Acronym | hexathex |
Name | (degenerate) hex atop thex |
Circumradius | ∞ i.e. flat in euclidean space |
Face vector | 56, 192, 248, 136, 26 |
Confer |
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It either can be thought of as a degenerate 5D segmentotope with zero height, or as a 4D euclidean decomposition of the larger base into smaller bits.
Incidence matrix according to Dynkin symbol
xx3ox3oo4oo&#x → height = 0
(hex || thex)
o.3o.3o.4o. | 8 * | 6 6 0 0 | 12 6 12 0 0 | 8 12 8 0 0 | 1 8 1 0
.o3.o3.o4.o | * 48 | 0 1 1 4 | 0 1 4 4 4 | 0 4 4 4 1 | 0 4 1 1
---------------+------+-------------+----------------+---------------+---------
x. .. .. .. | 2 0 | 24 * * * | 4 1 0 0 0 | 4 4 0 0 0 | 1 4 0 0
oo3oo3oo4oo&#x | 1 1 | * 48 * * | 0 1 4 0 0 | 0 4 4 0 0 | 0 4 1 0
.x .. .. .. | 0 2 | * * 24 * | 0 1 0 4 0 | 0 4 0 4 0 | 0 4 0 1
.. .x .. .. | 0 2 | * * * 96 | 0 0 1 1 2 | 0 1 2 2 1 | 0 2 1 1
---------------+------+-------------+----------------+---------------+---------
x.3o. .. .. | 3 0 | 3 0 0 0 | 32 * * * * | 2 1 0 0 0 | 1 2 0 0
xx .. .. ..&#x | 2 2 | 1 2 1 0 | * 24 * * * | 0 4 0 0 0 | 0 4 0 0
.. ox .. ..&#x | 1 2 | 0 2 0 1 | * * 96 * * | 0 1 2 0 0 | 0 2 1 0
.x3.x .. .. | 0 6 | 0 0 3 3 | * * * 32 * | 0 1 0 2 0 | 0 2 0 1
.. .x3.o .. | 0 3 | 0 0 0 3 | * * * * 64 | 0 0 1 1 1 | 0 1 1 1
---------------+------+-------------+----------------+---------------+---------
x.3o.3o. .. ♦ 4 0 | 6 0 0 0 | 4 0 0 0 0 | 16 * * * * | 1 1 0 0
xx3ox .. ..&#x ♦ 3 6 | 3 6 3 3 | 1 3 3 1 0 | * 32 * * * | 0 2 0 0
.. ox3oo ..&#x ♦ 1 3 | 0 3 0 3 | 0 0 3 0 1 | * * 64 * * | 0 1 1 0
.x3.x3.o .. ♦ 0 12 | 0 0 6 12 | 0 0 0 4 4 | * * * 16 * | 0 1 0 1
.. .x3.o4.o ♦ 0 6 | 0 0 0 12 | 0 0 0 0 8 | * * * * 8 | 0 0 1 1
---------------+------+-------------+----------------+---------------+---------
x.3o.3o.4o. ♦ 8 0 | 24 0 0 0 | 32 0 0 0 0 | 16 0 0 0 0 | 1 * * *
xx3ox3oo ..&#x ♦ 4 12 | 6 12 6 12 | 4 6 12 4 4 | 1 4 4 1 0 | * 16 * *
.. ox3oo4oo&#x ♦ 1 6 | 0 6 0 12 | 0 0 12 0 8 | 0 0 8 0 1 | * * 8 *
.x3.x3.o4.o ♦ 0 48 | 0 0 24 96 | 0 0 0 32 64 | 0 0 0 16 8 | * * * 1
oo3ox3oo *b3xx&#x → height = 0
(hex || thex)
o.3o.3o. *b3o. | 8 * | 6 6 0 0 | 12 12 6 0 0 0 | 4 4 4 4 12 0 0 0 | 1 1 4 4 0
.o3.o3.o *b3.o | * 48 | 0 1 4 1 | 0 4 1 2 2 4 | 0 0 2 2 4 1 2 2 | 0 1 2 2 1
------------------+------+-------------+-------------------+--------------------+----------
.. .. .. x. | 2 0 | 24 * * * | 4 0 1 0 0 0 | 2 2 0 0 4 0 0 0 | 1 0 2 2 0
oo3oo3oo *b3oo&#x | 1 1 | * 48 * * | 0 4 1 0 0 0 | 0 0 2 2 4 0 0 0 | 0 1 2 2 0
.. .x .. .. | 0 2 | * * 96 * | 0 1 0 1 1 1 | 0 0 1 1 1 1 1 1 | 0 1 1 1 1
.. .. .. .x | 0 2 | * * * 24 | 0 0 1 0 0 4 | 0 0 0 0 4 0 2 2 | 0 0 2 2 1
------------------+------+-------------+-------------------+--------------------+----------
.. o. .. *b3x. | 3 0 | 3 0 0 0 | 32 * * * * * | 1 1 0 0 1 0 0 0 | 1 0 1 1 0
.. ox .. ..&#x | 1 2 | 0 2 1 0 | * 96 * * * * | 0 0 1 1 1 0 0 0 | 0 1 1 1 0
.. .. .. xx&#x | 2 2 | 1 2 0 1 | * * 24 * * * | 0 0 0 0 4 0 0 0 | 0 0 2 2 0
.o3.x .. .. | 0 3 | 0 0 3 0 | * * * 32 * * | 0 0 1 0 0 1 1 0 | 0 1 1 0 1
.. .x3.o .. | 0 3 | 0 0 3 0 | * * * * 32 * | 0 0 0 1 0 1 0 1 | 0 1 0 1 1
.. .x .. *b3.x | 0 6 | 0 0 3 3 | * * * * * 32 | 0 0 0 0 1 0 1 1 | 0 0 1 1 1
------------------+------+-------------+-------------------+--------------------+----------
o.3o. .. *b3x. ♦ 4 0 | 6 0 0 0 | 4 0 0 0 0 0 | 8 * * * * * * * | 1 0 1 0 0
.. o.3o. *b3x. ♦ 4 0 | 6 0 0 0 | 4 0 0 0 0 0 | * 8 * * * * * * | 1 0 0 1 0
oo3ox .. ..&#x ♦ 1 3 | 0 3 3 0 | 0 3 0 1 0 0 | * * 32 * * * * * | 0 1 1 0 0
.. ox3oo ..&#x ♦ 1 3 | 0 3 3 0 | 0 3 0 0 1 0 | * * * 32 * * * * | 0 1 0 1 0
.. ox .. *b3xx&#x ♦ 3 6 | 3 6 3 3 | 1 3 3 0 0 1 | * * * * 32 * * * | 0 0 1 1 0
.o3.x3.o .. ♦ 0 6 | 0 0 12 0 | 0 0 0 4 4 0 | * * * * * 8 * * | 0 1 0 0 1
.o3.x .. *b3.x ♦ 0 12 | 0 0 12 6 | 0 0 0 4 0 4 | * * * * * * 8 * | 0 0 1 0 1
.. .x3.o *b3.x ♦ 0 12 | 0 0 12 6 | 0 0 0 0 4 4 | * * * * * * * 8 | 0 0 0 1 1
------------------+------+-------------+-------------------+--------------------+----------
o.3o.3o. *b3x. ♦ 8 0 | 24 0 0 0 | 32 0 0 0 0 0 | 8 8 0 0 0 0 0 0 | 1 * * * *
oo3ox3oo ..&#x ♦ 1 6 | 0 6 12 0 | 0 12 0 4 4 0 | 0 0 4 4 0 1 0 0 | * 8 * * *
oo3ox .. *b3xx&#x ♦ 4 12 | 6 12 12 6 | 4 12 6 4 0 4 | 1 0 4 0 4 0 1 0 | * * 8 * *
.. ox3oo *b3xx&#x ♦ 4 12 | 6 12 12 6 | 4 12 6 0 4 4 | 0 1 0 4 4 0 0 1 | * * * 8 *
.o3.x3.o *b3.x ♦ 0 48 | 0 0 96 24 | 0 0 0 32 32 32 | 0 0 0 0 0 8 8 8 | * * * * 1
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