Acronym girhax
Name great rhombated hemihexeract,
cantitruncated demihexeract,
runcicantic hexeract
Circumradius sqrt(43)/2 = 3.278719
Coordinates (5/sqrt(8), 5/sqrt(8), 5/sqrt(8), 3/sqrt(8), 1/sqrt(8), 1/sqrt(8))     & all permutations, all even changes of sign
External
links
wikipedia  

Incidence matrix according to Dynkin symbol

x3x3o *b3x3o3o

. . .    . . . | 1920 |   1    2    3 |   2    3   1    6    3 |   1   6   3   3   6   1 |  3   6   1   3   2 |  3  2  1
---------------+------+---------------+------------------------+-------------------------+--------------------+---------
x . .    . . . |    2 | 960    *    * |   2    3   0    0    0 |   1   6   3   0   0   0 |  3   6   1   0   0 |  3  2  0
. x .    . . . |    2 |   * 1920    * |   1    0   1    3    0 |   1   3   0   3   3   0 |  3   3   0   3   1 |  3  1  1
. . .    x . . |    2 |   *    * 2880 |   0    1   0    2    2 |   0   2   2   1   4   1 |  1   4   1   2   2 |  2  2  1
---------------+------+---------------+------------------------+-------------------------+--------------------+---------
x3x .    . . . |    6 |   3    3    0 | 640    *   *    *    * |   1   3   0   0   0   0 |  3   3   0   0   0 |  3  1  0
x . .    x . . |    4 |   2    0    2 |   * 1440   *    *    * |   0   2   2   0   0   0 |  1   4   1   0   0 |  2  2  0
. x3o    . . . |    3 |   0    3    0 |   *    * 640    *    * |   1   0   0   3   0   0 |  3   0   0   3   0 |  3  0  1
. x . *b3x . . |    6 |   0    3    3 |   *    *   * 1920    * |   0   1   0   1   2   0 |  1   2   0   2   1 |  2  1  1
. . .    x3o . |    3 |   0    0    3 |   *    *   *    * 1920 |   0   0   1   0   2   1 |  0   2   1   1   2 |  1  2  1
---------------+------+---------------+------------------------+-------------------------+--------------------+---------
x3x3o    . . .    12 |   6   12    0 |   4    0   4    0    0 | 160   *   *   *   *   * |  3   0   0   0   0 |  3  0  0
x3x . *b3x . .    24 |  12   12   12 |   4    6   0    4    0 |   * 480   *   *   *   * |  1   2   0   0   0 |  2  1  0
x . .    x3o .     6 |   3    0    6 |   0    3   0    0    2 |   *   * 960   *   *   * |  0   2   1   0   0 |  1  2  0
. x3o *b3x . .    12 |   0   12    6 |   0    0   4    4    0 |   *   *   * 480   *   * |  1   0   0   2   0 |  2  0  1
. x . *b3x3o .    12 |   0    6   12 |   0    0   0    4    4 |   *   *   *   * 960   * |  0   1   0   1   1 |  1  1  1
. . .    x3o3o     4 |   0    0    6 |   0    0   0    0    4 |   *   *   *   *   * 480 |  0   0   1   0   2 |  0  2  1
---------------+------+---------------+------------------------+-------------------------+--------------------+---------
x3x3o *b3x . .    96 |  48   96   48 |  32   24  32   32    0 |   8   8   0   8   0   0 | 60   *   *   *   * |  2  0  0
x3x . *b3x3o .    60 |  30   30   60 |  10   30   0   20   20 |   0   5  10   0   5   0 |  * 192   *   *   * |  1  1  0
x . .    x3o3o     8 |   4    0   12 |   0    6   0    0    8 |   0   0   4   0   0   2 |  *   * 240   *   * |  0  2  0
. x3o *b3x3o .    30 |   0   30   30 |   0    0  10   20   10 |   0   0   0   5   5   0 |  *   *   * 192   * |  1  0  1
. x . *b3x3o3o    20 |   0   10   30 |   0    0   0   10   20 |   0   0   0   0   5   5 |  *   *   *   * 192 |  0  1  1
---------------+------+---------------+------------------------+-------------------------+--------------------+---------
x3x3o *b3x3o .   480 | 240  480  480 | 160  240 160  320  160 |  40  80  80  80  80   0 | 10  16   0  16   0 | 12  *  *
x3x . *b3x3o3o   120 |  60   60  180 |  20   90   0   60  120 |   0  15  60   0  30  30 |  0   6  15   0   6 |  * 32  *
. x3o *b3x3o3o    60 |   0   60   90 |   0    0  20   60   60 |   0   0   0  15  30  15 |  0   0   0   6   6 |  *  * 32

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