Acronym octrap Name octahedron - rectified-pentachoron duoprism Circumradius sqrt(11/10) = 1.048809

Incidence matrix according to Dynkin symbol

```x3o4o o3x3o3o

. . . . . . . | 60 |   4   6 |  4  24  3   6 |  1  24  12  24  3  2 |  6 12  24 12  8 1 |  3  6 12  8  4 | 3 2 4
--------------+----+---------+---------------+----------------------+-------------------+----------------+------
x . . . . . . |  2 | 120   * |  2   6  0   0 |  1  12   3   6  0  0 |  6  6  12  3  2 0 |  3  6  6  4  1 | 3 2 2
. . . . x . . |  2 |   * 180 |  0   4  1   2 |  0   4   4   8  2  1 |  1  4   8  8  4 1 |  1  2  8  4  4 | 2 1 4
--------------+----+---------+---------------+----------------------+-------------------+----------------+------
x3o . . . . . |  3 |   3   0 | 80   *  *   * |  1   6   0   0  0  0 |  6  3   6  0  0 0 |  3  6  3  2  0 | 3 2 1
x . . . x . . |  4 |   2   2 |  * 360  *   * |  0   2   1   2  0  0 |  1  2   4  2  1 0 |  1  2  4  2  1 | 2 1 2
. . . o3x . . |  3 |   0   3 |  *   * 60   * |  0   0   4   0  2  0 |  0  4   0  8  0 1 |  1  0  8  0  4 | 2 0 4
. . . . x3o . |  3 |   0   3 |  *   *  * 120 |  0   0   0   4  1  1 |  0  0   4  4  4 1 |  0  1  4  4  4 | 1 1 4
--------------+----+---------+---------------+----------------------+-------------------+----------------+------
x3o4o . . . . ♦  6 |  12   0 |  8   0  0   0 | 10   *   *   *  *  * ♦  6  0   0  0  0 0 |  3  6  0  0  0 | 3 2 0
x3o . . x . . ♦  6 |   6   3 |  2   3  0   0 |  * 240   *   *  *  * |  1  1   2  0  0 0 |  1  2  2  1  0 | 2 1 1
x . . o3x . . ♦  6 |   3   6 |  0   3  2   0 |  *   * 120   *  *  * |  0  2   0  2  0 0 |  1  0  4  0  1 | 2 0 2
x . . . x3o . ♦  6 |   3   6 |  0   3  0   2 |  *   *   * 240  *  * |  0  0   2  1  1 0 |  0  1  2  2  1 | 1 1 2
. . . o3x3o . ♦  6 |   0  12 |  0   0  4   4 |  *   *   *   * 30  * |  0  0   0  4  0 1 |  0  0  4  0  4 | 1 0 4
. . . . x3o3o ♦  4 |   0   6 |  0   0  0   4 |  *   *   *   *  * 30 |  0  0   0  0  4 1 |  0  0  0  4  4 | 0 1 4
--------------+----+---------+---------------+----------------------+-------------------+----------------+------
x3o4o . x . . ♦ 12 |  24   6 | 16  12  0   0 |  2   8   0   0  0  0 | 30  *   *  *  * * |  1  2  0  0  0 | 2 1 0
x3o . o3x . . ♦  9 |   9   9 |  3   9  3   0 |  0   3   3   0  0  0 |  * 80   *  *  * * |  1  0  2  0  0 | 2 0 1
x3o . . x3o . ♦  9 |   9   9 |  3   9  0   3 |  0   3   0   3  0  0 |  *  * 160  *  * * |  0  1  1  1  0 | 1 1 1
x . . o3x3o . ♦ 12 |   6  24 |  0  12  8   8 |  0   0   4   4  2  0 |  *  *   * 60  * * |  0  0  2  0  1 | 1 0 2
x . . . x3o3o ♦  8 |   4  12 |  0   6  0   8 |  0   0   0   4  0  2 |  *  *   *  * 60 * |  0  0  0  2  1 | 0 1 2
. . . o3x3o3o ♦ 10 |   0  30 |  0   0 10  20 |  0   0   0   0  5  5 |  *  *   *  *  * 6 |  0  0  0  0  4 | 0 0 4
--------------+----+---------+---------------+----------------------+-------------------+----------------+------
x3o4o o3x . . ♦ 18 |  36  18 | 24  36  6   0 |  3  24  12   0  0  0 |  3  8   0  0  0 0 | 10  *  *  *  * | 2 0 0
x3o4o . x3o . ♦ 18 |  36  18 | 24  36  0   6 |  3  24   0  12  0  0 |  3  0   8  0  0 0 |  * 20  *  *  * | 1 1 0
x3o . o3x3o . ♦ 18 |  18  36 |  6  36 12  12 |  0  12  12  12  3  0 |  0  4   4  3  0 0 |  *  * 40  *  * | 1 0 1
x3o . . x3o3o ♦ 12 |  12  18 |  4  18  0  12 |  0   6   0  12  0  3 |  0  0   4  0  3 0 |  *  *  * 40  * | 0 1 1
x . . o3x3o3o ♦ 20 |  10  60 |  0  30 20  40 |  0   0  10  20 10 10 |  0  0   0  5  5 2 |  *  *  *  * 12 | 0 0 2
--------------+----+---------+---------------+----------------------+-------------------+----------------+------
x3o4o o3x3o . ♦ 36 |  72  72 | 48 144 24  24 |  6  96  48  48  6  0 | 12 32  32 12  0 0 |  4  4  8  0  0 | 5 * *
x3o4o . x3o3o ♦ 24 |  48  36 | 32  72  0  24 |  4  48   0  48  0  6 |  6  0  32  0 12 0 |  0  4  0  8  0 | * 5 *
x3o . o3x3o3o ♦ 30 |  30  90 | 10  90 30  60 |  0  30  30  60 15 15 |  0 10  20 15 15 3 |  0  0  5  5  3 | * * 8
```

```o3x3o o3x3o3o

. . . . . . . | 60 |   4   6 |  2  2  24  3   6 |  1  12  12  12  24  3  2 |  6  6 12  6 12 12  8 1 |  3  6  6  4  6  4  4 | 3 2 2 2
--------------+----+---------+------------------+--------------------------+------------------------+----------------------+--------
. x . . . . . |  2 | 120   * |  1  1   6  0   0 |  1   6   6   3   6  0  0 |  6  3  6  3  6  3  2 0 |  3  6  3  2  3  2  1 | 3 2 1 1
. . . . x . . |  2 |   * 180 |  0  0   4  1   2 |  0   2   2   4   8  2  1 |  1  2  4  2  4  8  4 1 |  1  2  4  2  4  2  4 | 2 1 2 2
--------------+----+---------+------------------+--------------------------+------------------------+----------------------+--------
o3x . . . . . |  3 |   3   0 | 40  *   *  *   * |  1   6   0   0   0  0  0 |  6  3  6  0  0  0  0 0 |  3  6  3  2  0  0  0 | 3 2 1 0
. x3o . . . . |  3 |   3   0 |  * 40   *  *   * |  1   0   6   0   0  0  0 |  6  0  0  3  6  0  0 0 |  3  6  0  0  3  2  0 | 3 2 0 1
. x . . x . . |  4 |   2   2 |  *  * 360  *   * |  0   1   1   1   2  0  0 |  1  1  2  1  2  2  1 0 |  1  2  2  1  2  1  1 | 2 1 1 1
. . . o3x . . |  3 |   0   3 |  *  *   * 60   * |  0   0   0   4   0  2  0 |  0  2  0  2  0  8  0 1 |  1  0  4  0  4  0  4 | 2 0 2 2
. . . . x3o . |  3 |   0   3 |  *  *   *  * 120 |  0   0   0   0   4  1  1 |  0  0  2  0  2  4  4 1 |  0  1  2  2  2  2  4 | 1 1 2 2
--------------+----+---------+------------------+--------------------------+------------------------+----------------------+--------
o3x3o . . . . ♦  6 |  12   0 |  4  4   0  0   0 | 10   *   *   *   *  *  * ♦  6  0  0  0  0  0  0 0 |  3  6  0  0  0  0  0 | 3 2 0 0
o3x . . x . . ♦  6 |   6   3 |  2  0   3  0   0 |  * 120   *   *   *  *  * |  1  1  2  0  0  0  0 0 |  1  2  2  1  0  0  0 | 2 1 1 0
. x3o . x . . ♦  6 |   6   3 |  0  2   3  0   0 |  *   * 120   *   *  *  * |  1  0  0  1  2  0  0 0 |  1  2  0  0  2  1  0 | 2 1 0 1
. x . o3x . . ♦  6 |   3   6 |  0  0   3  2   0 |  *   *   * 120   *  *  * |  0  1  0  1  0  2  0 0 |  1  0  2  0  2  0  1 | 2 0 1 1
. x . . x3o . ♦  6 |   3   6 |  0  0   3  0   2 |  *   *   *   * 240  *  * |  0  0  1  0  1  1  1 0 |  0  1  1  1  1  1  1 | 1 1 1 1
. . . o3x3o . ♦  6 |   0  12 |  0  0   0  4   4 |  *   *   *   *   * 30  * |  0  0  0  0  0  4  0 1 |  0  0  2  0  2  0  4 | 1 0 2 2
. . . . x3o3o ♦  4 |   0   6 |  0  0   0  0   4 |  *   *   *   *   *  * 30 |  0  0  0  0  0  0  4 1 |  0  0  0  2  0  2  4 | 0 1 2 2
--------------+----+---------+------------------+--------------------------+------------------------+----------------------+--------
o3x3o . x . . ♦ 12 |  24   6 |  8  8  12  0   0 |  2   4   4   0   0  0  0 | 30  *  *  *  *  *  * * |  1  2  0  0  0  0  0 | 2 1 0 0
o3x . o3x . . ♦  9 |   9   9 |  3  0   9  3   0 |  0   3   0   3   0  0  0 |  * 40  *  *  *  *  * * |  1  0  2  0  0  0  0 | 2 0 1 0
o3x . . x3o . ♦  9 |   9   9 |  3  0   9  0   3 |  0   3   0   0   3  0  0 |  *  * 80  *  *  *  * * |  0  1  1  1  0  0  0 | 1 1 1 0
. x3o o3x . . ♦  9 |   9   9 |  0  3   9  3   0 |  0   0   3   3   0  0  0 |  *  *  * 40  *  *  * * |  1  0  0  0  2  0  0 | 2 0 0 1
. x3o . x3o . ♦  9 |   9   9 |  0  3   9  0   3 |  0   0   3   0   3  0  0 |  *  *  *  * 80  *  * * |  0  1  0  0  1  1  0 | 1 1 0 1
. x . o3x3o . ♦ 12 |   6  24 |  0  0  12  8   8 |  0   0   0   4   4  2  0 |  *  *  *  *  * 60  * * |  0  0  1  0  1  0  1 | 1 0 1 1
. x . . x3o3o ♦  8 |   4  12 |  0  0   6  0   8 |  0   0   0   0   4  0  2 |  *  *  *  *  *  * 60 * |  0  0  0  1  0  1  1 | 0 1 1 1
. . . o3x3o3o ♦ 10 |   0  30 |  0  0   0 10  20 |  0   0   0   0   0  5  5 |  *  *  *  *  *  *  * 6 |  0  0  0  0  0  0  4 | 0 0 2 2
--------------+----+---------+------------------+--------------------------+------------------------+----------------------+--------
o3x3o o3x . . ♦ 18 |  36  18 | 12 12  36  6   0 |  3  12  12  12   0  0  0 |  3  4  0  4  0  0  0 0 | 10  *  *  *  *  *  * | 2 0 0 0
o3x3o . x3o . ♦ 18 |  36  18 | 12 12  36  0   6 |  3  12  12   0  12  0  0 |  3  0  4  0  4  0  0 0 |  * 20  *  *  *  *  * | 1 1 0 0
o3x . o3x3o . ♦ 18 |  18  36 |  6  0  36 12  12 |  0  12   0  12  12  3  0 |  0  4  4  0  0  3  0 0 |  *  * 20  *  *  *  * | 1 0 1 0
o3x . . x3o3o ♦ 12 |  12  18 |  4  0  18  0  12 |  0   6   0   0  12  0  3 |  0  0  4  0  0  0  3 0 |  *  *  * 20  *  *  * | 0 1 1 0
. x3o o3x3o . ♦ 18 |  18  36 |  0  6  36 12  12 |  0   0  12  12  12  3  0 |  0  0  0  4  4  3  0 0 |  *  *  *  * 20  *  * | 1 0 0 1
. x3o . x3o3o ♦ 12 |  12  18 |  0  4  18  0  12 |  0   0   6   0  12  0  3 |  0  0  0  0  4  0  3 0 |  *  *  *  *  * 20  * | 0 1 0 1
. x . o3x3o3o ♦ 20 |  10  60 |  0  0  30 20  40 |  0   0   0  10  20 10 10 |  0  0  0  0  0  5  5 2 |  *  *  *  *  *  * 12 | 0 0 1 1
--------------+----+---------+------------------+--------------------------+------------------------+----------------------+--------
o3x3o o3x3o . ♦ 36 |  72  72 | 24 24 144 24  24 |  6  48  48  48  48  6  0 | 12 16 16 16 16 12  0 0 |  4  4  4  0  4  0  0 | 5 * * *
o3x3o . x3o3o ♦ 24 |  48  36 | 16 16  72  0  24 |  4  24  24   0  48  0  6 |  6  0 16  0 16  0 12 0 |  0  4  0  4  0  4  0 | * 5 * *
o3x . o3x3o3o ♦ 30 |  30  90 | 10  0  90 30  60 |  0  30   0  30  60 15 15 |  0 10 20  0  0 15 15 3 |  0  0  5  5  0  0  3 | * * 4 *
. x3o o3x3o3o ♦ 30 |  30  90 |  0 10  90 30  60 |  0   0  30  30  60 15 15 |  0  0  0 10 20 15 15 3 |  0  0  0  0  5  5  3 | * * * 4
```

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