- more general:
- n,toe-dip
- general polytopal classes:
- Wythoffian polytera
links
| Acronym | otoe (old: otto) |
| Name | octagon truncated-octahedron duoprism |
| Circumradius | sqrt[(7+sqrt(2))/2] = 2.051123 |
| Volume | 16[2+sqrt(2)] = 54.627417 |
| Face vector | 192, 480, 424, 156, 22 |
| Confer |
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External links |
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As abstract polyterton otoe is isomorphic to stotoe, thereby replacing the octagons by octagrams, resp. replacing op by stop, resp. replacing hodip by histodip and sodip by sistodip.
Incidence matrix according to Dynkin symbol
x8o x3x4o . . . . . | 192 | 2 1 2 | 1 2 4 2 1 | 1 2 4 2 1 | 2 1 2 ----------+-----+------------+-----------------+---------------+------ x . . . . | 2 | 192 * * | 1 1 2 0 0 | 1 2 2 1 0 | 2 1 1 . . x . . | 2 | * 96 * | 0 2 0 2 0 | 1 0 4 0 1 | 2 0 2 . . . x . | 2 | * * 192 | 0 0 2 1 1 | 0 1 2 2 1 | 1 1 2 ----------+-----+------------+-----------------+---------------+------ x8o . . . | 8 | 8 0 0 | 24 * * * * | 1 2 0 0 0 | 2 1 0 x . x . . | 4 | 2 2 0 | * 96 * * * | 1 0 2 0 0 | 2 0 1 x . . x . | 4 | 2 0 2 | * * 192 * * | 0 1 1 1 0 | 1 1 1 . . x3x . | 6 | 0 3 3 | * * * 64 * | 0 0 2 0 1 | 1 0 2 . . . x4o | 4 | 0 0 4 | * * * * 48 | 0 0 0 2 1 | 0 1 2 ----------+-----+------------+-----------------+---------------+------ x8o x . . ♦ 16 | 16 8 0 | 2 8 0 0 0 | 12 * * * * | 2 0 0 x8o . x . ♦ 16 | 16 0 8 | 2 0 8 0 0 | * 24 * * * | 1 1 0 x . x3x . ♦ 12 | 6 6 6 | 0 3 3 2 0 | * * 64 * * | 1 0 1 x . . x4o ♦ 8 | 4 0 8 | 0 0 4 0 2 | * * * 48 * | 0 1 1 . . x3x4o ♦ 24 | 0 12 24 | 0 0 0 8 6 | * * * * 8 | 0 0 2 ----------+-----+------------+-----------------+---------------+------ x8o x3x . ♦ 48 | 48 24 24 | 6 24 24 8 0 | 3 3 8 0 0 | 8 * * x8o . x4o ♦ 32 | 32 0 32 | 4 0 32 0 8 | 0 4 0 8 0 | * 6 * x . x3x4o ♦ 48 | 24 24 48 | 0 12 24 16 12 | 0 0 8 6 2 | * * 8
x4x x3x4o . . . . . | 192 | 1 1 1 2 | 1 1 2 1 2 1 1 | 1 2 2 1 2 1 1 | 2 1 1 1 ----------+-----+--------------+----------------------+---------------------+-------- x . . . . | 2 | 96 * * * | 1 1 2 0 0 0 0 | 1 2 2 1 0 0 0 | 2 1 1 0 . x . . . | 2 | * 96 * * | 1 0 0 1 2 0 0 | 1 2 0 0 2 1 0 | 2 1 0 1 . . x . . | 2 | * * 96 * | 0 1 0 1 0 2 0 | 1 0 2 0 2 0 1 | 2 0 1 1 . . . x . | 2 | * * * 192 | 0 0 1 0 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1 ----------+-----+--------------+----------------------+---------------------+-------- x4x . . . | 8 | 4 4 0 0 | 24 * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0 x . x . . | 4 | 2 0 2 0 | * 48 * * * * * | 1 0 2 0 0 0 0 | 2 0 1 0 x . . x . | 4 | 2 0 0 2 | * * 96 * * * * | 0 1 1 1 0 0 0 | 1 1 1 0 . x x . . | 4 | 0 2 2 0 | * * * 48 * * * | 1 0 0 0 2 0 0 | 2 0 0 1 . x . x . | 4 | 0 2 0 2 | * * * * 96 * * | 0 1 0 0 1 1 0 | 1 1 0 1 . . x3x . | 6 | 0 0 3 3 | * * * * * 64 * | 0 0 1 0 1 0 1 | 1 0 1 1 . . . x4o | 4 | 0 0 0 4 | * * * * * * 48 | 0 0 0 1 0 1 1 | 0 1 1 1 ----------+-----+--------------+----------------------+---------------------+-------- x4x x . . ♦ 16 | 8 8 8 0 | 2 4 0 4 0 0 0 | 12 * * * * * * | 2 0 0 0 x4x . x . ♦ 16 | 8 8 0 8 | 2 0 4 0 4 0 0 | * 24 * * * * * | 1 1 0 0 x . x3x . ♦ 12 | 6 0 6 6 | 0 3 3 0 0 2 0 | * * 32 * * * * | 1 0 1 0 x . . x4o ♦ 8 | 4 0 0 8 | 0 0 4 0 0 0 2 | * * * 24 * * * | 0 1 1 0 . x x3x . ♦ 12 | 0 6 6 6 | 0 0 0 3 3 2 0 | * * * * 32 * * | 1 0 0 1 . x . x4o ♦ 8 | 0 4 0 8 | 0 0 0 0 4 0 2 | * * * * * 24 * | 0 1 0 1 . . x3x4o ♦ 24 | 0 0 12 24 | 0 0 0 0 0 8 6 | * * * * * * 8 | 0 0 1 1 ----------+-----+--------------+----------------------+---------------------+-------- x4x x3x . ♦ 48 | 24 24 24 24 | 6 12 12 12 12 8 0 | 3 3 4 0 4 0 0 | 8 * * * x4x . x4o ♦ 32 | 16 16 0 32 | 4 0 16 0 16 0 8 | 0 4 0 4 0 4 0 | * 6 * * x . x3x4o ♦ 48 | 24 0 24 48 | 0 12 24 0 0 16 12 | 0 0 8 6 0 0 2 | * * 4 * . x x3x4o ♦ 48 | 0 24 24 48 | 0 0 0 12 24 16 12 | 0 0 0 0 8 6 2 | * * * 4
x8o x3x3x . . . . . | 192 | 2 1 1 1 | 1 2 2 2 1 1 1 | 1 1 1 2 2 2 1 | 1 1 1 2 ----------+-----+--------------+----------------------+---------------------+-------- x . . . . | 2 | 192 * * * | 1 1 1 1 0 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1 . . x . . | 2 | * 96 * * | 0 2 0 0 1 1 0 | 1 0 0 2 2 0 1 | 1 1 0 2 . . . x . | 2 | * * 96 * | 0 0 2 0 1 0 1 | 0 1 0 2 0 2 1 | 1 0 1 2 . . . . x | 2 | * * * 96 | 0 0 0 2 0 1 1 | 0 0 1 0 2 2 1 | 0 1 1 2 ----------+-----+--------------+----------------------+---------------------+-------- x8o . . . | 8 | 8 0 0 0 | 24 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0 x . x . . | 4 | 2 2 0 0 | * 96 * * * * * | 1 0 0 1 1 0 0 | 1 1 0 1 x . . x . | 4 | 2 0 2 0 | * * 96 * * * * | 0 1 0 1 0 1 0 | 1 0 1 1 x . . . x | 4 | 2 0 0 2 | * * * 96 * * * | 0 0 1 0 1 1 0 | 0 1 1 1 . . x3x . | 6 | 0 3 3 0 | * * * * 32 * * | 0 0 0 2 0 0 1 | 1 0 0 2 . . x . x | 4 | 0 2 0 2 | * * * * * 48 * | 0 0 0 0 2 0 1 | 0 1 0 2 . . . x3x | 6 | 0 0 3 3 | * * * * * * 64 | 0 0 0 0 0 2 1 | 0 0 1 2 ----------+-----+--------------+----------------------+---------------------+-------- x8o x . . ♦ 16 | 16 8 0 0 | 2 8 0 0 0 0 0 | 12 * * * * * * | 1 1 0 0 x8o . x . ♦ 16 | 16 0 8 0 | 2 0 8 0 0 0 0 | * 12 * * * * * | 1 0 1 0 x8o . . x ♦ 16 | 16 0 0 8 | 2 0 0 8 0 0 0 | * * 12 * * * * | 0 1 1 0 x . x3x . ♦ 12 | 6 6 6 0 | 0 3 3 0 2 0 0 | * * * 32 * * * | 1 0 0 1 x . x . x ♦ 8 | 4 4 0 4 | 0 2 0 2 0 2 0 | * * * * 48 * * | 0 1 0 1 x . . x3x ♦ 12 | 6 0 6 6 | 0 0 3 3 0 0 2 | * * * * * 32 * | 0 0 1 1 . . x3x3x ♦ 24 | 0 12 12 12 | 0 0 0 0 4 6 4 | * * * * * * 8 | 0 0 0 2 ----------+-----+--------------+----------------------+---------------------+-------- x8o x3x . ♦ 48 | 48 24 24 0 | 6 24 24 0 8 0 0 | 3 3 0 8 0 0 0 | 4 * * * x8o x . x ♦ 32 | 32 16 0 16 | 4 16 0 16 0 8 0 | 2 0 2 0 8 0 0 | * 6 * * x8o . x3x ♦ 48 | 48 0 24 24 | 6 0 24 24 0 0 8 | 0 3 3 0 0 8 0 | * * 4 * x . x3x3x ♦ 48 | 24 24 24 24 | 0 12 12 12 8 12 8 | 0 0 0 4 6 4 2 | * * * 8
x4x x3x3x . . . . . | 192 | 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1 ----------+-----+----------------+-------------------------------+------------------------------+---------- x . . . . | 2 | 96 * * * * | 1 1 1 1 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0 . x . . . | 2 | * 96 * * * | 1 0 0 0 1 1 1 0 0 0 | 1 1 1 0 0 0 1 1 1 0 | 1 1 1 0 1 . . x . . | 2 | * * 96 * * | 0 1 0 0 1 0 0 1 1 0 | 1 0 0 1 1 0 1 1 0 1 | 1 1 0 1 1 . . . x . | 2 | * * * 96 * | 0 0 1 0 0 1 0 1 0 1 | 0 1 0 1 0 1 1 0 1 1 | 1 0 1 1 1 . . . . x | 2 | * * * * 96 | 0 0 0 1 0 0 1 0 1 1 | 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1 ----------+-----+----------------+-------------------------------+------------------------------+---------- x4x . . . | 8 | 4 4 0 0 0 | 24 * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 x . x . . | 4 | 2 0 2 0 0 | * 48 * * * * * * * * | 1 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0 x . . x . | 4 | 2 0 0 2 0 | * * 48 * * * * * * * | 0 1 0 1 0 1 0 0 0 0 | 1 0 1 1 0 x . . . x | 4 | 2 0 0 0 2 | * * * 48 * * * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0 . x x . . | 4 | 0 2 2 0 0 | * * * * 48 * * * * * | 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1 . x . x . | 4 | 0 2 0 2 0 | * * * * * 48 * * * * | 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1 . x . . x | 4 | 0 2 0 0 2 | * * * * * * 48 * * * | 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1 . . x3x . | 6 | 0 0 3 3 0 | * * * * * * * 32 * * | 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1 . . x . x | 4 | 0 0 2 0 2 | * * * * * * * * 48 * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1 . . . x3x | 6 | 0 0 0 3 3 | * * * * * * * * * 32 | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 ----------+-----+----------------+-------------------------------+------------------------------+---------- x4x x . . ♦ 16 | 8 8 8 0 0 | 2 4 0 0 4 0 0 0 0 0 | 12 * * * * * * * * * | 1 1 0 0 0 x4x . x . ♦ 16 | 8 8 0 8 0 | 2 0 4 0 0 4 0 0 0 0 | * 12 * * * * * * * * | 1 0 1 0 0 x4x . . x ♦ 16 | 8 8 0 0 8 | 2 0 0 4 0 0 4 0 0 0 | * * 12 * * * * * * * | 0 1 1 0 0 x . x3x . ♦ 12 | 6 0 6 6 0 | 0 3 3 0 0 0 0 2 0 0 | * * * 16 * * * * * * | 1 0 0 1 0 x . x . x ♦ 8 | 4 0 4 0 4 | 0 2 0 2 0 0 0 0 2 0 | * * * * 24 * * * * * | 0 1 0 1 0 x . . x3x ♦ 12 | 6 0 0 6 6 | 0 0 3 3 0 0 0 0 0 2 | * * * * * 16 * * * * | 0 0 1 1 0 . x x3x . ♦ 12 | 0 6 6 6 0 | 0 0 0 0 3 3 0 2 0 0 | * * * * * * 16 * * * | 1 0 0 0 1 . x x . x ♦ 8 | 0 4 4 0 4 | 0 0 0 0 2 0 2 0 2 0 | * * * * * * * 24 * * | 0 1 0 0 1 . x . x3x ♦ 12 | 0 6 0 6 6 | 0 0 0 0 0 3 3 0 0 2 | * * * * * * * * 16 * | 0 0 1 0 1 . . x3x3x ♦ 24 | 0 0 12 12 12 | 0 0 0 0 0 0 0 4 6 4 | * * * * * * * * * 8 | 0 0 0 1 1 ----------+-----+----------------+-------------------------------+------------------------------+---------- x4x x3x . ♦ 48 | 24 24 24 24 0 | 6 12 12 0 12 12 0 8 0 0 | 3 3 0 4 0 0 4 0 0 0 | 4 * * * * x4x x . x ♦ 32 | 16 16 16 0 16 | 4 8 0 8 8 0 8 0 8 0 | 2 0 2 0 4 0 0 4 0 0 | * 6 * * * x4x . x3x ♦ 48 | 24 24 0 24 24 | 6 0 12 12 0 12 12 0 0 8 | 0 3 3 0 0 4 0 0 4 0 | * * 4 * * x . x3x3x ♦ 48 | 24 0 24 24 24 | 0 12 12 12 0 0 0 8 12 8 | 0 0 0 4 6 4 0 0 0 2 | * * * 4 * . x x3x3x ♦ 48 | 0 24 24 24 24 | 0 0 0 0 12 12 12 8 12 8 | 0 0 0 0 0 0 4 6 4 2 | * * * * 4
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