Acronym trope (old: troctip) Name triangle-octahedron duoprismatic prism Circumradius sqrt(13/12) = 1.040833 Volume sqrt(6)/12 = 0.204124 Confer n-oct-dippip

Incidence matrix according to Dynkin symbol

```x x3o x3o4o

. . . . . . | 36 |  1  2  4 |  2  4  1  8  4 | 1  8  4  4  8 1 |  4  8 1  4 2 | 4 2 1
------------+----+----------+----------------+-----------------+--------------+------
x . . . . . |  2 | 18  *  * |  2  4  0  0  0 | 1  8  4  0  0 0 |  4  8 1  0 0 | 4 2 0
. x . . . . |  2 |  * 36  * |  1  0  1  4  0 | 1  4  0  4  4 0 |  4  4 0  4 1 | 4 1 1
. . . x . . |  2 |  *  * 72 |  0  1  0  2  2 | 0  2  2  1  4 1 |  1  4 1  2 2 | 2 2 1
------------+----+----------+----------------+-----------------+--------------+------
x x . . . . |  4 |  2  2  0 | 18  *  *  *  * | 1  4  0  0  0 0 |  4  4 0  0 0 | 4 1 0
x . . x . . |  4 |  2  0  2 |  * 36  *  *  * | 0  2  2  0  0 0 |  1  4 1  0 0 | 2 2 0
. x3o . . . |  3 |  0  3  0 |  *  * 12  *  * | 1  0  0  4  0 0 |  4  0 0  4 0 | 4 0 1
. x . x . . |  4 |  0  2  2 |  *  *  * 72  * | 0  1  0  1  2 0 |  1  2 0  2 1 | 2 1 1
. . . x3o . |  3 |  0  0  3 |  *  *  *  * 48 | 0  0  1  0  2 1 |  0  2 1  1 2 | 1 2 1
------------+----+----------+----------------+-----------------+--------------+------
x x3o . . . ♦  6 |  3  6  0 |  3  0  2  0  0 | 6  *  *  *  * * |  4  0 0  0 0 | 4 0 0
x x . x . . ♦  8 |  4  4  4 |  2  2  0  2  0 | * 36  *  *  * * |  1  2 0  0 0 | 2 1 0
x . . x3o . ♦  6 |  3  0  6 |  0  3  0  0  2 | *  * 24  *  * * |  0  2 1  0 0 | 1 2 0
. x3o x . . ♦  6 |  0  6  3 |  0  0  2  3  0 | *  *  * 24  * * |  1  0 0  2 0 | 2 0 1
. x . x3o . ♦  6 |  0  3  6 |  0  0  0  3  2 | *  *  *  * 48 * |  0  1 0  1 1 | 1 1 1
. . . x3o4o ♦  6 |  0  0 12 |  0  0  0  0  8 | *  *  *  *  * 6 |  0  0 1  0 2 | 0 2 1
------------+----+----------+----------------+-----------------+--------------+------
x x3o x . . ♦ 12 |  6 12  6 |  6  3  4  6  0 | 2  3  0  2  0 0 | 12  * *  * * | 2 0 0
x x . x3o . ♦ 12 |  6  6 12 |  3  6  0  6  4 | 0  3  2  0  2 0 |  * 24 *  * * | 1 1 0
x . . x3o4o ♦ 12 |  6  0 24 |  0 12  0  0 16 | 0  0  8  0  0 2 |  *  * 3  * * | 0 2 0
. x3o x3o . ♦  9 |  0  9  9 |  0  0  3  9  3 | 0  0  0 3  3  0 |  *  * * 16 * | 1 0 1
. x . x3o4o ♦ 12 |  0  6 24 |  0  0  0 12 16 | 0  0  0  0  8 2 |  *  * *  * 6 | 0 1 1
------------+----+----------+----------------+-----------------+--------------+------
x x3o x3o . ♦ 18 |  9 18 18 |  9  9  6 18  6 | 3  9  3  6  6 0 |  3  3 0  2 0 | 8 * *
x x . x3o4o ♦ 24 | 12 12 48 |  6 24  0 24 32 | 0 12 16  0 16 4 |  0  8 2  0 2 | * 3 *
. x3o x3o4o ♦ 18 |  0 18 36 |  0  0  6 36 24 | 0  0  0 12 24 3 |  0  0 0  8 3 | * * 2
```

```x x3o o3x3o

. . . . . . | 36 |  1  2  4 |  2  4  1  8  2  2 | 1   8  2  2  4  4  4 1 |  4  4  4 1 2 2 2 | 2 2 2 1
------------+----+----------+-------------------+------------------------+------------------+--------
x . . . . . |  2 | 18  *  * |  2  4  0  0  0  0 | 1   8  2  2  0  0  0 0 |  4  4  4 1 0 0 0 | 2 2 2 0
. x . . . . |  2 |  * 36  * |  1  0  1  4  0  0 | 1   4  0  0  4  2  2 0 |  4  2  2 0 2 2 1 | 2 2 1 1
. . . . x . |  2 |  *  * 72 |  0  1  0  2  1  1 | 0   2  1  1  1  2  2 1 |  1  2  2 1 1 1 2 | 1 1 2 1
------------+----+----------+-------------------+------------------------+------------------+--------
x x . . . . |  4 |  2  2  0 | 18  *  *  *  *  * | 1   4  0  0  0  0  0 0 |  4  2  2 0 0 0 0 | 2 2 1 0
x . . . x . |  4 |  2  0  2 |  * 36  *  *  *  * | 0   2  1  1  0  0  0 0 |  1  2  2 1 0 0 0 | 1 1 2 0
. x3o . . . |  3 |  0  3  0 |  *  * 12  *  *  * | 1   0  0  0  4  0  0 0 |  4  0  0 0 2 2 0 | 2 2 0 1
. x . . x . |  4 |  0  2  2 |  *  *  * 72  *  * | 0   1  0  0  1  1  1 0 |  1  1  1 0 1 1 1 | 1 1 1 1
. . . o3x . |  3 |  0  0  3 |  *  *  *  * 24  * | 0   0  1  0  0  2  0 1 |  0  2  0 1 1 0 2 | 1 0 2 1
. . . . x3o |  3 |  0  0  3 |  *  *  *  *  * 24 | 0   0  0  1  0  0  2 1 |  0  0  2 1 0 1 2 | 0 1 2 1
------------+----+----------+-------------------+------------------------+------------------+--------
x x3o . . . ♦  6 |  3  6  0 |  3  0  2  0  0  0 | 6   *  *  *  *  *  * * |  4  0  0 0 0 0 0 | 2 2 0 0
x x . . x . ♦  8 |  4  4  4 |  2  2  0  2  0  0 | *  36  *  *  *  *  * * |  1  1  1 0 0 0 0 | 1 1 1 0
x . . o3x . ♦  6 |  3  0  6 |  0  3  0  0  2  0 | *   * 12  *  *  *  * * |  0  2  0 1 0 0 0 | 1 0 2 0
x . . . x3o ♦  6 |  3  0  6 |  0  3  0  0  0  2 | *   *  * 12  *  *  * * |  0  0  2 1 0 0 0 | 0 1 2 0
. x3o . x . ♦  6 |  0  6  3 |  0  0  2  3  0  0 | *   *  *  * 24  *  * * |  1  0  0 0 1 1 0 | 1 1 0 1
. x . o3x . ♦  6 |  0  3  6 |  0  0  0  3  2  0 | *   *  *  *  * 24  * * |  0  1  0 0 1 0 1 | 1 0 1 1
. x . . x3o ♦  6 |  0  3  6 |  0  0  0  3  0  2 | *   *  *  *  *  * 24 * |  0  0  1 0 0 1 1 | 0 1 1 1
. . . o3x3o ♦  6 |  0  0 12 |  0  0  0  0  4  4 | *   *  *  *  *  *  * 6 |  0  0  0 1 0 0 2 | 0 0 2 1
------------+----+----------+-------------------+------------------------+------------------+--------
x x3o . x . ♦ 12 |  6 12  6 |  6  3  4  6  0  0 | 2   3  0  0  2  0  0 0 | 12  *  * * * * * | 1 1 0 0
x x . o3x . ♦ 12 |  6  6 12 |  3  6  0  6  4  0 | 0   3  2  0  0  2  0 0 |  * 12  * * * * * | 1 0 1 0
x x . . x3o ♦ 12 |  6  6 12 |  3  6  0  6  0  4 | 0   3  0  2  0  0  2 0 |  *  * 12 * * * * | 0 1 1 0
x . . o3x3o ♦ 12 |  6  0 24 |  0 12  0  0  8  8 | 0   0  4  4  0  0  0 2 |  *  *  * 3 * * * | 0 0 2 0
. x3o o3x . ♦  9 |  0  9  9 |  0  0  3  9  3  0 | 0   0  0  0  3  3  0 0 |  *  *  * * 8 * * | 1 0 0 1
. x3o . x3o ♦  9 |  0  9  9 |  0  0  3  9  0  3 | 0   0  0  0  3  0  3 0 |  *  *  * * * 8 * | 0 1 0 1
. x . o3x3o ♦ 12 |  0  6 24 |  0  0  0 12  8  8 | 0   0  0  0  0  4  4 2 |  *  *  * * * * 6 | 0 0 1 1
------------+----+----------+-------------------+------------------------+------------------+--------
x x3o o3x . ♦ 18 |  9 18 18 |  9  9  6 18  6  0 | 3   9  3  0  6  6  0 0 |  3  3  0 0 2 0 0 | 4 * * *
x x3o . x3o ♦ 18 |  9 18 18 |  9  9  6 18  0  6 | 3   9  0  3  6  0  6 0 |  3  0  3 0 2 0 0 | * 4 * *
x x . o3x3o ♦ 24 | 12 12 48 |  6 24  0 24 16 16 | 0  12  8  8  0  8  8 4 |  0  4  4 2 0 0 2 | * * 3 *
. x3o o3x3o ♦ 18 |  0 18 36 |  0  0  6 36 12 12 | 0   0  0  0 12 12 12 3 |  0  0  0 0 4 4 3 | * * * 2
```

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