Acronym sirhax
Name small rhombated hemihexeract,
cantellated demihexeract,
runcic hexeract
Circumradius sqrt(15)/2 = 1.936492
Coordinates (3/sqrt(8), 3/sqrt(8), 3/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8))     & all permutations, all even changes of sign
External
links
wikipedia  

Incidence matrix according to Dynkin symbol

x3o3o *b3x3o3o

. . .    . . . | 640 |   3    9 |   3    9    9    9 |   1   9   9   3   9   3 |  3   9   3   3   3 |  3  3  1
---------------+-----+----------+--------------------+-------------------------+--------------------+---------
x . .    . . . |   2 | 960    * |   2    3    0    0 |   1   6   3   0   0   0 |  3   6   1   0   0 |  3  2  0
. . .    x . . |   2 |   * 2880 |   0    1    2    2 |   0   2   2   1   4   1 |  1   4   1   2   2 |  2  2  1
---------------+-----+----------+--------------------+-------------------------+--------------------+---------
x3o .    . . . |   3 |   3    0 | 640    *    *    * |   1   3   0   0   0   0 |  3   3   0   0   0 |  3  1  0
x . .    x . . |   4 |   2    2 |   * 1440    *    * |   0   2   2   0   0   0 |  1   4   1   0   0 |  2  2  0
. o . *b3x . . |   3 |   0    3 |   *    * 1920    * |   0   1   0   1   2   0 |  1   2   0   2   1 |  2  1  1
. . .    x3o . |   3 |   0    3 |   *    *    * 1920 |   0   0   1   0   2   1 |  0   2   1   1   2 |  1  2  1
---------------+-----+----------+--------------------+-------------------------+--------------------+---------
x3o3o    . . .    4 |   6    0 |   4    0    0    0 | 160   *   *   *   *   * |  3   0   0   0   0 |  3  0  0
x3o . *b3x . .   12 |  12   12 |   4    6    4    0 |   * 480   *   *   *   * |  1   2   0   0   0 |  2  1  0
x . .    x3o .    6 |   3    6 |   0    3    0    2 |   *   * 960   *   *   * |  0   2   1   0   0 |  1  2  0
. o3o *b3x . .    4 |   0    6 |   0    0    4    0 |   *   *   * 480   *   * |  1   0   0   2   0 |  2  0  1
. o . *b3x3o .    6 |   0   12 |   0    0    4    4 |   *   *   *   * 960   * |  0   1   0   1   1 |  1  1  1
. . .    x3o3o    4 |   0    6 |   0    0    0    4 |   *   *   *   *   * 480 |  0   0   1   0   2 |  0  2  1
---------------+-----+----------+--------------------+-------------------------+--------------------+---------
x3o3o *b3x . .   32 |  48   48 |  32   24   32    0 |   8   8   0   8   0   0 | 60   *   *   *   * |  2  0  0
x3o . *b3x3o .   30 |  30   60 |  10   30   20   20 |   0   5  10   0   5   0 |  * 192   *   *   * |  1  1  0
x . .    x3o3o    8 |   4   12 |   0    6    0    8 |   0   0   4   0   0   2 |  *   * 240   *   * |  0  2  0
. o3o *b3x3o .   10 |   0   30 |   0    0   20   10 |   0   0   0   5   5   0 |  *   *   * 192   * |  1  0  1
. o . *b3x3o3o   10 |   0   30 |   0    0   10   20 |   0   0   0   0   5   5 |  *   *   *   * 192 |  0  1  1
---------------+-----+----------+--------------------+-------------------------+--------------------+---------
x3o3o *b3x3o .  160 | 240  480 | 160  240  320  160 |  40  80  80  80  80   0 | 10  16   0  16   0 | 12  *  *
x3o . *b3x3o3o   60 |  60  180 |  20   90   60  120 |   0  15  60   0  30  30 |  0   6  15   0   6 |  * 32  *
. o3o *b3x3o3o   20 |   0   90 |   0    0   60   60 |   0   0   0  15  30  15 |  0   0   0   6   6 |  *  * 32

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