Acronym cocube Name cuboctahedron-cube duoprism Circumradius sqrt(7)/2 = 1.322876 Volume 5 sqrt(2)/3 = 2.357023

Incidence matrix according to Dynkin symbol

```o3x4o o3o4x

. . . . . . | 96 |   4   3 |  2  2  12  3 | 1  6  6  12  1 |  3  6  6  4 | 3 2 2
------------+----+---------+--------------+----------------+-------------+------
. x . . . . |  2 | 192   * |  1  1   3  0 | 1  3  3   3  0 |  3  3  3  1 | 3 1 1
. . . . . x |  2 |   * 144 |  0  0   4  2 | 0  2  2   8  1 |  1  4  4  4 | 2 2 2
------------+----+---------+--------------+----------------+-------------+------
o3x . . . . |  3 |   3   0 | 64  *   *  * | 1  3  0   0  0 |  3  3  0  0 | 3 1 0
. x4o . . . |  4 |   4   0 |  * 48   *  * | 1  0  3   0  0 |  3  0  3  0 | 3 0 1
. x . . . x |  4 |   2   2 |  *  * 288  * | 0  1  1   2  0 |  1  2  2  1 | 2 1 1
. . . . o4x |  4 |   0   4 |  *  *   * 72 | 0  0  0   4  1 |  0  2  2  4 | 1 2 2
------------+----+---------+--------------+----------------+-------------+------
o3x4o . . . ♦ 12 |  24   0 |  8  6   0  0 | 8  *  *   *  * |  3  0  0  0 | 3 0 0
o3x . . . x ♦  6 |   6   3 |  2  0   3  0 | * 96  *   *  * |  1  2  0  0 | 2 1 0
. x4o . . x ♦  8 |   8   4 |  0  2   4  0 | *  * 72   *  * |  1  0  2  0 | 2 0 1
. x . . o4x ♦  8 |   4   8 |  0  0   4  2 | *  *  * 144  * |  0  1  1  1 | 1 1 1
. . . o3o4x ♦  8 |   0  12 |  0  0   0  6 | *  *  *   * 12 |  0  0  0  4 | 0 2 2
------------+----+---------+--------------+----------------+-------------+------
o3x4o . . x ♦ 24 |  48  12 | 16 12  24  0 | 2  8  6   0  0 | 12  *  *  * | 2 0 0
o3x . . o4x ♦ 12 |  12  12 |  4  0  12  3 | 0  4  0   3  0 |  * 48  *  * | 1 1 0
. x4o . o4x ♦ 16 |  16  16 |  0  4  16  4 | 0  0  4   4  0 |  *  * 36  * | 1 0 1
. x . o3o4x ♦ 16 |   8  24 |  0  0  12 12 | 0  0  0   6  2 |  *  *  * 24 | 0 1 1
------------+----+---------+--------------+----------------+-------------+------
o3x4o . o4x ♦ 48 |  96  48 | 32 24  96 12 | 4 32 24  24  0 |  4  8  6  0 | 6 * *
o3x . o3o4x ♦ 24 |  24  36 |  8  0  36 18 | 0 12  0  18  3 |  0  6  0  3 | * 8 *
. x4o o3o4x ♦ 32 |  32  48 |  0  8  48 24 | 0  0 12  24  4 |  0  0  6  4 | * * 6
```

```x x4o o3x4o

. . . . . . | 96 |  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 | 48  *   * |  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 |  * 96   * |  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 |  *  * 192 |  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 | 48  *  *   *  *  * |  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 |  * 96  *   *  *  * |  0  2  1  1  0  0  0 0 |  1  2  2 1  0  0 0 | 1 1 2 0
. x4o . . . |  4 |  0  4   0 |  *  * 24   *  *  * |  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 |  *  *  * 192  *  * |  0  1  0  0  1  1  1 0 |  1  1  1 0  1  1 1 | 1 1 1 1
. . . o3x . |  3 |  0  0   3 |  *  *  *   * 64  * |  0  0  1  0  0  2  0 1 |  0  2  0 1  1  0 2 | 1 0 2 1
. . . . x4o |  4 |  0  0   4 |  *  *  *   *  * 48 |  0  0  0  1  0  0  2 1 |  0  0  2 1  0  1 2 | 0 1 2 1
------------+----+-----------+--------------------+------------------------+--------------------+--------
x x4o . . . ♦  8 |  4  8   0 |  4  0  2   0  0  0 | 12  *  *  *  *  *  * * |  4  0  0 0  0  0 0 | 2 2 0 0
x x . . x . ♦  8 |  4  4   4 |  2  2  0   2  0  0 |  * 96  *  *  *  *  * * |  1  1  1 0  0  0 0 | 1 1 1 0
x . . o3x . ♦  6 |  3  0   6 |  0  3  0   0  2  0 |  *  * 32  *  *  *  * * |  0  2  0 1  0  0 0 | 1 0 2 0
x . . . x4o ♦  8 |  4  0   8 |  0  4  0   0  0  2 |  *  *  * 24  *  *  * * |  0  0  2 1  0  0 0 | 0 1 2 0
. x4o . x . ♦  8 |  0  8   4 |  0  0  2   4  0  0 |  *  *  *  * 48  *  * * |  1  0  0 0  1  1 0 | 1 1 0 1
. x . o3x . ♦  6 |  0  3   6 |  0  0  0   3  2  0 |  *  *  *  *  * 64  * * |  0  1  0 0  1  0 1 | 1 0 1 1
. x . . x4o ♦  8 |  0  4   8 |  0  0  0   4  0  2 |  *  *  *  *  *  * 48 * |  0  0  1 0  0  1 1 | 0 1 1 1
. . . o3x4o ♦ 12 |  0  0  24 |  0  0  0   0  8  6 |  *  *  *  *  *  *  * 8 |  0  0  0 1  0  0 2 | 0 0 2 1
------------+----+-----------+--------------------+------------------------+--------------------+--------
x x4o . x . ♦ 16 |  8 16   8 |  8  4  4   8  0  0 |  2  4  0  0  2  0  0 0 | 24  *  * *  *  * * | 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 |  * 32  * *  *  * * | 1 0 1 0
x x . . x4o ♦ 16 |  8  8  16 |  4  8  0   8  0  4 |  0  4  0  2  0  0  2 0 |  *  * 24 *  *  * * | 0 1 1 0
x . . o3x4o ♦ 24 | 12  0  48 |  0 24  0   0 16 12 |  0  0  8  6  0  0  0 2 |  *  *  * 4  *  * * | 0 0 2 0
. x4o o3x . ♦ 12 |  0 12  12 |  0  0  3  12  4  0 |  0  0  0  0  3  4  0 0 |  *  *  * * 16  * * | 1 0 0 1
. x4o . x4o ♦ 16 |  0 16  16 |  0  0  4  16  0  4 |  0  0  0  0  4  0  4 0 |  *  *  * *  * 12 * | 0 1 0 1
. x . o3x4o ♦ 24 |  0 12  48 |  0  0  0  24 16 12 |  0  0  0  0  0  8  6 2 |  *  *  * *  *  * 8 | 0 0 1 1
------------+----+-----------+--------------------+------------------------+--------------------+--------
x x4o o3x . ♦ 24 | 12 24  24 | 12 12  6  24  8  0 |  3 12  4  0  6  8  0 0 |  3  4  0 0  2  0 0 | 8 * * *
x x4o . x4o ♦ 32 | 16 32  32 | 16 16  8  32  0  8 |  4 16  0  4  8  0  8 0 |  4  0  4 0  0  2 0 | * 6 * *
x x . o3x4o ♦ 48 | 24 24  96 | 12 48  0  48 32 24 |  0 24 16 12  0 16 12 4 |  0  8  6 2  0  0 2 | * * 4 *
. x4o o3x4o ♦ 48 |  0 48  96 |  0  0 12  96 32 24 |  0  0  0  0 24 32 24 4 |  0  0  0 0  8  6 4 | * * * 2
```

```x x x o3x4o

. . . . . . | 96 |  1  1  1   4 |  1  1  4  1  4  4  2  2 |  1  4  4  2  2  4  2  2  2  2 1 |  4  2  2  2  2 1  2  2 2 | 2 2 1 1 1
------------+----+--------------+-------------------------+---------------------------------+--------------------------+----------
x . . . . . |  2 | 48  *  *   * |  1  1  4  0  0  0  0  0 |  1  4  4  2  2  0  0  0  0  0 0 |  4  2  2  2  2 1  0  0 0 | 2 2 1 1 0
. x . . . . |  2 |  * 48  *   * |  1  0  0  1  4  0  0  0 |  1  4  0  0  0  4  2  2  0  0 0 |  4  2  2  0  0 0  2  2 1 | 2 2 1 0 1
. . x . . . |  2 |  *  * 48   * |  0  1  0  1  0  4  0  0 |  1  0  4  0  0  4  0  0  2  2 0 |  4  0  0  2  2 0  2  2 1 | 2 2 0 1 1
. . . . x . |  2 |  *  *  * 192 |  0  0  1  0  1  1  1  1 |  0  1  1  1  1  1  1  1  1  1 1 |  1  1  1  1  1 1  1  1 2 | 1 1 1 1 1
------------+----+--------------+-------------------------+---------------------------------+--------------------------+----------
x x . . . . |  4 |  2  2  0   0 | 24  *  *  *  *  *  *  * |  1  2  2  0  0  0  0  0  0  0 0 |  4  2  2  0  0 0  0  0 0 | 2 2 1 0 0
x . x . . . |  4 |  2  2  0   0 |  * 24  *  *  *  *  *  * |  1  2  2  0  0  0  0  0  0  0 0 |  4  0  0  2  2 0  0  0 0 | 2 2 0 1 0
x . . . x . |  4 |  2  0  0   2 |  *  * 96  *  *  *  *  * |  0  2  0  1  1  0  0  0  0  0 0 |  1  1  1  1  1 1  0  0 0 | 1 1 1 1 0
. x x . . . |  4 |  0  2  2   0 |  *  *  * 24  *  *  *  * |  1  0  0  0  0  4  0  0  0  0 0 |  4  0  0  0  0 0  2  2 0 | 2 2 0 0 1
. x . . x . |  4 |  0  2  0   2 |  *  *  *  * 96  *  *  * |  0  1  0  0  0  1  1  1  0  0 0 |  1  1  1  0  0 0  1  1 1 | 1 1 1 0 1
. . x . x . |  4 |  0  0  2   2 |  *  *  *  *  * 96  *  * |  0  0  1  0  0  1  0  0  1  1 0 |  1  0  0  1  1 0  1  1 1 | 1 1 0 1 1
. . . o3x . |  3 |  0  0  0   3 |  *  *  *  *  *  * 64  * |  0  0  0  1  0  0  1  0  1  0 1 |  0  1  0  1  0 1  1  0 2 | 1 0 1 1 1
. . . . x4o |  4 |  0  0  0   4 |  *  *  *  *  *  *  * 48 |  0  0  0  0  1  0  0  1  0  1 1 |  0  0  1  0  1 1  0  1 2 | 0 1 1 1 1
------------+----+--------------+-------------------------+---------------------------------+--------------------------+----------
x x x . . . ♦  8 |  4  4  4   0 |  2  2  0  2  0  0  0  0 | 12  *  *  *  *  *  *  *  *  * * |  4  0  0  0  0 0  0  0 0 | 2 2 0 0 0
x x . . x . ♦  8 |  4  4  0   4 |  2  0  2  0  2  0  0  0 |  * 48  *  *  *  *  *  *  *  * * |  1  1  1  0  0 0  0  0 0 | 1 1 1 0 0
x . x . x . ♦  8 |  4  0  4   4 |  0  2  2  0  0  2  0  0 |  *  * 48  *  *  *  *  *  *  * * |  1  0  0  1  1 0  0  0 0 | 1 1 0 1 0
x . . o3x . ♦  6 |  3  0  0   6 |  0  0  3  0  0  0  2  0 |  *  *  * 32  *  *  *  *  *  * * |  0  1  0  1  0 1  0  0 0 | 1 0 1 1 0
x . . . x4o ♦  8 |  4  0  0   8 |  0  0  4  0  0  0  0  2 |  *  *  *  * 24  *  *  *  *  * * |  0  0  1  0  1 1  0  0 0 | 0 1 1 1 0
. x x . x . ♦  8 |  0  4  4   4 |  0  0  0  2  2  2  0  0 |  *  *  *  *  * 48  *  *  *  * * |  1  0  0  0  0 0  1  1 0 | 1 1 0 0 1
. x . o3x . ♦  6 |  0  3  0   6 |  0  0  0  0  3  0  2  0 |  *  *  *  *  *  * 32  *  *  * * |  0  1  0  0  0 0  1  0 1 | 1 0 1 0 1
. x . . x4o ♦  8 |  0  4  0   8 |  0  0  0  0  4  0  0  2 |  *  *  *  *  *  *  * 24  *  * * |  0  0  1  0  0 0  0  1 1 | 0 1 1 0 1
. . x o3x . ♦  6 |  0  0  3   6 |  0  0  0  0  0  3  2  0 |  *  *  *  *  *  *  *  * 32  * * |  0  0  0  1  0 0  1  0 1 | 1 0 0 1 1
. . x . x4o ♦  8 |  0  0  4   8 |  0  0  0  0  0  4  0  2 |  *  *  *  *  *  *  *  *  * 24 * |  0  0  0  0  1 0  0  1 1 | 0 1 0 1 1
. . . o3x4o ♦ 12 |  0  0  0  24 |  0  0  0  0  0  0  8  6 |  *  *  *  *  *  *  *  *  *  * 8 |  0  0  0  0  0 1  0  0 2 | 0 0 1 1 1
------------+----+--------------+-------------------------+---------------------------------+--------------------------+----------
x x x . x . ♦ 16 |  8  8  8   8 |  4  4  4  4  4  4  0  0 |  2  2  2  0  0  2  0  0  0  0 0 | 24  *  *  *  * *  *  * * | 1 1 0 0 0
x x . o3x . ♦ 12 |  6  6  0  12 |  3  0  6  0  6  0  4  0 |  0  3  0  2  0  0  2  0  0  0 0 |  * 16  *  *  * *  *  * * | 1 0 1 0 0
x x . . x4o ♦ 16 |  8  8  0  16 |  4  0  8  0  8  0  0  4 |  0  4  0  0  2  0  0  2  0  0 0 |  *  * 12  *  * *  *  * * | 0 1 1 0 0
x . x o3x . ♦ 12 |  6  0  6  12 |  0  3  6  0  0  6  4  0 |  0  0  3  2  0  0  0  0  2  0 0 |  *  *  * 16  * *  *  * * | 1 0 0 1 0
x . x . x4o ♦ 16 |  8  0  8  16 |  0  4  8  0  0  8  0  4 |  0  0  4  0  2  0  0  0  0  2 0 |  *  *  *  * 12 *  *  * * | 0 1 0 1 0
x . . o3x4o ♦ 24 | 12  0  0  48 |  0  0 24  0  0  0 16 12 |  0  0  0  8  6  0  0  0  0  0 2 |  *  *  *  *  * 4  *  * * | 0 0 1 1 0
. x x o3x . ♦ 12 |  0  6  6  12 |  0  0  0  3  6  6  4  0 |  0  0  0  0  0  3  2  0  2  0 0 |  *  *  *  *  * * 16  * * | 1 0 0 0 1
. x x . x4o ♦ 16 |  0  8  8  16 |  0  0  0  4  8  8  0  4 |  0  0  0  0  0  4  0  2  0  2 0 |  *  *  *  *  * *  * 12 * | 0 1 0 0 1
. x . o3x4o ♦ 24 |  0 12  0  48 |  0  0  0  0 24  0 16 12 |  0  0  0  0  0  0  8  6  0  0 2 |  *  *  *  *  * *  *  * 4 | 0 0 1 0 1
. . x o3x4o ♦ 24 |  0  0 12  48 |  0  0  0  0  0 24 16 12 |  0  0  0  0  0  0  0  0  8  6 2 |  *  *  *  *  * *  *  * 4 | 0 0 0 1 1
------------+----+--------------+-------------------------+---------------------------------+--------------------------+----------
x x x o3x . ♦ 24 | 12 12 12  24 |  6  6 12  6 12 12  8  0 |  3  6  6  4  0  6  4  0  4  0 0 |  3  2  0  2  0 0  2  0 0 | 8 * * * *
x x x . x4o ♦ 32 | 16 16 16  32 |  8  8 16  8 16 16  0  8 |  4  8  8  0  4  8  0  4  0  4 0 |  4  0  2  0  2 0  0  2 0 | * 6 * * *
x x . o3x4o ♦ 48 | 24 24  0  96 | 12  0 48  0 48  0 32 24 |  0 24  0 16 12  0 16 12  0  0 4 |  0  8  6  0  0 2  0  0 2 | * * 2 * *
x . x o3x4o ♦ 48 | 24  0 24  96 |  0 12 48  0  0 48 32 24 |  0  0 24 16 12  0  0  0 16 12 4 |  0  0  0  8  6 2  0  0 2 | * * * 2 *
. x x o3x4o ♦ 48 |  0 24 24  96 |  0  0  0 12 48 48 32 24 |  0  0  0  0  0 24 16 12 16 12 4 |  0  0  0  0  0 0  8  6 4 | * * * * 2
```