Acronym | rit | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Name |
rectified tesseract, rectified octachoron, birectified hexadecachoron, runcic tesseract, equatorial cross-section of ico-first nit | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Cross sections |
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Circumradius | sqrt(3/2) = 1.224745 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. tet | 3/sqrt(8) = 1.060660 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. co | 1/sqrt(2) = 0.707107 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Vertex figure |
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Vertex layers |
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Lace city in approx. ASCII-art |
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x3o x3x o3x -- o3x4o (co) o3o u3o o3u o3o -- o3o4q (q-cube) x3o x3x o3x -- o3x4o (co) \ \ \ \ \ \ \ +-- x3o3o (tet) \ \ +----- x3x3o (tut) \ +-------- o3x3x (inv. tut) +----------- o3o3x (dual tet) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Coordinates |
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Volume | 23/6 = 3.833333 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Surface | 44 sqrt(2)/3 = 20.741799 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
General of army | (is itself convex) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Colonel of regiment |
(is itself locally convex
– uniform polychoral members:
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Dual | o4m3o3o | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Dihedral angles
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Face vector | 32, 96, 88, 24 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Confer |
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External links |
Note that rit can be thought of as the external blend of 1 hex + 16 further hexes + 24 squascs + 8 copies. This decomposition is described as the (also subdimensioanlly) degenerate segmentoteron xo3oo3ox4oo&#x.
Incidence matrix according to Dynkin symbol
o3o3x4o . . . . | 32 ♦ 6 | 6 3 | 2 3 --------+----+----+-------+----- . . x . | 2 | 96 | 1 2 | 1 2 --------+----+----+-------+----- . o3x . | 3 | 3 | 64 * | 1 1 . . x4o | 4 | 4 | * 24 | 0 2 --------+----+----+-------+----- o3o3x . ♦ 4 | 6 | 4 0 | 16 * . o3x4o ♦ 12 | 24 | 8 6 | * 8 snubbed forms: o3o3β4o
o3o3x4/3o . . . . | 32 ♦ 6 | 6 3 | 2 3 ----------+----+----+-------+----- . . x . | 2 | 96 | 1 2 | 1 2 ----------+----+----+-------+----- . o3x . | 3 | 3 | 64 * | 1 1 . . x4/3o | 4 | 4 | * 24 | 0 2 ----------+----+----+-------+----- o3o3x . ♦ 4 | 6 | 4 0 | 16 * . o3x4/3o ♦ 12 | 24 | 8 6 | * 8
o3o3/2x4o . . . . | 32 ♦ 6 | 6 3 | 2 3 ----------+----+----+-------+----- . . x . | 2 | 96 | 1 2 | 1 2 ----------+----+----+-------+----- . o3/2x . | 3 | 3 | 64 * | 1 1 . . x4o | 4 | 4 | * 24 | 0 2 ----------+----+----+-------+----- o3o3/2x . ♦ 4 | 6 | 4 0 | 16 * . o3/2x4o ♦ 12 | 24 | 8 6 | * 8
o3o3/2x4/3o . . . . | 32 ♦ 6 | 6 3 | 2 3 ------------+----+----+-------+----- . . x . | 2 | 96 | 1 2 | 1 2 ------------+----+----+-------+----- . o3/2x . | 3 | 3 | 64 * | 1 1 . . x4/3o | 4 | 4 | * 24 | 0 2 ------------+----+----+-------+----- o3o3/2x . ♦ 4 | 6 | 4 0 | 16 * . o3/2x4/3o ♦ 12 | 24 | 8 6 | * 8
o3/2o3x4o . . . . | 32 ♦ 6 | 6 3 | 2 3 ----------+----+----+-------+----- . . x . | 2 | 96 | 1 2 | 1 2 ----------+----+----+-------+----- . o3x . | 3 | 3 | 64 * | 1 1 . . x4o | 4 | 4 | * 24 | 0 2 ----------+----+----+-------+----- o3/2o3x . ♦ 4 | 6 | 4 0 | 16 * . o3x4o ♦ 12 | 24 | 8 6 | * 8
o3/2o3x4/3o . . . . | 32 ♦ 6 | 6 3 | 2 3 ------------+----+----+-------+----- . . x . | 2 | 96 | 1 2 | 1 2 ------------+----+----+-------+----- . o3x . | 3 | 3 | 64 * | 1 1 . . x4/3o | 4 | 4 | * 24 | 0 2 ------------+----+----+-------+----- o3/2o3x . ♦ 4 | 6 | 4 0 | 16 * . o3x4/3o ♦ 12 | 24 | 8 6 | * 8
o3/2o3/2x4o . . . . | 32 ♦ 6 | 6 3 | 2 3 ------------+----+----+-------+----- . . x . | 2 | 96 | 1 2 | 1 2 ------------+----+----+-------+----- . o3/2x . | 3 | 3 | 64 * | 1 1 . . x4o | 4 | 4 | * 24 | 0 2 ------------+----+----+-------+----- o3/2o3/2x . ♦ 4 | 6 | 4 0 | 16 * . o3/2x4o ♦ 12 | 24 | 8 6 | * 8
o3/2o3/2x4/3o . . . . | 32 ♦ 6 | 6 3 | 2 3 --------------+----+----+-------+----- . . x . | 2 | 96 | 1 2 | 1 2 --------------+----+----+-------+----- . o3/2x . | 3 | 3 | 64 * | 1 1 . . x4/3o | 4 | 4 | * 24 | 0 2 --------------+----+----+-------+----- o3/2o3/2x . ♦ 4 | 6 | 4 0 | 16 * . o3/2x4/3o ♦ 12 | 24 | 8 6 | * 8
x3o3x *b3o . . . . | 32 ♦ 3 3 | 3 3 3 | 3 1 1 -----------+----+-------+----------+------ x . . . | 2 | 48 * | 2 1 0 | 2 1 0 . . x . | 2 | * 48 | 0 1 2 | 2 0 1 -----------+----+-------+----------+------ x3o . . | 3 | 3 0 | 32 * * | 1 1 0 x . x . | 4 | 2 2 | * 24 * | 2 0 0 . o3x . | 3 | 0 3 | * * 32 | 1 0 1 -----------+----+-------+----------+------ x3o3x . ♦ 12 | 12 12 | 4 6 4 | 8 * * x3o . *b3o ♦ 4 | 6 0 | 4 0 0 | * 8 * . o3x *b3o ♦ 4 | 0 6 | 0 0 4 | * * 8 snubbed forms: β3o3x *b3o, β3o3β *b3o
x3o3x *b3/2o . . . . | 32 ♦ 3 3 | 3 3 3 | 3 1 1 -------------+----+-------+----------+------ x . . . | 2 | 48 * | 2 1 0 | 2 1 0 . . x . | 2 | * 48 | 0 1 2 | 2 0 1 -------------+----+-------+----------+------ x3o . . | 3 | 3 0 | 32 * * | 1 1 0 x . x . | 4 | 2 2 | * 24 * | 2 0 0 . o3x . | 3 | 0 3 | * * 32 | 1 0 1 -------------+----+-------+----------+------ x3o3x . ♦ 12 | 12 12 | 4 6 4 | 8 * * x3o . *b3/2o ♦ 4 | 6 0 | 4 0 0 | * 8 * . o3x *b3/2o ♦ 4 | 0 6 | 0 0 4 | * * 8
x3/2o3/2x *b3o . . . . | 32 ♦ 3 3 | 3 3 3 | 3 1 1 ---------------+----+-------+----------+------ x . . . | 2 | 48 * | 2 1 0 | 2 1 0 . . x . | 2 | * 48 | 0 1 2 | 2 0 1 ---------------+----+-------+----------+------ x3/2o . . | 3 | 3 0 | 32 * * | 1 1 0 x . x . | 4 | 2 2 | * 24 * | 2 0 0 . o3/2x . | 3 | 0 3 | * * 32 | 1 0 1 ---------------+----+-------+----------+------ x3/2o3/2x . ♦ 12 | 12 12 | 4 6 4 | 8 * * x3/2o . *b3o ♦ 4 | 6 0 | 4 0 0 | * 8 * . o3/2x *b3o ♦ 4 | 0 6 | 0 0 4 | * * 8
x3/2o3/2x *b3/2o . . . . | 32 ♦ 3 3 | 3 3 3 | 3 1 1 -----------------+----+-------+----------+------ x . . . | 2 | 48 * | 2 1 0 | 2 1 0 . . x . | 2 | * 48 | 0 1 2 | 2 0 1 -----------------+----+-------+----------+------ x3/2o . . | 3 | 3 0 | 32 * * | 1 1 0 x . x . | 4 | 2 2 | * 24 * | 2 0 0 . o3/2x . | 3 | 0 3 | * * 32 | 1 0 1 -----------------+----+-------+----------+------ x3/2o3/2x . ♦ 12 | 12 12 | 4 6 4 | 8 * * x3/2o . *b3/2o ♦ 4 | 6 0 | 4 0 0 | * 8 * . o3/2x *b3/2o ♦ 4 | 0 6 | 0 0 4 | * * 8
s4x3o3o demi( . . . . ) | 32 ♦ 3 3 | 3 3 3 | 1 3 1 ----------------+----+-------+----------+------ demi( . x . . ) | 2 | 48 * | 2 1 0 | 1 2 0 sefa( s4x . . ) | 2 | * 48 | 0 1 2 | 0 2 1 ----------------+----+-------+----------+------ demi( . x3o . ) | 3 | 3 0 | 32 * * | 1 1 0 s4x . . ♦ 4 | 2 2 | * 24 * | 0 2 0 sefa( s4x3o . ) | 3 | 0 3 | * * 32 | 0 1 1 ----------------+----+-------+----------+------ demi( . x3o3o ) ♦ 4 | 6 0 | 4 0 0 | 8 * * s4x3o . ♦ 12 | 12 12 | 4 6 4 | * 8 * sefa( s4x3o3o ) ♦ 4 | 0 6 | 0 0 4 | * * 8 starting figure: x4x3o3o
s4o3o3x demi( . . . . ) | 32 ♦ 3 3 | 3 3 3 | 1 1 3 ----------------+----+-------+----------+------ demi( . . . x ) | 2 | 48 * | 2 1 0 | 1 0 2 s4o . . ♦ 2 | * 48 | 0 1 2 | 0 1 2 ----------------+----+-------+----------+------ demi( . . o3x ) | 3 | 3 0 | 32 * * | 1 0 1 s4o 2 x | 4 | 2 2 | * 24 * | 0 0 2 sefa( s4o3o . ) | 3 | 0 3 | * * 32 | 0 1 1 ----------------+----+-------+----------+------ demi( . o3o3x ) ♦ 4 | 6 0 | 4 0 0 | 8 * * s4o3o . ♦ 4 | 0 6 | 0 0 4 | * 8 * sefa( s4o3o3x ) ♦ 12 | 12 12 | 4 6 4 | * * 8 starting figure: x4o3o3x
xxoo3oxxo3ooxx&#xt → all heights = 1/sqrt(2) = 0.707107 (tet || pseudo tut || pseudo inv tut || inv tet) o...3o...3o... | 4 * * * ♦ 3 3 0 0 0 0 0 0 0 | 3 3 3 0 0 0 0 0 0 0 0 | 1 3 1 0 0 0 0 .o..3.o..3.o.. | * 12 * * ♦ 0 1 1 2 2 0 0 0 0 | 0 1 2 1 2 2 1 0 0 0 0 | 0 2 1 1 1 0 0 ..o.3..o.3..o. | * * 12 * ♦ 0 0 0 0 2 2 1 1 0 | 0 0 0 0 1 2 2 1 2 1 0 | 0 1 0 1 2 1 0 ...o3...o3...o | * * * 4 ♦ 0 0 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 3 3 3 | 0 0 0 0 3 1 1 -------------------+-----------+------------------------+----------------------------+-------------- x... .... .... | 2 0 0 0 | 6 * * * * * * * * | 2 1 0 0 0 0 0 0 0 0 0 | 1 2 0 0 0 0 0 oo..3oo..3oo..&#x | 1 1 0 0 | * 12 * * * * * * * | 0 1 2 0 0 0 0 0 0 0 0 | 0 2 1 0 0 0 0 .x.. .... .... | 0 2 0 0 | * * 6 * * * * * * | 0 1 0 0 2 0 0 0 0 0 0 | 0 2 0 1 0 0 0 .... .x.. .... | 0 2 0 0 | * * * 12 * * * * * | 0 0 1 1 0 1 0 0 0 0 0 | 0 1 1 0 1 0 0 .oo.3.oo.3.oo.&#x | 0 1 1 0 | * * * * 24 * * * * | 0 0 0 0 1 1 1 0 0 0 0 | 0 1 0 1 1 0 0 .... ..x. .... | 0 0 2 0 | * * * * * 12 * * * | 0 0 0 0 0 1 0 1 1 0 0 | 0 1 0 0 1 1 0 .... .... ..x. | 0 0 2 0 | * * * * * * 6 * * | 0 0 0 0 0 0 2 0 0 1 0 | 0 0 0 1 2 0 0 ..oo3..oo3..oo&#x | 0 0 1 1 | * * * * * * * 12 * | 0 0 0 0 0 0 0 0 2 1 0 | 0 0 0 0 2 1 0 .... .... ...x | 0 0 0 2 | * * * * * * * * 6 | 0 0 0 0 0 0 0 0 0 1 2 | 0 0 0 0 2 0 1 -------------------+-----------+------------------------+----------------------------+-------------- x...3o... .... | 3 0 0 0 | 3 0 0 0 0 0 0 0 0 | 4 * * * * * * * * * * | 1 1 0 0 0 0 0 xx.. .... ....&#x | 2 2 0 0 | 1 2 1 0 0 0 0 0 0 | * 6 * * * * * * * * * | 0 2 0 0 0 0 0 .... ox.. ....&#x | 1 2 0 0 | 0 2 0 1 0 0 0 0 0 | * * 12 * * * * * * * * | 0 1 1 0 0 0 0 .... .x..3.o.. | 0 3 0 0 | 0 0 0 3 0 0 0 0 0 | * * * 4 * * * * * * * | 0 0 1 0 1 0 0 .xo. .... ....&#x | 0 2 1 0 | 0 0 1 0 2 0 0 0 0 | * * * * 12 * * * * * * | 0 1 0 1 0 0 0 .... .xx. ....&#x | 0 2 2 0 | 0 0 0 1 2 1 0 0 0 | * * * * * 12 * * * * * | 0 1 0 0 1 0 0 .... .... .ox.&#x | 0 1 2 0 | 0 0 0 0 2 0 1 0 0 | * * * * * * 12 * * * * | 0 0 0 1 1 0 0 ..o.3..x. .... | 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 0 2 0 | * * * * * * * * 12 * * | 0 0 0 0 1 1 0 .... .... ..xx&#x | 0 0 2 2 | 0 0 0 0 0 0 1 2 1 | * * * * * * * * * 6 * | 0 0 0 0 2 0 0 .... ...o3...x | 0 0 0 3 | 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * 4 | 0 0 0 0 1 0 1 -------------------+-----------+------------------------+----------------------------+-------------- x...3o...3o... ♦ 4 0 0 0 | 6 0 0 0 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * xxo.3oxx. ....&#xt ♦ 3 6 3 0 | 3 6 3 3 6 3 0 0 0 | 1 3 3 0 3 3 0 1 0 0 0 | * 4 * * * * * .... ox..3oo..&#x ♦ 1 3 0 0 | 0 3 0 3 0 0 0 0 0 | 0 0 3 1 0 0 0 0 0 0 0 | * * 4 * * * * .xo. .... .ox.&#x ♦ 0 2 2 0 | 0 0 1 0 4 0 1 0 0 | 0 0 0 0 2 0 2 0 0 0 0 | * * * 6 * * * .... .xxo3.oxx&#xt ♦ 0 3 6 3 | 0 0 0 3 6 3 3 6 3 | 0 0 0 1 0 3 3 0 3 3 1 | * * * * 4 * * ..oo3..xo ....&#x ♦ 0 0 3 1 | 0 0 0 0 0 3 0 3 0 | 0 0 0 0 0 0 0 1 3 0 0 | * * * * * 4 * ...o3...o3...x ♦ 0 0 0 4 | 0 0 0 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 0 0 4 | * * * * * * 1
or o...3o...3o... & | 8 * ♦ 3 3 0 0 0 | 3 3 3 0 0 0 | 1 3 1 0 .o..3.o..3.o.. & | * 24 ♦ 0 1 1 2 2 | 0 1 2 1 3 2 | 0 3 1 1 ---------------------+------+----------------+-----------------+-------- x... .... .... & | 2 0 | 12 * * * * | 2 1 0 0 0 0 | 1 2 0 0 oo..3oo..3oo..&#x & | 1 1 | * 24 * * * | 0 1 2 0 0 0 | 0 2 1 0 .x.. .... .... & | 0 2 | * * 12 * * | 0 1 0 0 2 0 | 0 2 0 1 .... .x.. .... & | 0 2 | * * * 24 * | 0 0 1 1 0 1 | 0 2 1 0 .oo.3.oo.3.oo.&#x | 0 2 | * * * * 24 | 0 0 0 0 2 1 | 0 2 0 1 ---------------------+------+----------------+-----------------+-------- x...3o... .... & | 3 0 | 3 0 0 0 0 | 8 * * * * * | 1 1 0 0 xx.. .... ....&#x & | 2 2 | 1 2 1 0 0 | * 12 * * * * | 0 2 0 0 .... ox.. ....&#x & | 1 2 | 0 2 0 1 0 | * * 24 * * * | 0 1 1 0 .... .x..3.o.. & | 0 3 | 0 0 0 3 0 | * * * 8 * * | 0 1 1 0 .xo. .... ....&#x & | 0 3 | 0 0 1 0 2 | * * * * 24 * | 0 1 0 1 .... .xx. ....&#x | 0 4 | 0 0 0 2 2 | * * * * * 12 | 0 2 0 0 ---------------------+------+----------------+-----------------+-------- x...3o...3o... & ♦ 4 0 | 6 0 0 0 0 | 4 0 0 0 0 0 | 2 * * * xxo.3oxx. ....&#xt & ♦ 3 9 | 3 6 3 6 6 | 1 3 3 1 3 3 | * 8 * * .... ox..3oo..&#x & ♦ 1 3 | 0 3 0 3 0 | 0 0 3 1 0 0 | * * 8 * .xo. .... .ox.&#x ♦ 0 4 | 0 0 2 0 4 | 0 0 0 0 4 0 | * * * 6
ooo3xox4oqo&#xt → both heights = 1/sqrt(2) = 0.707107 (co || pseudo q-cube || co) o..3o..4o.. | 12 * * ♦ 4 2 0 0 | 2 2 4 1 0 0 0 | 1 2 2 0 0 .o.3.o.4.o. | * 8 * ♦ 0 3 3 0 | 0 0 3 3 3 0 0 | 0 1 3 1 0 ..o3..o4..o | * * 12 ♦ 0 0 2 4 | 0 0 0 1 4 2 2 | 0 0 2 2 1 ----------------+---------+-------------+------------------+---------- ... x.. ... | 2 0 0 | 24 * * * | 1 1 1 0 0 0 0 | 1 1 1 0 0 oo.3oo.4oo.&#x | 1 1 0 | * 24 * * | 0 0 2 1 0 0 0 | 0 1 2 0 0 .oo3.oo4.oo&#x | 0 1 1 | * * 24 * | 0 0 0 1 2 0 0 | 0 0 2 1 0 ... ..x ... | 0 0 2 | * * * 24 | 0 0 0 0 1 1 1 | 0 0 1 1 1 ----------------+---------+-------------+------------------+---------- o..3x.. ... | 3 0 0 | 3 0 0 0 | 8 * * * * * * | 1 1 0 0 0 ... x..4o.. | 4 0 0 | 4 0 0 0 | * 6 * * * * * | 1 0 1 0 0 ... xo. ...&#x | 2 1 0 | 1 2 0 0 | * * 24 * * * * | 0 1 1 0 0 ... ... oqo&#xt | 1 2 1 | 0 2 2 0 | * * * 12 * * * | 0 0 2 0 0 ... .ox ...&#x | 0 1 2 | 0 0 2 1 | * * * * 24 * * | 0 0 1 1 0 ..o3..x ... | 0 0 3 | 0 0 0 3 | * * * * * 8 * | 0 0 0 1 1 ... ..x4..o | 0 0 4 | 0 0 0 4 | * * * * * * 6 | 0 0 1 0 1 ----------------+---------+-------------+------------------+---------- o..3x..4o.. ♦ 12 0 0 | 24 0 0 0 | 8 6 0 0 0 0 0 | 1 * * * * oo.3xo. ...&#x ♦ 3 1 0 | 3 3 0 0 | 1 0 3 0 0 0 0 | * 8 * * * ... xox4oqo&#xt ♦ 4 4 4 | 4 8 8 4 | 0 1 4 4 4 0 1 | * * 6 * * .oo3.ox ...&#x ♦ 0 1 3 | 0 0 3 3 | 0 0 0 0 3 1 0 | * * * 8 * ..o3..x4..o ♦ 0 0 12 | 0 0 0 24 | 0 0 0 0 0 8 6 | * * * * 1
or o..3o..4o.. & | 24 * ♦ 4 2 | 2 2 4 1 | 1 2 2 .o.3.o.4.o. | * 8 ♦ 0 6 | 0 0 6 3 | 0 2 3 -------------------+------+-------+-------------+------- ... x.. ... & | 2 0 | 48 * | 1 1 1 0 | 1 1 1 oo.3oo.4oo.&#x & | 1 1 | * 48 | 0 0 2 1 | 0 1 2 -------------------+------+-------+-------------+------- o..3x.. ... & | 3 0 | 3 0 | 16 * * * | 1 1 0 ... x..4o.. & | 4 0 | 4 0 | * 12 * * | 1 0 1 ... xo. ...&#x & | 2 1 | 1 2 | * * 48 * | 0 1 1 ... ... oqo&#xt | 2 2 | 0 4 | * * * 12 | 0 0 2 -------------------+------+-------+-------------+------- o..3x..4o.. & ♦ 12 0 | 24 0 | 8 6 0 0 | 2 * * oo.3xo. ...&#x & ♦ 3 1 | 3 3 | 1 0 3 0 | * 16 * ... xox4oqo&#xt ♦ 8 4 | 8 16 | 0 2 8 4 | * * 6
oxuxo xoxox4oqoqo&#xt → all heights = 1/2 ({4} || gyro (q,q,x)-cube || (x,x,u)-cube || gyro (q,q,x)-cube || {4}) o.... o....4o.... & | 8 * * ♦ 2 4 0 0 0 0 | 1 2 4 2 0 0 0 0 | 2 2 1 0 .o... .o...4.o... & | * 16 * ♦ 0 2 1 2 1 0 | 0 2 1 2 1 2 1 0 | 1 1 2 1 ..o.. ..o..4..o.. | * * 8 ♦ 0 0 0 4 0 2 | 0 0 0 2 4 2 0 1 | 0 2 1 2 ------------------------+--------+---------------+----------------------+-------- ..... x.... ..... & | 2 0 0 | 8 * * * * * | 1 0 2 0 0 0 0 0 | 1 2 0 0 oo... oo...4oo...&#x & | 1 1 0 | * 32 * * * * | 0 1 1 1 0 0 0 0 | 1 1 1 0 .x... ..... ..... & | 0 2 0 | * * 8 * * * | 0 2 0 0 0 0 1 0 | 1 0 2 0 .oo.. .oo..4.oo..&#x & | 0 1 1 | * * * 32 * * | 0 0 0 1 1 1 0 0 | 0 1 1 1 .o.o. .o.o.4.o.o.&#x | 0 2 0 | * * * * 8 * | 0 0 0 0 0 2 1 0 | 0 0 2 1 ..... ..x.. ..... | 0 0 2 | * * * * * 8 | 0 0 0 0 2 0 0 1 | 0 2 0 1 ------------------------+--------+---------------+----------------------+-------- ..... x....4o.... & | 4 0 0 | 4 0 0 0 0 0 | 2 * * * * * * * | 0 2 0 0 ox... ..... .....&#x & | 1 2 0 | 0 2 1 0 0 0 | * 16 * * * * * * | 1 0 1 0 ..... xo... .....&#x & | 2 1 0 | 1 2 0 0 0 0 | * * 16 * * * * * | 1 1 0 0 ..... ..... oqo..&#xt & | 1 2 1 | 0 2 0 2 0 0 | * * * 16 * * * * | 0 1 1 0 ..... .ox.. .....&#x & | 0 1 2 | 0 0 0 2 0 1 | * * * * 16 * * * | 0 1 0 1 .ooo. .ooo.4.ooo.&#x | 0 2 1 | 0 0 0 2 1 0 | * * * * * 16 * * | 0 0 1 1 .x.x. ..... .....&#x | 0 4 0 | 0 0 2 0 2 0 | * * * * * * 4 * | 0 0 2 0 ..... ..x..4..o.. | 0 0 4 | 0 0 0 0 0 4 | * * * * * * * 2 | 0 2 0 0 ------------------------+--------+---------------+----------------------+-------- ox... xo... .....&#x & ♦ 2 2 0 | 1 4 1 0 0 0 | 0 2 2 0 0 0 0 0 | 8 * * * ..... xox..4oqo..&#xt & ♦ 4 4 4 | 4 8 0 8 0 4 | 1 0 4 4 4 0 0 1 | * 4 * * oxuxo ..... oqoqo&#xt ♦ 2 8 2 | 0 8 4 8 4 0 | 0 4 0 4 0 4 2 0 | * * 4 * ..... .oxo. .....&#x ♦ 0 2 2 | 0 0 0 4 1 1 | 0 0 0 0 2 2 0 0 | * * * 8
qo oo3xo4oq&#zx → height = 0 (tegum sum of (q,x,x)-cope and equatorial q-cube) o. o.3o.4o. | 24 * ♦ 4 2 | 2 2 4 1 | 1 2 2 .o .o3.o4.o | * 8 ♦ 0 6 | 0 0 6 3 | 0 3 2 ----------------+------+-------+-------------+------- .. .. x. .. | 2 0 | 48 * | 1 1 1 0 | 1 1 1 oo oo3oo4oo&#x | 1 1 | * 48 | 0 0 2 1 | 0 2 1 ----------------+------+-------+-------------+------- .. o.3x. .. | 3 0 | 3 0 | 16 * * * | 1 0 1 .. .. x.4o. | 4 0 | 4 0 | * 12 * * | 1 1 0 .. .. xo ..&#x | 2 1 | 1 2 | * * 48 * | 0 1 1 qo .. .. oq&#zx | 2 2 | 0 4 | * * * 12 | 0 2 0 ----------------+------+-------+-------------+------- .. o.3x.4o. ♦ 12 0 | 24 0 | 8 6 0 0 | 2 * * qo .. xo4oq&#zx ♦ 8 4 | 8 16 | 0 2 8 4 | * 6 * .. oo3xo ..&#x ♦ 3 1 | 3 3 | 1 0 3 0 | * * 16
ox4qo xo4oq&#zx → height = 0 (tegum sum of 2 interchanged (q,q,x,x)-tes) o.4o. o.4o. & | 32 ♦ 2 4 | 1 6 2 | 2 3 ------------------+----+-------+---------+----- .. .. x. .. & | 2 | 32 * | 1 2 0 | 1 2 oo4oo oo4oo&#x | 2 | * 64 | 0 2 1 | 1 2 ------------------+----+-------+---------+----- .. .. x.4o. & | 4 | 4 0 | 8 * * | 0 2 ox .. .. ..&#x & | 3 | 1 2 | * 64 * | 1 1 .. qo .. oq&#zx | 4 | 0 4 | * * 16 | 0 2 ------------------+----+-------+---------+----- ox .. xo ..&#x ♦ 4 | 2 4 | 0 4 0 | 16 * ox4qo .. oq&#zx & ♦ 12 | 8 16 | 2 8 4 | * 8
uxo oxu xox4oqo&#zx → height = 0 (tegum sum of 2 lacing-ortho (u,x,x)-cubes with an (x,x,q,q)-tes) o.. o.. o..4o.. & | 16 * ♦ 2 4 0 | 1 2 4 2 0 | 2 1 2 .o. .o. .o.4.o. | * 16 ♦ 0 4 2 | 0 4 2 2 1 | 2 2 1 ----------------------+-------+----------+--------------+------- ... ... x.. ... & | 2 0 | 16 * * | 1 0 2 0 0 | 1 0 2 oo. oo. oo.4oo.&#x & | 1 1 | * 64 * | 0 1 1 1 0 | 1 1 1 .x. ... ... ... & | 0 2 | * * 16 | 0 2 0 0 1 | 1 2 0 ----------------------+-------+----------+--------------+------- ... ... x..4o.. & | 4 0 | 4 0 0 | 4 * * * * | 0 0 2 ... ox. ... ...&#x & | 1 2 | 0 2 1 | * 32 * * * | 1 1 0 ... ... xo. ...&#x & | 2 1 | 1 2 0 | * * 32 * * | 1 0 1 ... ... ... oqo&#xt | 2 2 | 0 4 0 | * * * 16 * | 0 1 1 .x. .x. ... ... | 0 4 | 0 0 4 | * * * * 4 | 0 2 0 ----------------------+-------+----------+--------------+------- ... ox. xo. ...&#x & ♦ 2 2 | 1 4 1 | 0 2 2 0 0 | 16 * * uxo oxu ... oqo&#zx ♦ 4 8 | 0 16 8 | 0 8 0 4 2 | * 4 * ... ... xox4oqo&#xt ♦ 8 4 | 8 16 0 | 2 0 8 4 0 | * * 4
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