Acronym hatoe (old: hittoe)
Name hexagon truncated-octahedron duoprism
Circumradius sqrt(7/2) = 1.870829
Confer n,toe-dip  

Incidence matrix according to Dynkin symbol

x6o x3x4o

. . . . . | 144 |   2  1   2 |  1  2   4  2  1 |  1  2  4  2 1 | 2 1 2
----------+-----+------------+-----------------+---------------+------
x . . . . |   2 | 144  *   * |  1  1   2  0  0 |  1  2  2  1 0 | 2 1 1
. . x . . |   2 |   * 72   * |  0  2   0  2  0 |  1  0  4  0 1 | 2 0 2
. . . x . |   2 |   *  * 144 |  0  0   2  1  1 |  0  1  2  2 1 | 1 1 2
----------+-----+------------+-----------------+---------------+------
x6o . . . |   6 |   6  0   0 | 24  *   *  *  * |  1  2  0  0 0 | 2 1 0
x . x . . |   4 |   2  2   0 |  * 72   *  *  * |  1  0  2  0 0 | 2 0 1
x . . x . |   4 |   2  0   2 |  *  * 144  *  * |  0  1  1  1 0 | 1 1 1
. . x3x . |   6 |   0  3   3 |  *  *   * 48  * |  0  0  2  0 1 | 1 0 2
. . . x4o |   4 |   0  0   4 |  *  *   *  * 36 |  0  0  0  2 1 | 0 1 2
----------+-----+------------+-----------------+---------------+------
x6o x . .   12 |  12  6   0 |  2  6   0  0  0 | 12  *  *  * * | 2 0 0
x6o . x .   12 |  12  0   6 |  2  0   6  0  0 |  * 24  *  * * | 1 1 0
x . x3x .   12 |   6  6   6 |  0  3   3  2  0 |  *  * 48  * * | 1 0 1
x . . x4o    8 |   4  0   8 |  0  0   4  0  2 |  *  *  * 36 * | 0 1 1
. . x3x4o   24 |   0 12  24 |  0  0   0  8  6 |  *  *  *  * 6 | 0 0 2
----------+-----+------------+-----------------+---------------+------
x6o x3x .   36 |  36 18  18 |  6 18  18  6  0 |  3  3  6  0 0 | 8 * *
x6o . x4o   24 |  24  0  24 |  4  0  24  0  6 |  0  4  0  6 0 | * 6 *
x . x3x4o   48 |  24 24  48 |  0 12  24 16 12 |  0  0  8  6 2 | * * 6

x6o x3x3x

. . . . . | 144 |   2  1  1  1 |  1  2  2  2  1  1  1 |  1  1  1  2  2  2 1 | 1 1 1 2
----------+-----+--------------+----------------------+---------------------+--------
x . . . . |   2 | 144  *  *  * |  1  1  1  1  0  0  0 |  1  1  1  1  1  1 0 | 1 1 1 1
. . x . . |   2 |   * 72  *  * |  0  2  0  0  1  1  0 |  1  0  0  2  2  0 1 | 1 1 0 2
. . . x . |   2 |   *  * 72  * |  0  0  2  0  1  0  1 |  0  1  0  2  0  2 1 | 1 0 1 2
. . . . x |   2 |   *  *  * 72 |  0  0  0  2  0  1  1 |  0  0  1  0  2  2 1 | 0 1 1 2
----------+-----+--------------+----------------------+---------------------+--------
x6o . . . |   6 |   6  0  0  0 | 24  *  *  *  *  *  * |  1  1  1  0  0  0 0 | 1 1 1 0
x . x . . |   4 |   2  2  0  0 |  * 72  *  *  *  *  * |  1  0  0  1  1  0 0 | 1 1 0 1
x . . x . |   4 |   2  0  2  0 |  *  * 72  *  *  *  * |  0  1  0  1  0  1 0 | 1 0 1 1
x . . . x |   4 |   2  0  0  2 |  *  *  * 72  *  *  * |  0  0  1  0  1  1 0 | 0 1 1 1
. . x3x . |   6 |   0  3  3  0 |  *  *  *  * 24  *  * |  0  0  0  2  0  0 1 | 1 0 0 2
. . x . x |   4 |   0  2  0  2 |  *  *  *  *  * 36  * |  0  0  0  0  2  0 1 | 0 1 0 2
. . . x3x |   6 |   0  0  3  3 |  *  *  *  *  *  * 24 |  0  0  0  0  0  2 1 | 0 0 1 2
----------+-----+--------------+----------------------+---------------------+--------
x6o x . .   12 |  12  6  0  0 |  2  6  0  0  0  0  0 | 12  *  *  *  *  * * | 1 1 0 0
x6o . x .   12 |  12  0  6  0 |  2  0  6  0  0  0  0 |  * 12  *  *  *  * * | 1 0 1 0
x6o . . x   12 |  12  0  0  6 |  2  0  0  6  0  0  0 |  *  * 12  *  *  * * | 0 1 1 0
x . x3x .   12 |   6  6  6  0 |  0  3  3  0  2  0  0 |  *  *  * 24  *  * * | 1 0 0 1
x . x . x    8 |   4  4  0  4 |  0  2  0  2  0  2  0 |  *  *  *  * 36  * * | 0 1 0 1
x . . x3x   12 |   6  0  6  6 |  0  0  3  3  0  0  2 |  *  *  *  *  * 24 * | 0 0 1 1
. . x3x3x   24 |   0 12 12 12 |  0  0  0  0  4  6  4 |  *  *  *  *  *  * 6 | 0 0 0 2
----------+-----+--------------+----------------------+---------------------+--------
x6o x3x .   36 |  36 18 18  0 |  6 18 18  0  6  0  0 |  3  3  0  6  0  0 0 | 4 * * *
x6o x . x   24 |  24 12  0 12 |  4 12  0 12  0  6  0 |  2  0  2  0  6  0 0 | * 6 * *
x6o . x3x   36 |  36  0 18 18 |  6  0 18 18  0  0  6 |  0  3  3  0  0  6 0 | * * 4 *
x . x3x3x   48 |  24 24 24 24 |  0 12 12 12  8 12  8 |  0  0  0  4  6  4 2 | * * * 6

x3x x3x4o

. . . . . | 144 |  1  1  1   2 |  1  1  2  1  2  2  1 |  1  2  2  1  2  1 1 | 2 1 1 1
----------+-----+--------------+----------------------+---------------------+--------
x . . . . |   2 | 72  *  *   * |  1  1  2  0  0  0  0 |  1  2  2  1  0  0 0 | 2 1 1 0
. x . . . |   2 |  * 72  *   * |  1  0  0  1  2  0  0 |  1  2  0  0  2  1 0 | 2 1 0 1
. . x . . |   2 |  *  * 72   * |  0  1  0  1  0  2  0 |  1  0  2  0  2  0 1 | 2 0 1 1
. . . x . |   2 |  *  *  * 144 |  0  0  1  0  1  1  1 |  0  1  1  1  1  1 1 | 1 1 1 1
----------+-----+--------------+----------------------+---------------------+--------
x3x . . . |   6 |  3  3  0   0 | 24  *  *  *  *  *  * |  1  2  0  0  0  0 0 | 2 1 0 0
x . x . . |   4 |  2  0  2   0 |  * 36  *  *  *  *  * |  1  0  2  0  0  0 0 | 2 0 1 0
x . . x . |   4 |  2  0  0   2 |  *  * 72  *  *  *  * |  0  1  1  1  0  0 0 | 1 1 1 0
. x x . . |   4 |  0  2  2   0 |  *  *  * 36  *  *  * |  1  0  0  0  2  0 0 | 2 0 0 1
. x . x . |   4 |  0  2  0   2 |  *  *  *  * 72  *  * |  0  1  0  0  1  1 0 | 1 1 0 1
. . x3x . |   6 |  0  0  3   3 |  *  *  *  *  * 48  * |  0  0  1  0  1  0 1 | 1 0 1 1
. . . x4o |   4 |  0  0  0   4 |  *  *  *  *  *  * 36 |  0  0  0  1  0  1 1 | 0 1 1 1
----------+-----+--------------+----------------------+---------------------+--------
x3x x . .   12 |  6  6  6   0 |  2  3  0  3  0  0  0 | 12  *  *  *  *  * * | 2 0 0 0
x3x . x .   12 |  6  6  0   6 |  2  0  3  0  3  0  0 |  * 24  *  *  *  * * | 1 1 0 0
x . x3x .   12 |  6  0  6   6 |  0  3  3  0  0  2  0 |  *  * 24  *  *  * * | 1 0 1 0
x . . x4o    8 |  4  0  0   8 |  0  0  4  0  0  0  2 |  *  *  * 18  *  * * | 0 1 1 0
. x x3x .   12 |  0  6  6   6 |  0  0  0  3  3  2  0 |  *  *  *  * 24  * * | 1 0 0 1
. x . x4o    8 |  0  4  0   8 |  0  0  0  0  4  0  2 |  *  *  *  *  * 18 * | 0 1 0 1
. . x3x4o   24 |  0  0 12  24 |  0  0  0  0  0  8  6 |  *  *  *  *  *  * 6 | 0 0 1 1
----------+-----+--------------+----------------------+---------------------+--------
x3x x3x .   36 | 18 18 18  18 |  6  9  9  9  9  6  0 |  3  3  3  0  3  0 0 | 8 * * *
x3x . x4o   24 | 12 12  0  24 |  4  0 12  0 12  0  6 |  0  4  0  3  0  3 0 | * 6 * *
x . x3x4o   48 | 24  0 24  48 |  0 12 24  0  0 16 12 |  0  0  8  6  0  0 2 | * * 3 *
. x x3x4o   48 |  0 24 24  48 |  0  0  0 12 24 16 12 |  0  0  0  0  8  6 2 | * * * 3

x3x x3x3x

. . . . . | 144 |  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 | 72  *  *  *  * |  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 |  * 72  *  *  * |  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 |  *  * 72  *  * |  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 |  *  *  * 72  * |  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 |  *  *  *  * 72 |  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
----------+-----+----------------+-------------------------------+------------------------------+----------
x3x . . . |   6 |  3  3  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 |  * 36  *  *  *  *  *  *  *  * |  1  0  0  1  1  0  0  0  0 0 | 1 1 0 1 0
x . . x . |   4 |  2  0  0  2  0 |  *  * 36  *  *  *  *  *  *  * |  0  1  0  1  0  1  0  0  0 0 | 1 0 1 1 0
x . . . x |   4 |  2  0  0  0  2 |  *  *  * 36  *  *  *  *  *  * |  0  0  1  0  1  1  0  0  0 0 | 0 1 1 1 0
. x x . . |   4 |  0  2  2  0  0 |  *  *  *  * 36  *  *  *  *  * |  1  0  0  0  0  0  1  1  0 0 | 1 1 0 0 1
. x . x . |   4 |  0  2  0  2  0 |  *  *  *  *  * 36  *  *  *  * |  0  1  0  0  0  0  1  0  1 0 | 1 0 1 0 1
. x . . x |   4 |  0  2  0  0  2 |  *  *  *  *  *  * 36  *  *  * |  0  0  1  0  0  0  0  1  1 0 | 0 1 1 0 1
. . x3x . |   6 |  0  0  3  3  0 |  *  *  *  *  *  *  * 24  *  * |  0  0  0  1  0  0  1  0  0 1 | 1 0 0 1 1
. . x . x |   4 |  0  0  2  0  2 |  *  *  *  *  *  *  *  * 36  * |  0  0  0  0  1  0  0  1  0 1 | 0 1 0 1 1
. . . x3x |   6 |  0  0  0  3  3 |  *  *  *  *  *  *  *  *  * 24 |  0  0  0  0  0  1  0  0  1 1 | 0 0 1 1 1
----------+-----+----------------+-------------------------------+------------------------------+----------
x3x x . .   12 |  6  6  6  0  0 |  2  3  0  0  3  0  0  0  0  0 | 12  *  *  *  *  *  *  *  * * | 1 1 0 0 0
x3x . x .   12 |  6  6  0  6  0 |  2  0  3  0  0  3  0  0  0  0 |  * 12  *  *  *  *  *  *  * * | 1 0 1 0 0
x3x . . x   12 |  6  6  0  0  6 |  2  0  0  3  0  0  3  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 |  *  *  * 12  *  *  *  *  * * | 1 0 0 1 0
x . x . x    8 |  4  0  4  0  4 |  0  2  0  2  0  0  0  0  2  0 |  *  *  *  * 18  *  *  *  * * | 0 1 0 1 0
x . . x3x   12 |  6  0  0  6  6 |  0  0  3  3  0  0  0  0  0  2 |  *  *  *  *  * 12  *  *  * * | 0 0 1 1 0
. x x3x .   12 |  0  6  6  6  0 |  0  0  0  0  3  3  0  2  0  0 |  *  *  *  *  *  * 12  *  * * | 1 0 0 0 1
. x x . x    8 |  0  4  4  0  4 |  0  0  0  0  2  0  2  0  2  0 |  *  *  *  *  *  *  * 18  * * | 0 1 0 0 1
. x . x3x   12 |  0  6  0  6  6 |  0  0  0  0  0  3  3  0  0  2 |  *  *  *  *  *  *  *  * 12 * | 0 0 1 0 1
. . x3x3x   24 |  0  0 12 12 12 |  0  0  0  0  0  0  0  4  6  4 |  *  *  *  *  *  *  *  *  * 6 | 0 0 0 1 1
----------+-----+----------------+-------------------------------+------------------------------+----------
x3x x3x .   36 | 18 18 18 18  0 |  6  9  9  0  9  9  0  6  0  0 |  3  3  0  3  0  0  3  0  0 0 | 4 * * * *
x3x x . x   24 | 12 12 12  0 12 |  4  6  0  6  6  0  6  0  6  0 |  2  0  2  0  3  0  0  3  0 0 | * 6 * * *
x3x . x3x   36 | 18 18  0 18 18 |  6  0  9  9  0  9  9  0  0  6 |  0  3  3  0  0  3  0  0  3 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 | * * * 3 *
. 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 | * * * * 3

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