1 1 0 0 | 1 1 1 .x. ... ... ... & | 0 2 | * * 64 * | 0 1 1 0 1 0 | 1 1 1 ... .x. ... ... & | 0 2 | * * * 64 | 0 0 0 1 1 1 | 0 2 1 ----------------------+-------+--------------+------------------+-------- o..4x.. ... ... & | 4 0 | 4 0 0 0 | 8 * * * * * | 0 2 0 ox. ... ... ...&#x & | 1 2 | 0 2 1 0 | * 64 * * * * | 1 1 0 ... ... ox. ...&#x & | 1 2 | 0 2 1 0 | * * 64 * * * | 1 0 1 ... xx. ... ...&#x & | 2 2 | 1 2 0 1 | * * * 64 * * | 0 1 1 .x. ... ... .x. & | 0 4 | 0 0 2 2 | * * * * 32 * | 0 1 1 ... .x. ... .x. | 0 4 | 0 0 0 4 | * * * * * 16 | 0 2 0 ----------------------+-------+--------------+------------------+-------- oxo ... oxo ...&#xt ♦ 2 4 | 0 8 4 0 | 0 4 4 0 0 0 | 16 * * ox.4xx. ... wx.&#zx & ♦ 8 16 | 8 16 8 16 | 2 8 0 8 4 4 | * 8 * ... xx. ox. ...&#x & ♦ 2 4 | 1 4 2 2 | 0 0 2 2 1 0 | * * 32
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