Acronym | ohix |
Name | octagon - hexateron duoprism |
Circumradius | sqrt[(17+6 sqrt(2))/12] = 1.457317 |
Volume | [1+sqrt(2)] sqrt(3)/240 = 0.017423 |
Face vector | 48, 168, 286, 295, 188, 71, 14 |
Confer |
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As abstract polytope ohix is isomorphic to stohix, thereby replacing octagons by octagrams, resp. op by stop, resp. otet by stotet, resp. open by stopen.
Incidence matrix according to Dynkin symbol
x3o3o3o3o x4x . . . . . . . | 48 | 5 1 1 | 10 5 5 1 | 10 10 10 5 | 5 10 10 10 | 1 5 5 10 | 1 1 5 --------------+----+-----------+-------------+--------------+-------------+------------+------ x . . . . . . | 2 | 120 * * | 4 1 1 0 | 6 4 4 1 | 4 6 6 4 | 1 4 4 6 | 1 1 4 . . . . . x . | 2 | * 24 * | 0 5 0 1 | 0 10 0 5 | 0 10 0 10 | 0 5 0 10 | 1 0 5 . . . . . . x | 2 | * * 24 | 0 0 5 1 | 0 0 10 5 | 0 0 10 10 | 0 0 5 10 | 0 1 5 --------------+----+-----------+-------------+--------------+-------------+------------+------ x3o . . . . . | 3 | 3 0 0 | 160 * * * | 3 1 1 0 | 3 3 3 1 | 1 3 3 3 | 1 1 3 x . . . . x . | 4 | 2 2 0 | * 60 * * | 0 4 0 1 | 0 6 0 4 | 0 4 0 6 | 1 0 4 x . . . . . x | 4 | 2 0 2 | * * 60 * | 0 0 4 1 | 0 0 6 4 | 0 0 4 6 | 0 1 4 . . . . . x4x | 8 | 0 4 4 | * * * 6 ♦ 0 0 0 5 | 0 0 0 10 | 0 0 0 10 | 0 0 5 --------------+----+-----------+-------------+--------------+-------------+------------+------ x3o3o . . . . ♦ 4 | 6 0 0 | 4 0 0 0 | 120 * * * | 2 1 1 0 | 1 2 2 1 | 1 1 2 x3o . . . x . ♦ 6 | 6 3 0 | 2 3 0 0 | * 80 * * | 0 3 0 1 | 0 3 0 3 | 1 0 3 x3o . . . . x ♦ 6 | 6 0 3 | 2 0 3 0 | * * 80 * | 0 0 3 1 | 0 0 3 3 | 0 1 3 x . . . . x4x ♦ 16 | 8 8 8 | 0 4 4 2 | * * * 15 ♦ 0 0 0 4 | 0 0 0 6 | 0 0 4 --------------+----+-----------+-------------+--------------+-------------+------------+------ x3o3o3o . . . ♦ 5 | 10 0 0 | 10 0 0 0 | 5 0 0 0 | 48 * * * | 1 1 1 0 | 1 1 1 x3o3o . . x . ♦ 8 | 12 4 0 | 8 6 0 0 | 2 4 0 0 | * 60 * * | 0 2 0 1 | 1 0 2 x3o3o . . . x ♦ 8 | 12 0 4 | 8 0 6 0 | 2 0 4 0 | * * 60 * | 0 0 2 1 | 0 1 2 x3o . . . x4x ♦ 24 | 24 12 12 | 8 12 12 3 | 0 4 4 3 | * * * 20 | 0 0 0 3 | 0 0 3 --------------+----+-----------+-------------+--------------+-------------+------------+------ x3o3o3o3o . . ♦ 6 | 15 0 0 | 20 0 0 0 | 15 0 0 0 | 6 0 0 0 | 8 * * * | 1 1 0 x3o3o3o . x . ♦ 10 | 20 5 0 | 20 10 0 0 | 10 10 0 0 | 2 5 0 0 | * 24 * * | 1 0 1 x3o3o3o . . x ♦ 10 | 20 0 5 | 20 0 10 0 | 10 0 10 0 | 2 0 5 0 | * * 24 * | 0 1 1 x3o3o . . x4x ♦ 32 | 48 16 16 | 32 24 24 4 | 8 16 16 6 | 0 4 4 4 | * * * 15 | 0 0 2 --------------+----+-----------+-------------+--------------+-------------+------------+------ x3o3o3o3o x . ♦ 12 | 30 6 0 | 40 15 0 0 | 30 20 0 0 | 12 15 0 0 | 2 6 0 0 | 4 * * x3o3o3o3o . x ♦ 12 | 30 0 6 | 40 0 15 0 | 30 0 20 0 | 12 0 15 0 | 2 0 6 0 | * 4 * x3o3o3o . x4x ♦ 40 | 80 20 20 | 80 40 40 5 | 40 40 40 10 | 8 20 20 10 | 0 4 4 5 | * * 6
ox3oo3oo3oo xx4xx&#x → height = sqrt(3/5) = 0.774597
({8} || open)
o.3o.3o.3o. o.4o. | 8 * | 1 1 5 0 0 0 | 1 10 5 5 0 0 0 0 | 10 10 10 5 0 0 0 0 | 5 10 10 10 0 0 0 0 | 1 5 5 10 0 0 0 | 1 1 5 0
.o3.o3.o3.o .o4.o | * 40 | 0 0 1 4 1 1 | 0 4 1 1 6 4 4 1 | 6 4 4 1 4 6 6 4 | 4 6 6 4 1 4 4 6 | 1 4 4 6 1 1 4 | 1 1 4 1
---------------------+------+-----------------+-----------------------+------------------------+------------------------+------------------+--------
.. .. .. .. x. .. | 2 0 | 4 * * * * * | 1 0 5 0 0 0 0 0 | 0 10 0 5 0 0 0 0 | 0 10 0 10 0 0 0 0 | 0 5 0 10 0 0 0 | 1 0 5 0
.. .. .. .. .. x. | 2 0 | * 4 * * * * | 1 0 0 5 0 0 0 0 | 0 0 10 5 0 0 0 0 | 0 0 10 10 0 0 0 0 | 0 0 5 10 0 0 0 | 0 1 5 0
oo3oo3oo3oo oo4oo&#x | 1 1 | * * 40 * * * | 0 4 1 1 0 0 0 0 | 6 4 4 1 0 0 0 0 | 4 6 6 4 0 0 0 0 | 1 4 4 6 0 0 0 | 1 1 4 0
.x .. .. .. .. .. | 0 2 | * * * 80 * * | 0 1 0 0 3 1 1 0 | 3 1 1 0 3 3 3 1 | 3 3 3 1 1 3 3 3 | 1 3 3 3 1 1 3 | 1 1 3 1
.. .. .. .. .x .. | 0 2 | * * * * 20 * | 0 0 1 0 0 4 0 1 | 0 4 0 1 0 6 0 4 | 0 6 0 4 0 4 0 6 | 0 4 0 6 1 0 4 | 1 0 4 1
.. .. .. .. .. .x | 0 2 | * * * * * 20 | 0 0 0 1 0 0 4 1 | 0 0 4 1 0 0 6 4 | 0 0 6 4 0 0 4 6 | 0 0 4 6 0 1 4 | 0 1 4 1
---------------------+------+-----------------+-----------------------+------------------------+------------------------+------------------+--------
.. .. .. .. x.4x. | 8 0 | 4 4 0 0 0 0 | 1 * * * * * * * ♦ 0 0 0 5 0 0 0 0 | 0 0 0 10 0 0 0 0 | 0 0 0 10 0 0 0 | 0 0 5 0
ox .. .. .. .. ..&#x | 1 2 | 0 0 2 1 0 0 | * 80 * * * * * * | 3 1 1 0 0 0 0 0 | 3 3 3 1 0 0 0 0 | 1 3 3 3 0 0 0 | 1 1 3 0
.. .. .. .. xx ..&#x | 2 2 | 1 0 2 0 1 0 | * * 20 * * * * * | 0 4 0 1 0 0 0 0 | 0 6 0 4 0 0 0 0 | 0 4 0 6 0 0 0 | 1 0 4 0
.. .. .. .. .. xx&#x | 2 2 | 0 1 2 0 0 1 | * * * 20 * * * * | 0 0 4 1 0 0 0 0 | 0 0 6 4 0 0 0 0 | 0 0 4 6 0 0 0 | 0 1 4 0
.x3.o .. .. .. .. | 0 3 | 0 0 0 3 0 0 | * * * * 80 * * * | 1 0 0 0 2 1 1 0 | 2 1 1 0 1 2 2 1 | 1 2 2 1 1 1 2 | 1 1 2 1
.x .. .. .. .x .. | 0 4 | 0 0 0 2 2 0 | * * * * * 40 * * | 0 1 0 0 0 3 0 1 | 0 3 0 1 0 3 0 3 | 0 3 0 3 1 0 3 | 1 0 3 1
.x .. .. .. .. .x | 0 4 | 0 0 0 2 0 2 | * * * * * * 40 * | 0 0 1 0 0 0 3 1 | 0 0 3 1 0 0 3 3 | 0 0 3 3 0 1 3 | 0 1 3 1
.. .. .. .. .x4.x | 0 8 | 0 0 0 0 4 4 | * * * * * * * 5 ♦ 0 0 0 1 0 0 0 4 | 0 0 0 4 0 0 0 6 | 0 0 0 6 0 0 4 | 0 0 4 1
---------------------+------+-----------------+-----------------------+------------------------+------------------------+------------------+--------
ox3oo .. .. .. ..&#x ♦ 1 3 | 0 0 3 3 0 0 | 0 3 0 0 1 0 0 0 | 80 * * * * * * * | 2 1 1 0 0 0 0 0 | 1 2 2 1 0 0 0 | 1 1 2 0
ox .. .. .. xx ..&#x ♦ 2 4 | 1 0 4 2 2 0 | 0 2 2 0 0 1 0 0 | * 40 * * * * * * | 0 3 0 1 0 0 0 0 | 0 3 0 3 0 0 0 | 1 0 3 0
ox .. .. .. .. xx&#x ♦ 2 4 | 0 1 4 2 0 2 | 0 2 0 2 0 0 1 0 | * * 40 * * * * * | 0 0 3 1 0 0 0 0 | 0 0 3 3 0 0 0 | 0 1 3 0
.. .. .. .. xx4xx&#x ♦ 8 8 | 4 4 8 0 4 4 | 1 0 4 4 0 0 0 1 | * * * 5 * * * * ♦ 0 0 0 4 0 0 0 0 | 0 0 0 6 0 0 0 | 0 0 4 0
.x3.o3.o .. .. .. ♦ 0 4 | 0 0 0 6 0 0 | 0 0 0 0 4 0 0 0 | * * * * 40 * * * | 1 0 0 0 1 1 1 0 | 1 1 1 0 1 1 1 | 1 1 1 1
.x3.o .. .. .x .. ♦ 0 6 | 0 0 0 6 3 0 | 0 0 0 0 2 3 0 0 | * * * * * 40 * * | 0 1 0 0 0 2 0 1 | 0 2 0 1 1 0 2 | 1 0 2 1
.x3.o .. .. .. .x ♦ 0 6 | 0 0 0 6 0 3 | 0 0 0 0 2 0 3 0 | * * * * * * 40 * | 0 0 1 0 0 0 2 1 | 0 0 2 1 0 1 2 | 0 1 2 1
.x .. .. .. .x4.x ♦ 0 16 | 0 0 0 8 8 8 | 0 0 0 0 0 4 4 2 | * * * * * * * 10 ♦ 0 0 0 1 0 0 0 3 | 0 0 0 3 0 0 3 | 0 0 3 1
---------------------+------+-----------------+-----------------------+------------------------+------------------------+------------------+--------
ox3oo3oo .. .. ..&#x |♦1 4 | 0 0 4 6 0 0 | 0 6 0 0 4 0 0 0 | 4 0 0 0 1 0 0 0 | 40 * * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0
ox3oo .. .. xx ..&#x ♦ 2 6 | 1 0 6 6 3 0 | 0 6 3 0 2 3 0 0 | 2 3 0 0 0 1 0 0 | * 40 * * * * * * | 0 2 0 1 0 0 0 | 1 0 2 0
ox3oo .. .. .. xx&#x ♦ 2 6 | 0 1 6 6 0 3 | 0 6 0 3 2 0 3 0 | 2 0 3 0 0 0 1 0 | * * 40 * * * * * | 0 0 2 1 0 0 0 | 0 1 2 0
ox .. .. .. xx4xx&#x ♦ 8 16 | 4 4 16 8 8 8 | 1 8 8 8 0 4 4 2 | 0 4 4 2 0 0 0 1 | * * * 10 * * * * | 0 0 0 3 0 0 0 | 0 0 3 0
.x3.o3.o3.o .. .. ♦ 0 5 | 0 0 0 10 0 0 | 0 0 0 0 10 0 0 0 | 0 0 0 0 5 0 0 0 | * * * * 8 * * * | 1 0 0 0 1 1 0 | 1 1 0 1
.x3.o3.o .. .x .. ♦ 0 8 | 0 0 0 12 4 0 | 0 0 0 0 8 6 0 0 | 0 0 0 0 2 4 0 0 | * * * * * 20 * * | 0 1 0 0 1 0 1 | 1 0 1 1
.x3.o3.o .. .. .x ♦ 0 8 | 0 0 0 12 0 4 | 0 0 0 0 8 0 6 0 | 0 0 0 0 2 0 4 0 | * * * * * * 20 * | 0 0 1 0 0 1 1 | 0 1 1 1
.x3.o .. .. .x4.x ♦ 0 24 | 0 0 0 24 12 12 | 0 0 0 0 8 12 12 3 | 0 0 0 0 0 4 4 3 | * * * * * * * 10 | 0 0 0 1 0 0 2 | 0 0 2 1
---------------------+------+-----------------+-----------------------+------------------------+------------------------+------------------+--------
ox3oo3oo3oo .. ..&#x ♦ 1 5 | 0 0 5 10 0 0 | 0 10 0 0 10 0 0 0 | 10 0 0 0 5 0 0 0 | 5 0 0 0 1 0 0 0 | 8 * * * * * * | 1 1 0 0
ox3oo3oo .. xx ..&#x ♦ 2 8 | 1 0 8 12 4 0 | 0 12 4 0 8 6 0 0 | 8 6 0 0 2 4 0 0 | 2 4 0 0 0 1 0 0 | * 20 * * * * * | 1 0 1 0
ox3oo3oo .. .. xx&#x ♦ 2 8 | 0 1 8 12 0 4 | 0 12 0 4 8 0 6 0 | 8 0 6 0 2 0 4 0 | 2 0 4 0 0 0 1 0 | * * 20 * * * * | 0 1 1 0
ox3oo .. .. xx4xx&#x ♦ 8 24 | 4 4 24 24 12 12 | 1 24 12 12 8 12 12 3 | 8 12 12 3 0 4 4 3 | 0 4 4 3 0 0 0 1 | * * * 10 * * * | 0 0 2 0
.x3.o3.o3.o .x .. ♦ 0 10 | 0 0 0 20 5 0 | 0 0 0 0 20 10 0 0 | 0 0 0 0 10 10 0 0 | 0 0 0 0 2 5 0 0 | * * * * 4 * * | 1 0 0 1
.x3.o3.o3.o .. .x ♦ 0 10 | 0 0 0 20 0 5 | 0 0 0 0 20 0 10 0 | 0 0 0 0 10 0 10 0 | 0 0 0 0 2 0 5 0 | * * * * * 4 * | 0 1 0 1
.x3.o3.o .. .x4.x ♦ 0 32 | 0 0 0 48 16 16 | 0 0 0 0 32 24 24 4 | 0 0 0 0 8 16 16 6 | 0 0 0 0 0 4 4 4 | * * * * * * 5 | 0 0 1 1
---------------------+------+-----------------+-----------------------+------------------------+------------------------+------------------+--------
ox3oo3oo3oo xx ..&#x ♦ 2 10 | 1 0 10 20 5 0 | 0 20 5 0 20 10 0 0 | 20 10 0 0 10 10 0 0 | 10 10 0 0 2 5 0 0 | 2 5 0 0 1 0 0 | 4 * * *
ox3oo3oo3oo .. xx&#x ♦ 2 10 | 0 1 10 20 0 5 | 0 20 0 5 20 0 10 0 | 20 0 10 0 10 0 10 0 | 10 0 10 0 2 0 5 0 | 2 0 5 0 0 1 0 | * 4 * *
ox3oo3oo .. xx4xx&#x ♦ 8 32 | 4 4 32 48 16 16 | 1 48 16 16 32 24 24 4 | 32 24 24 4 8 16 16 6 | 8 16 16 6 0 4 4 4 | 0 4 4 4 0 0 1 | * * 5 *
.x3.o3.o3.o .x4.x ♦ 0 40 | 0 0 0 80 20 20 | 0 0 0 0 80 40 40 5 | 0 0 0 0 40 40 40 10 | 0 0 0 0 8 20 20 10 | 0 0 0 0 4 4 5 | * * * 1
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