Acronym | hatet (old: hittet, alt. hipdaw) |
Name |
hexagon-tetrahedron duoprism, hexagon duofastegium, hip disphenoid |
Circumradius | sqrt(11/8) = 1.172604 |
Lace city in approx. ASCII-art |
x x3x o x3x o x3x |
Lace hyper city in approx. ASCII-art |
x3x x3x x3x x3x(disphenoid in configuration space) |
Volume | sqrt(6)/8 = 0.306186 |
Face vector | 24, 60, 64, 36, 10 |
Confer |
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External links |
Incidence matrix according to Dynkin symbol
x6o x3o3o . . . . . | 24 | 2 3 | 1 6 3 | 3 6 1 | 3 2 ----------+----+-------+---------+--------+---- x . . . . | 2 | 24 * | 1 3 0 | 3 3 0 | 3 1 . . x . . | 2 | * 36 | 0 2 2 | 1 4 1 | 2 2 ----------+----+-------+---------+--------+---- x6o . . . | 6 | 6 0 | 4 * * | 3 0 0 | 3 0 x . x . . | 4 | 2 2 | * 36 * | 1 2 0 | 2 1 . . x3o . | 3 | 0 3 | * * 24 | 0 2 1 | 1 2 ----------+----+-------+---------+--------+---- x6o x . . ♦ 12 | 12 6 | 2 6 0 | 6 * * | 2 0 x . x3o . ♦ 6 | 3 6 | 0 3 2 | * 24 * | 1 1 . . x3o3o ♦ 4 | 0 6 | 0 0 4 | * * 6 | 0 2 ----------+----+-------+---------+--------+---- x6o x3o . ♦ 18 | 18 18 | 3 18 6 | 3 6 0 | 4 * x . x3o3o ♦ 8 | 4 12 | 0 6 8 | 0 4 2 | * 6
x3x x3o3o . . . . . | 24 | 1 1 3 | 1 3 3 3 | 3 3 3 1 | 3 1 1 ----------+----+----------+------------+-----------+------ x . . . . | 2 | 12 * * | 1 3 0 0 | 3 3 0 0 | 3 1 0 . x . . . | 2 | * 12 * | 1 0 3 0 | 3 0 3 0 | 3 0 1 . . x . . | 2 | * * 36 | 0 1 1 2 | 1 2 2 1 | 2 1 1 ----------+----+----------+------------+-----------+------ x3x . . . | 6 | 3 3 0 | 4 * * * | 3 0 0 0 | 3 0 0 x . x . . | 4 | 2 0 2 | * 18 * * | 1 2 0 0 | 2 1 0 . x x . . | 4 | 0 2 2 | * * 18 * | 1 0 2 0 | 2 0 1 . . x3o . | 3 | 0 0 3 | * * * 24 | 0 1 1 1 | 1 1 1 ----------+----+----------+------------+-----------+------ x3x x . . ♦ 12 | 6 6 6 | 2 3 3 0 | 6 * * * | 2 0 0 x . x3o . ♦ 6 | 3 0 6 | 0 3 0 2 | * 12 * * | 1 1 0 . x x3o . ♦ 6 | 0 3 6 | 0 0 3 2 | * * 12 * | 1 0 1 . . x3o3o ♦ 4 | 0 0 6 | 0 0 0 4 | * * * 6 | 0 1 1 ----------+----+----------+------------+-----------+------ x3x x3o . ♦ 18 | 9 9 18 | 3 9 9 6 | 3 3 3 0 | 4 * * x . x3o3o ♦ 8 | 4 0 12 | 0 6 0 8 | 0 4 0 2 | * 3 * . x x3o3o ♦ 8 | 0 4 12 | 0 0 6 8 | 0 0 4 2 | * * 3
ox3oo xx6oo&#x → height = sqrt(2/3) = 0.816497
({6} || thiddip)
o.3o. o.6o. | 6 * | 2 3 0 0 | 1 3 6 0 0 0 | 1 6 3 0 0 | 2 3 0
.o3.o .o6.o | * 18 | 0 1 2 2 | 0 2 2 1 4 1 | 1 4 1 2 2 | 2 2 1
---------------+------+------------+----------------+------------+------
.. .. x. .. | 2 0 | 6 * * * | 1 0 3 0 0 0 | 0 3 3 0 0 | 1 3 0
oo3oo oo6oo&#x | 1 1 | * 18 * * | 0 2 2 0 0 0 | 1 4 1 0 0 | 2 2 0
.x .. .. .. | 0 2 | * * 18 * | 0 1 0 1 2 0 | 1 2 0 2 1 | 2 1 1
.. .. .x .. | 0 2 | * * * 18 | 0 0 1 0 2 1 | 0 2 1 1 2 | 1 2 1
---------------+------+------------+----------------+------------+------
.. .. x.6o. | 6 0 | 6 0 0 0 | 1 * * * * * | 0 0 3 0 0 | 0 3 0
ox .. .. ..&#x | 1 2 | 0 2 1 0 | * 18 * * * * | 1 2 0 0 0 | 2 1 0
.. .. xx ..&#x | 2 2 | 1 2 0 1 | * * 18 * * * | 0 2 1 0 0 | 1 2 0
.x3.o .. .. | 0 3 | 0 0 3 0 | * * * 6 * * | 1 0 0 2 0 | 2 0 1
.x .. .x .. | 0 4 | 0 0 2 2 | * * * * 18 * | 0 1 0 1 1 | 1 1 1
.. .. .x6.o | 0 6 | 0 0 0 6 | * * * * * 3 | 0 0 1 0 2 | 0 2 1
---------------+------+------------+----------------+------------+------
ox3oo .. ..&#x ♦ 1 3 | 0 3 3 0 | 0 3 0 1 0 0 | 6 * * * * | 2 0 0
ox .. xx ..&#x ♦ 2 4 | 1 4 2 2 | 0 2 2 0 1 0 | * 18 * * * | 1 1 0
.. .. xx6oo&#x ♦ 6 6 | 6 6 0 6 | 1 0 6 0 0 1 | * * 3 * * | 0 2 0
.x3.o .x .. ♦ 0 6 | 0 0 6 3 | 0 0 0 2 3 0 | * * * 6 * | 1 0 1
.x .. .x6.o ♦ 0 12 | 0 0 6 12 | 0 0 0 0 6 2 | * * * * 3 | 0 1 1
---------------+------+------------+----------------+------------+------
ox3oo xx .. ♦ 2 6 | 1 6 6 3 | 0 6 3 2 3 0 | 2 3 0 1 0 | 6 * *
ox .. xx6oo&#x ♦ 6 12 | 6 12 6 12 | 1 6 12 0 6 2 | 0 6 2 0 1 | * 3 *
.x3.o .x6.o ♦ 0 18 | 0 0 18 18 | 0 0 0 6 18 3 | 0 0 0 6 3 | * * 1
ox3oo xx3xx&#x → height = sqrt(2/3) = 0.816497
({6} || thiddip)
o.3o. o.3o. | 6 * | 1 1 3 0 0 0 | 1 3 3 3 0 0 0 0 | 1 3 3 3 0 0 0 | 1 1 3 0
.o3.o .o3.o | * 18 | 0 0 1 2 1 1 | 0 2 1 1 1 2 2 1 | 1 2 2 1 1 1 2 | 1 1 2 1
---------------+------+---------------+------------------+---------------+--------
.. .. x. .. | 2 0 | 3 * * * * * | 1 0 3 0 0 0 0 0 | 0 3 0 3 0 0 0 | 1 0 3 0
.. .. .. x. | 2 0 | * 3 * * * * | 1 0 0 3 0 0 0 0 | 0 0 3 3 0 0 0 | 0 1 3 0
oo3oo oo3oo&#x | 1 1 | * * 18 * * * | 0 2 1 1 0 0 0 0 | 1 2 2 1 0 0 0 | 1 1 2 0
.x .. .. .. | 0 2 | * * * 18 * * | 0 1 0 0 1 1 1 0 | 1 1 1 0 1 1 1 | 1 1 1 1
.. .. .x .. | 0 2 | * * * * 9 * | 0 0 1 0 0 2 0 1 | 0 2 0 1 1 0 2 | 1 0 2 1
.. .. .. .x | 0 2 | * * * * * 9 | 0 0 0 1 0 0 2 1 | 0 0 2 1 0 1 2 | 0 1 2 1
---------------+------+---------------+------------------+---------------+--------
.. .. x.3x. | 6 0 | 3 3 0 0 0 0 | 1 * * * * * * * | 0 0 0 3 0 0 0 | 0 0 3 0
ox .. .. ..&#x | 1 2 | 0 0 2 1 0 0 | * 18 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0
.. .. xx ..&#x | 2 2 | 1 0 2 0 1 0 | * * 9 * * * * * | 0 2 0 1 0 0 0 | 1 0 2 0
.. .. .. xx&#x | 2 2 | 0 1 2 0 0 1 | * * * 9 * * * * | 0 0 2 1 0 0 0 | 0 1 2 0
.x3.o .. .. | 0 3 | 0 0 0 3 0 0 | * * * * 6 * * * | 1 0 0 0 1 1 0 | 1 1 0 1
.x .. .x .. | 0 4 | 0 0 0 2 2 0 | * * * * * 9 * * | 0 1 0 0 1 0 1 | 1 0 1 1
.x .. .. .x | 0 4 | 0 0 0 2 0 2 | * * * * * * 9 * | 0 0 1 0 0 1 1 | 0 1 1 1
.. .. .x3.x | 0 6 | 0 0 0 0 3 3 | * * * * * * * 3 | 0 0 0 1 0 0 2 | 0 0 2 1
---------------+------+---------------+------------------+---------------+--------
ox3oo .. ..&#x ♦ 1 3 | 0 0 3 3 0 0 | 0 3 0 0 1 0 0 0 | 6 * * * * * * | 1 1 0 0
ox .. xx ..&#x ♦ 2 4 | 1 0 4 2 2 0 | 0 2 2 0 0 1 0 0 | * 9 * * * * * | 1 0 1 0
ox .. .. xx&#x ♦ 2 4 | 0 1 4 2 0 2 | 0 2 0 2 0 0 1 0 | * * 9 * * * * | 0 1 1 0
.. .. xx3xx&#x ♦ 6 6 | 3 3 6 0 3 3 | 1 0 3 3 0 0 0 1 | * * * 3 * * * | 0 0 2 0
.x3.o .x .. ♦ 0 6 | 0 0 0 6 3 0 | 0 0 0 0 2 3 0 0 | * * * * 3 * * | 1 0 0 1
.x3.o .. .x ♦ 0 6 | 0 0 0 6 0 3 | 0 0 0 0 2 0 3 0 | * * * * * 3 * | 0 1 0 1
.x .. .x3.x ♦ 0 12 | 0 0 0 6 6 6 | 0 0 0 0 0 3 3 2 | * * * * * * 3 | 0 0 1 1
---------------+------+---------------+------------------+---------------+--------
ox3oo xx .. ♦ 2 6 | 1 0 6 6 3 0 | 0 6 3 0 2 3 0 0 | 2 3 0 0 1 0 0 | 3 * * *
ox3oo .. xx ♦ 2 6 | 0 1 6 6 0 3 | 0 6 0 3 2 0 3 0 | 2 0 3 0 0 1 0 | * 3 * *
ox .. xx3xx&#x ♦ 6 12 | 3 3 12 6 6 6 | 1 6 6 6 0 3 3 2 | 0 3 3 2 0 0 1 | * * 3 *
.x3.o .x3.x ♦ 0 18 | 0 0 0 18 9 9 | 0 0 0 0 6 9 9 3 | 0 0 0 0 3 3 3 | * * * 1
ox xo xx6oo&#x → height = 1/sqrt(2) = 0.707107
(hip || lacing-ortho hip)
o. o. o.6o. | 12 * | 1 2 2 0 0 | 2 1 1 2 4 0 0 | 1 1 2 4 2 0 | 2 1 2
.o .o .o6.o | * 12 | 0 0 2 1 2 | 0 0 2 1 4 2 1 | 0 1 4 2 2 1 | 2 2 1
---------------+-------+--------------+------------------+---------------+------
.. x. .. .. | 2 0 | 6 * * * * | 2 0 0 2 0 0 0 | 1 1 0 2 0 0 | 2 0 2
.. .. x. .. | 2 0 | * 12 * * * | 1 1 0 0 2 0 0 | 1 0 1 2 2 0 | 1 1 2
oo oo oo6oo&#x | 1 1 | * * 24 * * | 0 0 1 1 2 0 0 | 0 1 2 2 1 0 | 2 1 1
.x .. .. .. | 0 2 | * * * 6 * | 0 0 2 0 0 2 0 | 0 1 4 0 0 1 | 2 2 0
.. .. .x .. | 0 2 | * * * * 12 | 0 0 0 0 2 1 1 | 0 0 2 1 2 1 | 1 2 1
---------------+-------+--------------+------------------+---------------+------
.. x. x. .. | 4 0 | 2 2 0 0 0 | 6 * * * * * * | 1 0 0 2 0 0 | 1 0 2
.. .. x.6o. | 6 0 | 0 6 0 0 0 | * 2 * * * * * | 1 0 0 0 2 0 | 0 1 2
ox .. .. ..&#x | 1 2 | 0 0 2 1 0 | * * 12 * * * * | 0 1 2 0 0 0 | 2 1 0
.. xo .. ..&#x | 2 1 | 1 0 2 0 0 | * * * 12 * * * | 0 1 0 2 0 0 | 2 0 1
.. .. xx ..&#x | 2 2 | 0 1 2 0 1 | * * * * 24 * * | 0 0 1 1 1 0 | 1 1 1
.x .. .x .. | 0 4 | 0 0 0 2 2 | * * * * * 6 * | 0 0 2 0 0 1 | 1 2 0
.. .. .x6.o | 0 6 | 0 0 0 0 6 | * * * * * * 2 | 0 0 0 0 2 1 | 0 2 1
---------------+-------+--------------+------------------+---------------+------
.. x. x.6o. ♦ 12 0 | 6 12 0 0 0 | 6 2 0 0 0 0 0 | 1 * * * * * | 0 0 2
ox xo .. ..&#x ♦ 2 2 | 1 0 4 1 0 | 0 0 2 2 0 0 0 | * 6 * * * * | 2 0 0
ox .. xx ..&#x ♦ 2 4 | 0 1 4 2 2 | 0 0 2 0 2 1 0 | * * 12 * * * | 1 1 0
.. xo xx ..&#x ♦ 4 2 | 2 2 4 0 1 | 1 0 0 2 2 0 0 | * * * 12 * * | 1 0 1
.. .. xx6oo&#x ♦ 6 6 | 0 6 6 0 6 | 0 1 0 0 6 0 1 | * * * * 4 * | 0 1 1
.x .. .x6.o ♦ 0 12 | 0 0 0 6 12 | 0 0 0 0 0 6 2 | * * * * * 1 | 0 2 0
---------------+-------+--------------+------------------+---------------+------
ox xo xx ..&#x ♦ 4 4 | 2 2 8 2 2 | 1 0 4 4 4 1 0 | 0 2 2 2 0 0 | 6 * *
ox .. xx6oo&#x ♦ 6 12 | 0 6 12 6 12 | 0 1 6 0 12 6 2 | 0 0 6 0 2 1 | * 2 *
.. xo xx6oo&#x ♦ 12 6 | 6 12 12 0 6 | 6 2 0 6 12 0 1 | 1 0 0 6 2 0 | * * 2
ox xo xx3xx&#x → height = 1/sqrt(2) = 0.707107
(hip || lacing-ortho hip)
o. o. o.3o. | 12 * | 1 1 1 2 0 0 0 | 1 1 1 1 2 2 2 0 0 0 | 1 1 1 1 2 2 2 0 | 1 1 1 2
.o .o .o3.o | * 12 | 0 0 0 2 1 1 1 | 0 0 0 2 1 2 2 1 1 1 | 0 1 2 2 1 1 2 1 | 1 1 2 1
---------------+-------+----------------+-------------------------+-----------------+--------
.. x. .. .. | 2 0 | 6 * * * * * * | 1 1 0 0 2 0 0 0 0 0 | 1 1 0 0 1 1 0 0 | 1 1 0 2
.. .. x. .. | 2 0 | * 6 * * * * * | 1 0 1 0 0 2 0 0 0 0 | 1 0 1 0 2 0 2 0 | 1 0 1 2
.. .. .. x. | 2 0 | * * 6 * * * * | 0 1 1 0 0 0 2 0 0 0 | 1 0 0 1 0 2 2 0 | 0 1 1 2
oo oo oo3oo&#x | 1 1 | * * * 24 * * * | 0 0 0 1 1 1 1 0 0 0 | 0 1 1 1 1 1 1 0 | 1 1 1 1
.x .. .. .. | 0 2 | * * * * 6 * * | 0 0 0 2 0 0 0 1 1 0 | 0 1 2 2 0 0 0 1 | 1 1 2 0
.. .. .x .. | 0 2 | * * * * * 6 * | 0 0 0 0 0 2 0 1 0 1 | 0 0 2 0 1 0 2 1 | 1 0 2 1
.. .. .. .x | 0 2 | * * * * * * 6 | 0 0 0 0 0 0 2 0 1 1 | 0 0 0 2 0 1 2 1 | 0 1 2 1
---------------+-------+----------------+-------------------------+-----------------+--------
.. x. x. .. | 4 0 | 2 2 0 0 0 0 0 | 3 * * * * * * * * * | 1 0 0 0 2 0 0 0 | 1 0 0 2
.. x. .. x. | 4 0 | 2 0 2 0 0 0 0 | * 3 * * * * * * * * | 1 0 0 0 0 2 0 0 | 0 1 0 2
.. .. x.3x. | 6 0 | 0 3 3 0 0 0 0 | * * 2 * * * * * * * | 1 0 0 0 0 0 2 0 | 0 0 1 2
ox .. .. ..&#x | 1 2 | 0 0 0 2 1 0 0 | * * * 12 * * * * * * | 0 1 1 1 0 0 0 0 | 1 1 1 0
.. xo .. ..&#x | 2 1 | 1 0 0 2 0 0 0 | * * * * 12 * * * * * | 0 1 0 0 1 1 0 0 | 1 1 0 1
.. .. xx ..&#x | 2 2 | 0 1 0 2 0 1 0 | * * * * * 12 * * * * | 0 0 1 0 1 0 1 0 | 1 0 1 1
.. .. .. xx&#x | 2 2 | 0 0 1 2 0 0 1 | * * * * * * 12 * * * | 0 0 0 1 0 1 1 0 | 0 1 1 1
.x .. .x .. | 0 4 | 0 0 0 0 2 2 0 | * * * * * * * 3 * * | 0 0 2 0 0 0 0 1 | 1 0 2 0
.x .. .. .x | 0 4 | 0 0 0 0 2 0 2 | * * * * * * * * 3 * | 0 0 0 2 0 0 0 1 | 0 1 2 0
.. .. .x3.x | 0 6 | 0 0 0 0 0 3 3 | * * * * * * * * * 2 | 0 0 0 0 0 0 2 1 | 0 0 2 1
---------------+-------+----------------+-------------------------+-----------------+--------
.. x. x.3x. ♦ 12 0 | 6 6 6 0 0 0 0 | 3 3 2 0 0 0 0 0 0 0 | 1 * * * * * * * | 0 0 0 2
ox xo .. ..&#x ♦ 2 2 | 1 0 0 4 1 0 0 | 0 0 0 2 2 0 0 0 0 0 | * 6 * * * * * * | 1 1 0 0
ox .. xx ..&#x ♦ 2 4 | 0 1 0 4 2 2 0 | 0 0 0 2 0 2 0 1 0 0 | * * 6 * * * * * | 1 0 1 0
ox .. .. xx&#x ♦ 2 4 | 0 0 1 4 2 0 2 | 0 0 0 2 0 0 2 0 1 0 | * * * 6 * * * * | 0 1 1 0
.. xo xx ..&#x ♦ 4 2 | 2 2 0 4 0 1 0 | 1 0 0 0 2 2 0 0 0 0 | * * * * 6 * * * | 1 0 0 1
.. xo .. xx&#x ♦ 4 2 | 2 0 2 4 0 0 1 | 0 1 0 0 2 0 2 0 0 0 | * * * * * 6 * * | 0 1 0 1
.. .. xx3xx&#x ♦ 6 6 | 0 3 3 6 0 3 3 | 0 0 1 0 0 3 3 0 0 1 | * * * * * * 4 * | 0 0 1 1
.x .. .x3.x ♦ 0 12 | 0 0 0 0 6 6 6 | 0 0 0 0 0 0 0 3 3 2 | * * * * * * * 1 | 0 0 2 0
---------------+-------+----------------+-------------------------+-----------------+--------
ox xo xx ..&#x ♦ 4 4 | 2 2 0 8 2 2 0 | 1 0 0 4 4 4 0 1 0 0 | 0 2 2 0 2 0 0 0 | 3 * * *
ox xo .. xx&#x ♦ 4 4 | 2 0 2 8 2 0 2 | 0 1 0 4 4 0 4 0 1 0 | 0 2 0 2 0 2 0 0 | * 3 * *
ox .. xx3xx&#x ♦ 6 12 | 0 3 3 12 6 6 6 | 0 0 1 6 0 6 6 3 3 2 | 0 0 3 3 0 0 2 1 | * * 2 *
.. xo xx3xx&#x ♦ 12 6 | 6 6 6 12 0 3 3 | 3 3 2 0 6 6 6 0 0 1 | 1 0 0 0 3 3 2 0 | * * * 2
oox xxx3xxx&#x → height(1,2) = 1
height(1,3) = height(2,3) = sqrt(3)/2 = 0.866025
height(12,3) = 1/sqrt(2) = 0.707107 (hip || lacing-ortho hip)
o.. o..3o.. | 6 * * | 1 1 1 2 0 0 0 0 0 0 | 1 1 1 2 1 2 2 0 0 0 0 0 0 0 | 1 1 2 2 1 1 2 0 0 0 0 | 1 1 2 1 0
.o. .o.3.o. | * 6 * | 0 0 1 0 1 1 2 0 0 0 | 0 1 1 2 0 0 0 1 1 2 2 0 0 0 | 1 1 2 2 0 0 0 1 1 2 0 | 1 1 2 0 1
..o ..o3..o | * * 12 | 0 0 0 1 0 0 1 1 1 1 | 0 0 0 1 1 1 1 0 1 1 1 1 1 1 | 0 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1
---------------+--------+-----------------------+------------------------------+-----------------------+----------
... x.. ... | 2 0 0 | 3 * * * * * * * * * | 1 1 0 0 0 2 0 0 0 0 0 0 0 0 | 1 0 2 0 1 0 2 0 0 0 0 | 1 0 2 1 0
... ... x.. | 2 0 0 | * 3 * * * * * * * * | 1 0 1 0 0 0 2 0 0 0 0 0 0 0 | 1 0 0 2 0 1 2 0 0 0 0 | 0 1 2 1 0
oo. oo.3oo.&#x | 1 1 0 | * * 6 * * * * * * * | 0 1 1 2 0 0 0 0 0 0 0 0 0 0 | 1 1 2 2 0 0 0 0 0 0 0 | 1 1 2 0 0
o.o o.o3o.o&#x | 1 0 1 | * * * 12 * * * * * * | 0 0 0 1 1 1 1 0 0 0 0 0 0 0 | 0 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0
... .x. ... | 0 2 0 | * * * * 3 * * * * * | 0 1 0 0 0 0 0 1 0 2 0 0 0 0 | 1 0 2 0 0 0 0 1 0 2 0 | 1 0 2 0 1
... ... .x. | 0 2 0 | * * * * * 3 * * * * | 0 0 1 0 0 0 0 1 0 0 2 0 0 0 | 1 0 0 2 0 0 0 0 1 2 0 | 0 1 2 0 1
.oo .oo3.oo&#x | 0 1 1 | * * * * * * 12 * * * | 0 0 0 1 0 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0 0 0 1 1 1 0 | 1 1 1 0 1
..x ... ... | 0 0 2 | * * * * * * * 6 * * | 0 0 0 0 1 0 0 0 1 0 0 1 1 0 | 0 1 0 0 1 1 0 1 1 0 1 | 1 1 0 1 1
... ..x ... | 0 0 2 | * * * * * * * * 6 * | 0 0 0 0 0 1 0 0 0 1 0 1 0 1 | 0 0 1 0 1 0 1 1 0 1 1 | 1 0 1 1 1
... ... ..x | 0 0 2 | * * * * * * * * * 6 | 0 0 0 0 0 0 1 0 0 0 1 0 1 1 | 0 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1
---------------+--------+-----------------------+------------------------------+-----------------------+----------
... x..3x.. | 6 0 0 | 3 3 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * | 1 0 0 0 0 0 2 0 0 0 0 | 0 0 2 1 0
... xx. ...&#x | 2 2 0 | 1 0 2 0 1 0 0 0 0 0 | * 3 * * * * * * * * * * * * | 1 0 2 0 0 0 0 0 0 0 0 | 1 0 2 0 0
... ... xx.&#x | 2 2 0 | 0 1 2 0 0 1 0 0 0 0 | * * 3 * * * * * * * * * * * | 1 0 0 2 0 0 0 0 0 0 0 | 0 1 2 0 0
ooo ooo3ooo&#x | 1 1 1 | 0 0 1 1 0 0 1 0 0 0 | * * * 12 * * * * * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0
o.x ... ...&#x | 1 0 2 | 0 0 0 2 0 0 0 1 0 0 | * * * * 6 * * * * * * * * * | 0 1 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0
... x.x ...&#x | 2 0 2 | 1 0 0 2 0 0 0 0 1 0 | * * * * * 6 * * * * * * * * | 0 0 1 0 1 0 1 0 0 0 0 | 1 0 1 1 0
... ... x.x&#x | 2 0 2 | 0 1 0 2 0 0 0 0 0 1 | * * * * * * 6 * * * * * * * | 0 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0
... .x.3.x. | 0 6 0 | 0 0 0 0 3 3 0 0 0 0 | * * * * * * * 1 * * * * * * | 1 0 0 0 0 0 0 0 0 2 0 | 0 0 2 0 1
.ox ... ...&#x | 0 1 2 | 0 0 0 0 0 0 2 1 0 0 | * * * * * * * * 6 * * * * * | 0 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1
... .xx ...&#x | 0 2 2 | 0 0 0 0 1 0 2 0 1 0 | * * * * * * * * * 6 * * * * | 0 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1
... ... .xx&#x | 0 2 2 | 0 0 0 0 0 1 2 0 0 1 | * * * * * * * * * * 6 * * * | 0 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1
..x ..x ... | 0 0 4 | 0 0 0 0 0 0 0 2 2 0 | * * * * * * * * * * * 3 * * | 0 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1
..x ... ..x | 0 0 4 | 0 0 0 0 0 0 0 2 0 2 | * * * * * * * * * * * * 3 * | 0 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1
... ..x3..x | 0 0 6 | 0 0 0 0 0 0 0 0 3 3 | * * * * * * * * * * * * * 2 | 0 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1
---------------+--------+-----------------------+------------------------------+-----------------------+----------
... xx.3xx.&#x ♦ 6 6 0 | 3 3 6 0 3 3 0 0 0 0 | 1 3 3 0 0 0 0 1 0 0 0 0 0 0 | 1 * * * * * * * * * * | 0 0 2 0 0
oox ... ...&#x ♦ 1 1 2 | 0 0 1 2 0 0 2 1 0 0 | 0 0 0 2 1 0 0 0 1 0 0 0 0 0 | * 6 * * * * * * * * * | 1 1 0 0 0
... xxx ...&#x ♦ 2 2 2 | 1 0 2 2 1 0 2 0 1 0 | 0 1 0 2 0 1 0 0 0 1 0 0 0 0 | * * 6 * * * * * * * * | 1 0 1 0 0
... ... xxx&#x ♦ 2 2 2 | 0 1 2 2 0 1 2 0 0 1 | 0 0 1 2 0 0 1 0 0 0 1 0 0 0 | * * * 6 * * * * * * * | 0 1 1 0 0
o.x x.x ...&#x ♦ 2 0 4 | 1 0 0 4 0 0 0 2 2 0 | 0 0 0 0 2 2 0 0 0 0 0 1 0 0 | * * * * 3 * * * * * * | 1 0 0 1 0
o.x ... x.x&#x ♦ 2 0 4 | 0 1 0 4 0 0 0 2 0 2 | 0 0 0 0 2 0 2 0 0 0 0 0 1 0 | * * * * * 3 * * * * * | 0 1 0 1 0
... x.x3x.x&#x ♦ 6 0 6 | 3 3 0 6 0 0 0 0 3 3 | 1 0 0 0 0 3 3 0 0 0 0 0 0 1 | * * * * * * 2 * * * * | 0 0 1 1 0
.ox .xx ...&#x ♦ 0 2 4 | 0 0 0 0 1 0 4 2 2 0 | 0 0 0 0 0 0 0 0 2 2 0 1 0 0 | * * * * * * * 3 * * * | 1 0 0 0 1
.ox ... .xx&#x ♦ 0 2 4 | 0 0 0 0 0 1 4 2 0 2 | 0 0 0 0 0 0 0 0 2 0 2 0 1 0 | * * * * * * * * 3 * * | 0 1 0 0 1
... .xx3.xx&#x ♦ 0 6 6 | 0 0 0 0 3 3 6 0 3 3 | 0 0 0 0 0 0 0 1 0 3 3 0 0 1 | * * * * * * * * * 2 * | 0 0 1 0 1
..x ..x3..x ♦ 0 0 12 | 0 0 0 0 0 0 0 6 6 6 | 0 0 0 0 0 0 0 0 0 0 0 3 3 2 | * * * * * * * * * * 1 | 0 0 0 1 1
---------------+--------+-----------------------+------------------------------+-----------------------+----------
oox xxx ...&#x ♦ 2 2 4 | 1 0 2 4 1 0 4 2 2 0 | 0 1 0 4 2 2 0 0 2 2 0 1 0 0 | 0 2 2 0 1 0 0 1 0 0 0 | 3 * * * *
oox ... xxx&#x ♦ 2 2 4 | 0 1 2 4 0 1 4 2 0 2 | 0 0 1 4 2 0 2 0 2 0 2 0 1 0 | 0 2 0 2 0 1 0 0 1 0 0 | * 3 * * *
... xxx3xxx&#x ♦ 6 6 6 | 3 3 6 6 3 3 6 0 3 3 | 1 3 3 6 0 3 3 1 0 3 3 0 0 1 | 1 0 3 3 0 0 1 0 0 1 0 | * * 2 * *
o.x x.x3x.x&#x ♦ 6 0 12 | 3 3 0 12 0 0 0 6 6 6 | 1 0 0 0 6 6 6 0 0 0 0 3 3 2 | 0 0 0 0 3 3 2 0 0 0 1 | * * * 1 *
.ox .xx3.xx&#x ♦ 0 6 12 | 0 0 0 0 3 3 12 6 6 6 | 0 0 0 0 0 0 0 1 6 6 6 3 3 2 | 0 0 0 0 0 0 0 3 3 2 1 | * * * * 1
xxxx3xxxx&#x → all pairwise heights = 1
height(12,34) = 1/sqrt(2) = 0.707107 (hip || lacing-ortho hip)
o...3o... | 6 * * * | 1 1 1 1 1 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 | 1 1 1 1 1 0
.o..3.o.. | * 6 * * | 0 0 1 0 0 1 1 1 1 0 0 0 0 0 | 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 | 1 1 1 1 0 1
..o.3..o. | * * 6 * | 0 0 0 1 0 0 0 1 0 1 1 1 0 0 | 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 | 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 | 1 1 1 0 1 1
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-------------+---------+-----------------------------+-----------------------------------------+-------------------------------+------------
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-------------+---------+-----------------------------+-----------------------------------------+-------------------------------+------------
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...x3...x | 0 0 0 6 | 0 0 0 0 0 0 0 0 0 0 0 0 3 3 | * * * * * * * * * * * * * * * * * * * 1 | 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
-------------+---------+-----------------------------+-----------------------------------------+-------------------------------+------------
xx..3xx..&#x ♦ 6 6 0 0 | 3 3 6 0 0 3 3 0 0 0 0 0 0 0 | 1 3 3 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * | 1 0 0 1 0 0
xxx. ....&#x ♦ 2 2 2 0 | 1 0 2 2 0 1 0 2 0 1 0 0 0 0 | 0 1 0 2 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * * | 1 1 0 0 0 0
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oooo3oooo&#x ♦ 1 1 1 1 | 0 0 1 1 1 0 0 1 1 0 0 1 0 0 | 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 | * * * 6 * * * * * * * * * * * | 0 1 1 0 0 0
xx.x ....&#x ♦ 2 2 0 2 | 1 0 2 0 2 1 0 0 2 0 0 0 1 0 | 0 1 0 0 2 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 | * * * * 3 * * * * * * * * * * | 0 1 0 1 0 0
.... xx.x&#x ♦ 2 2 0 2 | 0 1 2 0 2 0 1 0 2 0 0 0 0 1 | 0 0 1 0 2 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 | * * * * * 3 * * * * * * * * * | 0 0 1 1 0 0
x.x.3x.x.&#x ♦ 6 0 6 0 | 3 3 0 6 0 0 0 0 0 3 3 0 0 0 | 1 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 1 0 0 0 | * * * * * * 1 * * * * * * * * | 1 0 0 0 1 0
x.xx ....&#x ♦ 2 0 2 2 | 1 0 0 2 2 0 0 0 0 1 0 2 1 0 | 0 0 0 0 0 1 0 2 1 0 0 0 0 0 0 0 0 1 0 0 | * * * * * * * 3 * * * * * * * | 0 1 0 0 1 0
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x..x3x..x&#x ♦ 6 0 0 6 | 3 3 0 0 6 0 0 0 0 0 0 0 3 3 | 1 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 1 | * * * * * * * * * 1 * * * * * | 0 0 0 1 1 0
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.x.x3.x.x&#x ♦ 0 6 0 6 | 0 0 0 0 0 3 3 0 6 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 3 3 0 0 0 1 | * * * * * * * * * * * * * 1 * | 0 0 0 1 0 1
..xx3..xx&#x ♦ 0 0 6 6 | 0 0 0 0 0 0 0 0 0 3 3 6 3 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 3 1 | * * * * * * * * * * * * * * 1 | 0 0 0 0 1 1
-------------+---------+-----------------------------+-----------------------------------------+-------------------------------+------------
xxx.3xxx.&#x ♦ 6 6 6 0 | 3 3 6 6 0 3 3 6 0 3 3 0 0 0 | 1 3 3 6 0 3 3 0 0 0 1 3 3 0 0 0 1 0 0 0 | 1 3 3 0 0 0 1 0 0 0 1 0 0 0 0 | 1 * * * * *
xxxx ....&#x ♦ 2 2 2 2 | 1 0 2 2 2 1 0 2 2 1 0 2 1 0 | 0 1 0 2 2 1 0 2 1 0 0 1 0 2 1 0 0 1 0 0 | 0 1 0 2 1 0 0 1 0 0 0 1 0 0 0 | * 3 * * * *
.... xxxx&#x ♦ 2 2 2 2 | 0 1 2 2 2 0 1 2 2 0 1 2 0 1 | 0 0 1 2 2 0 1 2 0 1 0 0 1 2 0 1 0 0 1 0 | 0 0 1 2 0 1 0 0 1 0 0 0 1 0 0 | * * 3 * * *
xx.x3xx.x&#x ♦ 6 6 0 6 | 3 3 6 0 6 3 3 0 6 0 0 0 3 3 | 1 3 3 0 6 0 0 0 3 3 1 0 0 0 3 3 0 0 0 1 | 1 0 0 0 3 3 0 0 0 1 0 0 0 1 0 | * * * 1 * *
x.xx3x.xx&#x ♦ 6 0 6 6 | 3 3 0 6 6 0 0 0 0 3 3 6 3 3 | 1 0 0 0 0 3 3 6 3 3 0 0 0 0 0 0 1 3 3 1 | 0 0 0 0 0 0 1 3 3 1 0 0 0 0 1 | * * * * 1 *
.xxx3.xxx&#x ♦ 0 6 6 6 | 0 0 0 0 0 3 3 6 6 3 3 6 3 3 | 0 0 0 0 0 0 0 0 0 0 1 3 3 6 3 3 1 3 3 1 | 0 0 0 0 0 0 0 0 0 0 1 3 3 1 1 | * * * * * 1
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