octagon duofastegium
- more general:
- n,tet-dip
- general polytopal classes:
- Wythoffian polytera segmentotera
links
| Acronym | otet |
| Name |
octagon-tetrahedron duoprism, octagon duofastegium |
| Circumradius | sqrt[(11+4 sqrt(2))/8] = 1.442951 |
| Volume | [2+sqrt(2)]/6 = 0.569036 |
| Face vector | 32, 80, 84, 46, 12 |
| Confer |
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External links |
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As abstract polytope otet is isomorphic to stotet, thereby replacing octagons by octagrams, resp. op by stop, resp. todip by tistodip.
Incidence matrix according to Dynkin symbol
x8o x3o3o . . . . . | 32 | 2 3 | 1 6 3 | 3 6 1 | 3 2 ----------+----+-------+---------+--------+---- x . . . . | 2 | 32 * | 1 3 0 | 3 3 0 | 3 1 . . x . . | 2 | * 48 | 0 2 2 | 1 4 1 | 2 2 ----------+----+-------+---------+--------+---- x8o . . . | 8 | 8 0 | 4 * * | 3 0 0 | 3 0 x . x . . | 4 | 2 2 | * 48 * | 1 2 0 | 2 1 . . x3o . | 3 | 0 3 | * * 32 | 0 2 1 | 1 2 ----------+----+-------+---------+--------+---- x8o x . . ♦ 16 | 16 8 | 2 8 0 | 6 * * | 2 0 x . x3o . ♦ 6 | 3 6 | 0 3 2 | * 32 * | 1 1 . . x3o3o ♦ 4 | 0 6 | 0 0 4 | * * 8 | 0 2 ----------+----+-------+---------+--------+---- x8o x3o . ♦ 24 | 24 24 | 3 24 8 | 3 8 0 | 4 * x . x3o3o ♦ 8 | 4 12 | 0 6 8 | 0 4 2 | * 8
x4x x3o3o . . . . . | 32 | 1 1 3 | 1 3 3 3 | 3 3 3 1 | 3 1 1 ----------+----+----------+------------+-----------+------ x . . . . | 2 | 16 * * | 1 3 0 0 | 3 3 0 0 | 3 1 0 . x . . . | 2 | * 16 * | 1 0 3 0 | 3 0 3 0 | 3 0 1 . . x . . | 2 | * * 48 | 0 1 1 2 | 1 2 2 1 | 2 1 1 ----------+----+----------+------------+-----------+------ x4x . . . | 8 | 4 4 0 | 4 * * * | 3 0 0 0 | 3 0 0 x . x . . | 4 | 2 0 2 | * 24 * * | 1 2 0 0 | 2 1 0 . x x . . | 4 | 0 2 2 | * * 24 * | 1 0 2 0 | 2 0 1 . . x3o . | 3 | 0 0 3 | * * * 32 | 0 1 1 1 | 1 1 1 ----------+----+----------+------------+-----------+------ x4x x . . ♦ 16 | 8 8 8 | 2 4 4 0 | 6 * * * | 2 0 0 x . x3o . ♦ 6 | 3 0 6 | 0 3 0 2 | * 16 * * | 1 1 0 . x x3o . ♦ 6 | 0 3 6 | 0 0 3 2 | * * 16 * | 1 0 1 . . x3o3o ♦ 4 | 0 0 6 | 0 0 0 4 | * * * 8 | 0 1 1 ----------+----+----------+------------+-----------+------ x4x x3o . ♦ 24 | 12 12 24 | 3 12 12 8 | 3 4 4 0 | 4 * * x . x3o3o ♦ 8 | 4 0 12 | 0 6 0 8 | 0 4 0 2 | * 4 * . x x3o3o ♦ 8 | 0 4 12 | 0 0 6 8 | 0 0 4 2 | * * 4
ox3oo xx8oo&#x → height = sqrt(2/3) = 0.816497
({8} || todip)
o.3o. o.8o. | 8 * | 2 3 0 0 | 1 3 6 0 0 0 | 1 6 3 0 0 | 2 3 0
.o3.o .o8.o | * 24 | 0 1 2 2 | 0 2 2 1 4 1 | 1 4 1 2 2 | 2 2 1
---------------+------+------------+----------------+------------+------
.. .. x. .. | 2 0 | 8 * * * | 1 0 3 0 0 0 | 0 3 3 0 0 | 1 3 0
oo3oo oo8oo&#x | 1 1 | * 24 * * | 0 2 2 0 0 0 | 1 4 1 0 0 | 2 2 0
.x .. .. .. | 0 2 | * * 24 * | 0 1 0 1 2 0 | 1 2 0 2 1 | 2 1 1
.. .. .x .. | 0 2 | * * * 24 | 0 0 1 0 2 1 | 0 2 1 1 2 | 1 2 1
---------------+------+------------+----------------+------------+------
.. .. x.8o. | 8 0 | 8 0 0 0 | 1 * * * * * | 0 0 3 0 0 | 0 3 0
ox .. .. ..&#x | 1 2 | 0 2 1 0 | * 24 * * * * | 1 2 0 0 0 | 2 1 0
.. .. xx ..&#x | 2 2 | 1 2 0 1 | * * 24 * * * | 0 2 1 0 0 | 1 2 0
.x3.o .. .. | 0 3 | 0 0 3 0 | * * * 8 * * | 1 0 0 2 0 | 2 0 1
.x .. .x .. | 0 4 | 0 0 2 2 | * * * * 24 * | 0 1 0 1 1 | 1 1 1
.. .. .x8.o | 0 8 | 0 0 0 8 | * * * * * 3 | 0 0 1 0 2 | 0 2 1
---------------+------+------------+----------------+------------+------
ox3oo .. ..&#x ♦ 1 3 | 0 3 3 0 | 0 3 0 1 0 0 | 8 * * * * | 2 0 0
ox .. xx ..&#x ♦ 2 4 | 1 4 2 2 | 0 2 2 0 1 0 | * 24 * * * | 1 1 0
.. .. xx8oo&#x ♦ 8 8 | 8 8 0 8 | 1 0 8 0 0 1 | * * 3 * * | 0 2 0
.x3.o .x .. ♦ 0 6 | 0 0 6 3 | 0 0 0 2 3 0 | * * * 8 * | 1 0 1
.x .. .x8.o ♦ 0 16 | 0 0 8 16 | 0 0 0 0 8 2 | * * * * 3 | 0 1 1
---------------+------+------------+----------------+------------+------
ox3oo xx .. ♦ 2 6 | 1 6 6 3 | 0 6 3 2 3 0 | 2 3 0 1 0 | 8 * *
ox .. xx8oo&#x ♦ 8 16 | 8 16 8 16 | 1 8 16 0 8 2 | 0 8 2 0 1 | * 3 *
.x3.o .x8.o ♦ 0 24 | 0 0 24 24 | 0 0 0 8 24 3 | 0 0 0 8 3 | * * 1
ox xo xx8oo&#x → height = 1/sqrt(2) = 0.707107
(op || lacing-ortho op)
o. o. o.8o. | 16 * | 1 2 2 0 0 | 2 1 1 2 4 0 0 | 1 1 2 4 2 0 | 2 1 2
.o .o .o8.o | * 16 | 0 0 2 1 2 | 0 0 2 1 4 2 1 | 0 1 4 2 2 1 | 2 2 1
---------------+-------+--------------+------------------+---------------+------
.. x. .. .. | 2 0 | 8 * * * * | 2 0 0 2 0 0 0 | 1 1 0 2 0 0 | 2 0 2
.. .. x. .. | 2 0 | * 16 * * * | 1 1 0 0 2 0 0 | 1 0 1 2 2 0 | 1 1 2
oo oo oo8oo&#x | 1 1 | * * 32 * * | 0 0 1 1 2 0 0 | 0 1 2 2 1 0 | 2 1 1
.x .. .. .. | 0 2 | * * * 8 * | 0 0 2 0 0 2 0 | 0 1 4 0 0 1 | 2 2 0
.. .. .x .. | 0 2 | * * * * 16 | 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 | 8 * * * * * * | 1 0 0 2 0 0 | 1 0 2
.. .. x.8o. | 8 0 | 0 8 0 0 0 | * 2 * * * * * | 1 0 0 0 2 0 | 0 1 2
ox .. .. ..&#x | 1 2 | 0 0 2 1 0 | * * 16 * * * * | 0 1 2 0 0 0 | 2 1 0
.. xo .. ..&#x | 2 1 | 1 0 2 0 0 | * * * 16 * * * | 0 1 0 2 0 0 | 2 0 1
.. .. xx ..&#x | 2 2 | 0 1 2 0 1 | * * * * 32 * * | 0 0 1 1 1 0 | 1 1 1
.x .. .x .. | 0 4 | 0 0 0 2 2 | * * * * * 8 * | 0 0 2 0 0 1 | 1 2 0
.. .. .x8.o | 0 8 | 0 0 0 0 8 | * * * * * * 2 | 0 0 0 0 2 1 | 0 2 1
---------------+-------+--------------+------------------+---------------+------
.. x. x.8o. ♦ 16 0 | 8 16 0 0 0 | 8 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 | * 8 * * * * | 2 0 0
ox .. xx ..&#x ♦ 2 4 | 0 1 4 2 2 | 0 0 2 0 2 1 0 | * * 16 * * * | 1 1 0
.. xo xx ..&#x ♦ 4 2 | 2 2 4 0 1 | 1 0 0 2 2 0 0 | * * * 16 * * | 1 0 1
.. .. xx8oo&#x ♦ 8 8 | 0 8 8 0 8 | 0 1 0 0 8 0 1 | * * * * 4 * | 0 1 1
.x .. .x8.o ♦ 0 16 | 0 0 0 8 16 | 0 0 0 0 0 8 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 | 8 * *
ox .. xx8oo&#x ♦ 8 16 | 0 8 16 8 16 | 0 1 8 0 16 8 2 | 0 0 8 0 2 1 | * 2 *
.. xo xx8oo&#x ♦ 16 8 | 8 16 16 0 8 | 8 2 0 8 16 0 1 | 1 0 0 8 2 0 | * * 2
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