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
Face vector 1920, 5760, 6560, 3520, 876, 76
Confer
general polytopal classes:
Wythoffian polypeta   lace simplices  
External
links
wikipedia   polytopewiki  

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

o3o3x3x3o4s

demi( . . . . . . ) | 1920 |    3    2   1 |    3    6   1    3   2 |   1   6   3   3   1   6 |   2   3   1  3   6 |  1  3  2
--------------------+------+---------------+------------------------+-------------------------+--------------------+---------
demi( . . x . . . ) |    2 | 2880    *   * |    2    2   0    1   0 |   1   4   1   2   0   2 |   2   2   1  1   4 |  1  2  2
demi( . . . x . . ) |    2 |    * 1920   * |    0    3   1    0   1 |   0   3   3   0   1   3 |   1   3   0  3   3 |  1  3  1
      . . . . o4s   |    2 |    *    * 960 |    0    0   0    3   2 |   0   0   0   3   1   6 |   0   0   1  3   6 |  0  3  2
--------------------+------+---------------+------------------------+-------------------------+--------------------+---------
demi( . o3x . . . ) |    3 |    3    0   0 | 1920    *   *    *   * |   1   2   0   2   0   0 |   2   1   1  0   2 |  1  1  2
demi( . . x3x . . ) |    6 |    3    3   0 |    * 1920   *    *   * |   0   2   1   0   0   1 |   1   2   0  1   2 |  1  2  1
demi( . . . x3o . ) |    3 |    0    3   0 |    *    * 640    *   * |   0   0   3   0   1   0 |   0   3   0  3   0 |  1  3  0
      . . x 2 o4s   |    4 |    2    0   2 |    *    *   * 1440   * |   0   0   0   2   0   2 |   0   0   1  1   4 |  0  2  2
sefa( . . . x3o4s ) |    6 |    0    3   3 |    *    *   *    * 640 |   0   0   0   0   1   3 |   0   0   0  3   3 |  0  3  1
--------------------+------+---------------+------------------------+-------------------------+--------------------+---------
demi( o3o3x . . . )     4 |    6    0   0 |    4    0   0    0   0 | 480   *   *   *   *   * |   2   0   1  0   0 |  1  0  2
demi( . o3x3x . . )    12 |   12    6   0 |    4    4   0    0   0 |   * 960   *   *   *   * |   1   1   0  0   1 |  1  1  1
demi( . . x3x3o . )    12 |    6   12   0 |    0    4   4    0   0 |   *   * 480   *   *   * |   0   2   0  1   0 |  1  2  0
      . o3x 2 o4s       6 |    6    0   3 |    2    0   0    3   0 |   *   *   * 960   *   * |   0   0   1  0   2 |  0  1  2
      . . . x3o4s      12 |    0   12   6 |    0    0   4    0   4 |   *   *   *   * 160   * |   0   0   0  3   0 |  0  3  0
sefa( . . x3x3o4s )    24 |   12   12  12 |    0    4   0    6   4 |   *   *   *   *   * 480 |   0   0   0  1   2 |  0  2  1
--------------------+------+---------------+------------------------+-------------------------+--------------------+---------
demi( o3o3x3x . . )    20 |   30   10   0 |   20   10   0    0   0 |   5   5   0   0   0   0 | 192   *   *  *   * |  1  0  1
demi( . o3x3x3o . )    30 |   30   30   0 |   10   20  10    0   0 |   0   5   5   0   0   0 |   * 192   *  *   * |  1  1  0
      o3o3x 2 o4s       8 |   12    0   4 |    8    0   0    6   0 |   2   0   0   4   0   0 |   *   * 240  *   * |  0  0  2
      . . x3x3o4s      96 |   48   96  48 |    0   32  32   24  32 |   0   0   8   0   8   8 |   *   *   * 60   * |  0  2  0
sefa( . o3x3x3o4s )    60 |   60   30  30 |   20   20   0   30  10 |   0   5   0  10   0   5 |   *   *   *  * 192 |  0  1  1
--------------------+------+---------------+------------------------+-------------------------+--------------------+---------
demi( o3o3x3x3o . )    60 |   90   60   0 |   60   60  20    0   0 |  15  30  15   0   0   0 |   6   6   0  0   0 | 32  *  *
      . o3x3x3o4s     480 |  480  480 240 |  160  320 160  240 160 |   0  80  80  80  40  80 |   0  16   0 10  16 |  * 12  *
sefa( o3o3x3x3o4s )   120 |  180   60  60 |  120   60   0   90  20 |  30  30   0  60   0  15 |   6   0  15  0   6 |  *  * 32


starting figure: o3o3x3x3o4x

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