Acronym tetco
Name tetrahedron-cuboctahedron duoprism
Circumradius sqrt(11/8) = 1.172604

Incidence matrix according to Dynkin symbol

x3o3o o3x4o

. . . . . . | 48 |  3  4 |  3  12  2  2 |  1 12  6  6 1 |  4  6  6 3 | 2 2 3
------------+----+-------+--------------+---------------+------------+------
x . . . . . |  2 | 72  * |  2   4  0  0 |  1  8  2  2 0 |  4  4  4 1 | 2 2 2
. . . . x . |  2 |  * 96 |  0   3  1  1 |  0  3  3  3 1 |  1  3  3 3 | 1 1 3
------------+----+-------+--------------+---------------+------------+------
x3o . . . . |  3 |  3  0 | 48   *  *  * |  1  4  0  0 0 |  4  2  2 0 | 2 2 1
x . . . x . |  4 |  2  2 |  * 144  *  * |  0  2  1  1 0 |  1  2  2 1 | 1 1 2
. . . o3x . |  3 |  0  3 |  *   * 32  * |  0  0  3  0 1 |  0  3  0 3 | 1 0 3
. . . . x4o |  4 |  0  4 |  *   *  * 24 |  0  0  0  3 1 |  0  0  3 3 | 0 1 3
------------+----+-------+--------------+---------------+------------+------
x3o3o . . .   4 |  6  0 |  4   0  0  0 | 12  *  *  * * |  4  0  0 0 | 2 2 0
x3o . . x .   6 |  6  3 |  2   3  0  0 |  * 96  *  * * |  1  1  1 0 | 1 1 1
x . . o3x .   6 |  3  6 |  0   3  2  0 |  *  * 48  * * |  0  2  0 1 | 1 0 2
x . . . x4o   8 |  4  8 |  0   4  0  2 |  *  *  * 36 * |  0  0  2 1 | 0 1 2
. . . o3x4o  12 |  0 24 |  0   0  8  6 |  *  *  *  * 4 |  0  0  0 3 | 0 0 3
------------+----+-------+--------------+---------------+------------+------
x3o3o . x .   8 | 12  4 |  8   6  0  0 |  2  4  0  0 0 | 24  *  * * | 1 1 0
x3o . o3x .   9 |  9  9 |  3   9  3  0 |  0  3  3  0 0 |  * 32  * * | 1 0 1
x3o . . x4o  12 | 12 12 |  4  12  0  3 |  0  4  0  3 0 |  *  * 24 * | 0 1 1
x . . o3x4o  24 | 12 48 |  0  24 16 12 |  0  0  8  6 2 |  *  *  * 6 | 0 0 2
------------+----+-------+--------------+---------------+------------+------
x3o3o o3x .  12 | 18 12 | 12  18  4  0 |  3 12  6  0 0 |  3  4  0 0 | 8 * *
x3o3o . x4o  16 | 24 16 | 16  24  0  4 |  4 16  0  6 0 |  4  0  4 0 | * 6 *
x3o . o3x4o  36 | 36 72 | 12  72 24 18 |  0 24 24 18 3 |  0  8  6 3 | * * 4

x3o3o x3o3x

. . . . . . | 48 |  3  2  2 |  3  6  6  1  2  1 |  1  6  6  3  6  3 1 |  2  2  3  6  3 3 | 1 2 1 3
------------+----+----------+-------------------+---------------------+------------------+--------
x . . . . . |  2 | 72  *  * |  2  2  2  0  0  0 |  1  4  4  1  2  1 0 |  2  2  2  4  2 1 | 1 2 1 2
. . . x . . |  2 |  * 48  * |  0  3  0  1  1  0 |  0  3  0  3  3  0 1 |  1  0  3  3  0 3 | 1 1 0 3
. . . . . x |  2 |  *  * 48 |  0  0  3  0  1  1 |  0  0  3  0  3  3 1 |  0  1  0  3  3 3 | 0 1 1 3
------------+----+----------+-------------------+---------------------+------------------+--------
x3o . . . . |  3 |  3  0  0 | 48  *  *  *  *  * |  1  2  2  0  0  0 0 |  2  2  1  2  1 0 | 1 2 1 1
x . . x . . |  4 |  2  2  0 |  * 72  *  *  *  * |  0  2  0  1  1  0 0 |  1  0  2  2  0 1 | 1 1 0 2
x . . . . x |  4 |  2  0  2 |  *  * 72  *  *  * |  0  0  2  0  1  1 0 |  0  1  0  2  2 1 | 0 1 1 2
. . . x3o . |  3 |  0  3  0 |  *  *  * 16  *  * |  0  0  0  3  0  0 1 |  0  0  3  0  0 3 | 1 0 0 3
. . . x . x |  4 |  0  2  2 |  *  *  *  * 24  * |  0  0  0  0  3  0 1 |  0  0  0  3  0 3 | 0 1 0 3
. . . . o3x |  3 |  0  0  3 |  *  *  *  *  * 16 |  0  0  0  0  0  3 1 |  0  0  0  0  3 3 | 0 0 1 3
------------+----+----------+-------------------+---------------------+------------------+--------
x3o3o . . .   4 |  6  0  0 |  4  0  0  0  0  0 | 12  *  *  *  *  * * |  2  2  0  0  0 0 | 1 2 1 0
x3o . x . .   6 |  6  3  0 |  2  3  0  0  0  0 |  * 48  *  *  *  * * |  1  0  1  1  0 0 | 1 1 0 1
x3o . . . x   6 |  6  0  3 |  2  0  3  0  0  0 |  *  * 48  *  *  * * |  0  1  0  1  1 0 | 0 1 1 1
x . . x3o .   6 |  3  6  0 |  0  3  0  2  0  0 |  *  *  * 24  *  * * |  0  0  2  0  0 1 | 1 0 0 2
x . . x . x   8 |  4  4  4 |  0  2  2  0  2  0 |  *  *  *  * 36  * * |  0  0  0  2  0 1 | 0 1 0 2
x . . . o3x   6 |  3  0  6 |  0  0  3  0  0  2 |  *  *  *  *  * 24 * |  0  0  0  0  2 1 | 0 0 1 2
. . . x3o3x  12 |  0 12 12 |  0  0  0  4  6  4 |  *  *  *  *  *  * 4 |  0  0  0  0  0 3 | 0 0 0 3
------------+----+----------+-------------------+---------------------+------------------+--------
x3o3o x . .   8 | 12  4  0 |  8  6  0  0  0  0 |  2  4  0  0  0  0 0 | 12  *  *  *  * * | 1 1 0 0
x3o3o . . x   8 | 12  0  4 |  8  0  6  0  0  0 |  2  0  4  0  0  0 0 |  * 12  *  *  * * | 0 1 1 0
x3o . x3o .   9 |  9  9  0 |  3  9  0  3  0  0 |  0  3  0  3  0  0 0 |  *  * 16  *  * * | 1 0 0 1
x3o . x . x  12 | 12  6  6 |  4  6  6  0  3  0 |  0  2  2  0  3  0 0 |  *  *  * 24  * * | 0 1 0 1
x3o . . o3x   9 |  9  0  9 |  3  0  9  0  0  3 |  0  0  3  0  0  3 0 |  *  *  *  * 16 * | 0 0 1 1
x . . x3o3x  24 | 12 24 24 |  0 12 12  8 12  8 |  0  0  0  4  6  4 2 |  *  *  *  *  * 6 | 0 0 0 2
------------+----+----------+-------------------+---------------------+------------------+--------
x3o3o x3o .  12 | 18 12  0 | 12 18  0  4  0  0 |  3 12  0  6  0  0 0 |  3  0  4  0  0 0 | 4 * * *
x3o3o x . x  16 | 24  8  8 | 16 12 12  0  4  0 |  4  8  8  0  6  0 0 |  2  2  0  4  0 0 | * 6 * *
x3o3o . o3x  12 | 18  0 12 | 12  0 18  0  0  4 |  3  0 12  0  0  6 0 |  0  3  0  0  4 0 | * * 4 *
x3o . x3o3x  36 | 36 36 36 | 12 36 36 12 18 12 |  0 12 12 12 18 12 3 |  0  0  4  6  4 3 | * * * 4

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