Acronym sophax
Name small prismated hemihexeract,
runcinated demihexeract
Circumradius sqrt(11)/2 = 1.658312
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Incidence matrix according to Dynkin symbol

x3o3o *b3o3x3o

. . .    . . . | 480 |    6    8 |   12   24   12   4 |   4   4   24  12  12   8   6 |  1   8   8  12   6   2   4 |  2   4  4  1
---------------+-----+-----------+--------------------+------------------------------+----------------------------+-------------
x . .    . . . |   2 | 1440    * |    4    4    0   0 |   2   2    8   2   2   0   0 |  1   4   4   4   1   0   0 |  2   2  2  0
. . .    . x . |   2 |    * 1920 |    0    3    3   1 |   0   0    3   3   3   3   3 |  0   1   3   3   3   1   3 |  1   1  3  1
---------------+-----+-----------+--------------------+------------------------------+----------------------------+-------------
x3o .    . . . |   3 |    3    0 | 1920    *    *   * |   1   1    2   0   0   0   0 |  1   2   2   1   0   0   0 |  2   1  1  0
x . .    . x . |   4 |    2    2 |    * 2880    *   * |   0   0    2   1   1   0   0 |  0   1   2   2   1   0   0 |  1   1  2  0
. . .    o3x . |   3 |    0    3 |    *    * 1920   * |   0   0    0   1   0   2   1 |  0   0   2   0   1   1   2 |  1   0  2  1
. . .    . x3o |   3 |    0    3 |    *    *    * 640 |   0   0    0   0   3   0   3 |  0   0   0   3   3   0   3 |  0   1  3  1
---------------+-----+-----------+--------------------+------------------------------+----------------------------+-------------
x3o3o    . . .    4 |    6    0 |    4    0    0   0 | 480   *    *   *   *   *   * |  1   2   0   0   0   0   0 |  2   1  0  0
x3o . *b3o . .    4 |    6    0 |    4    0    0   0 |   * 480    *   *   *   *   * |  1   0   2   0   0   0   0 |  2   0  1  0
x3o .    . x .    6 |    6    3 |    2    3    0   0 |   *   * 1920   *   *   *   * |  0   1   1   1   0   0   0 |  1   1  1  0
x . .    o3x .    6 |    3    6 |    0    3    2   0 |   *   *    * 960   *   *   * |  0   0   2   0   1   0   0 |  1   0  2  0
x . .    . x3o    6 |    3    6 |    0    3    0   2 |   *   *    *   * 960   *   * |  0   0   0   2   1   0   0 |  0   1  2  0
. o . *b3o3x .    4 |    0    6 |    0    0    4   0 |   *   *    *   *   * 960   * |  0   0   1   0   0   1   1 |  1   0  1  1
. . .    o3x3o    6 |    0   12 |    0    0    4   4 |   *   *    *   *   *   * 480 |  0   0   0   0   1   0   2 |  0   0  2  1
---------------+-----+-----------+--------------------+------------------------------+----------------------------+-------------
x3o3o *b3o . .    8 |   24    0 |   32    0    0   0 |   8   8    0   0   0   0   0 | 60   *   *   *   *   *   * |  2   0  0  0
x3o3o    . x .    8 |   12    4 |    8    6    0   0 |   2   0    4   0   0   0   0 |  * 480   *   *   *   *   * |  1   1  0  0
x3o . *b3o3x .   20 |   30   30 |   20   30   20   0 |   0   5   10  10   0   5   0 |  *   * 192   *   *   *   * |  1   0  1  0
x3o .    . x3o    9 |    9    9 |    3    9    0   3 |   0   0    3   0   3   0   0 |  *   *   * 640   *   *   * |  0   1  1  0
x . .    o3x3o   12 |    6   24 |    0   12    8   8 |   0   0    0   4   4   0   2 |  *   *   *   * 240   *   * |  0   0  2  0
. o3o *b3o3x .    5 |    0   10 |    0    0   10   0 |   0   0    0   0   0   5   0 |  *   *   *   *   * 192   * |  1   0  0  1
. o . *b3o3x3o   10 |    0   30 |    0    0   20  10 |   0   0    0   0   0   5   5 |  *   *   *   *   *   * 192 |  0   0  1  1
---------------+-----+-----------+--------------------+------------------------------+----------------------------+-------------
x3o3o *b3o3x .   80 |  240  160 |  320  240  160   0 |  80  80  160  80   0  80   0 | 10  40  16   0   0  16   0 | 12   *  *  *
x3o3o    . x3o   12 |   18   12 |   12   18    0   4 |   3   0   12   0   6   0   0 |  0   3   0   4   0   0   0 |  * 160  *  *
x3o . *b3o3x3o   60 |   90  180 |   60  180  120  60 |   0  15   60  60  60  30  30 |  0   0   6  20  15   0   6 |  *   * 32  *
. o3o *b3o3x3o   15 |    0   60 |    0    0   60  20 |   0   0    0   0   0  30  15 |  0   0   0   0   0   6   6 |  *   *  * 32

xxoo3oooo3oooo *b3oxxo3xoox&#xt   → all heights = 1/sqrt(2) = 0.707107
(siphin || pseudo sirhin || pseudo alt sirhin || alt siphin)

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