Acronym otoe (old: otto) Name octagon truncated-octahedron duoprism Circumradius sqrt[(7+sqrt(2))/2] = 2.051123 Volume 16[2+sqrt(2)] = 54.627417 Confer n,toe-dip Externallinks

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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