Acronym pithax
Name prismatotruncated hemihexeract,
runcitruncated demihexeract,
stericantic hexeract
Circumradius sqrt(35)/2 = 2.958040
Coordinates (5/sqrt(8), 5/sqrt(8), 3/sqrt(8), 3/sqrt(8), 1/sqrt(8), 1/sqrt(8))     & all permutations, all even changes of sign
External
links
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Incidence matrix according to Dynkin symbol

x3x3o *b3o3x3o

o3o3o *b3o3o3o | 2880 |    1    4    4 |    4    4    2    2    8    2    2 |   2   2    8   2   2   1    4   4    4   1 |  1   4   4   4   1   2   2   2 |  2   2  2  1
---------------+------+----------------+------------------------------------+--------------------------------------------+--------------------------------+-------------
x . .    . . . |    2 | 1440    *    * |    4    4    0    0    0    0    0 |   2   2    8   2   2   0    0   0    0   0 |  1   4   4   4   1   0   0   0 |  2   2  2  0
. x .    . . . |    2 |    * 5760    * |    1    0    1    1    2    0    0 |   1   1    2   0   0   1    2   2    1   0 |  1   2   2   1   0   2   1   1 |  2   1  1  1
. . .    . x . |    2 |    *    * 5760 |    0    1    0    0    2    1    1 |   0   0    2   1   1   0    1   2    2   1 |  0   1   2   2   1   1   1   2 |  1   1  2  1
---------------+------+----------------+------------------------------------+--------------------------------------------+--------------------------------+-------------
x3x .    . . . |    6 |    3    3    0 | 1920    *    *    *    *    *    * |   1   1    2   0   0   0    0   0    0   0 |  1   2   2   1   0   0   0   0 |  2   1  1  0
x . .    . x . |    4 |    2    0    2 |    * 2880    *    *    *    *    * |   0   0    2   1   1   0    0   0    0   0 |  0   1   2   2   1   0   0   0 |  1   1  2  0
. x3o    . . . |    3 |    0    3    0 |    *    * 1920    *    *    *    * |   1   0    0   0   0   1    2   0    0   0 |  1   2   0   0   0   2   1   0 |  2   1  0  1
. x . *b3o . . |    3 |    0    3    0 |    *    *    * 1920    *    *    * |   0   1    0   0   0   1    0   2    0   0 |  1   0   2   0   0   2   0   1 |  2   0  1  1
. x .    . x . |    4 |    0    2    2 |    *    *    *    * 5760    *    * |   0   0    1   0   0   0    1   1    1   0 |  0   1   1   1   0   1   1   1 |  1   1  1  1
. . .    o3x . |    3 |    0    0    3 |    *    *    *    *    * 1920    * |   0   0    0   1   0   0    0   2    0   1 |  0   0   2   0   1   1   0   2 |  1   0  2  1
. . .    . x3o |    3 |    0    0    3 |    *    *    *    *    *    * 1920 |   0   0    0   0   1   0    0   0    2   1 |  0   0   0   2   1   0   1   2 |  0   1  2  1
---------------+------+----------------+------------------------------------+--------------------------------------------+--------------------------------+-------------
x3x3o    . . .    12 |    6   12    0 |    4    0    4    0    0    0    0 | 480   *    *   *   *   *    *   *    *   * |  1   2   0   0   0   0   0   0 |  2   1  0  0
x3x . *b3o . .    12 |    6   12    0 |    4    0    0    4    0    0    0 |   * 480    *   *   *   *    *   *    *   * |  1   0   2   0   0   0   0   0 |  2   0  1  0
x3x .    . x .    12 |    6    6    6 |    2    3    0    0    3    0    0 |   *   * 1920   *   *   *    *   *    *   * |  0   1   1   1   0   0   0   0 |  1   1  1  0
x . .    o3x .     6 |    3    0    6 |    0    3    0    0    0    2    0 |   *   *    * 960   *   *    *   *    *   * |  0   0   2   0   1   0   0   0 |  1   0  2  0
x . .    . x3o     6 |    3    0    6 |    0    3    0    0    0    0    2 |   *   *    *   * 960   *    *   *    *   * |  0   0   0   2   1   0   0   0 |  0   1  2  0
. x3o *b3o . .     6 |    0   12    0 |    0    0    4    4    0    0    0 |   *   *    *   *   * 480    *   *    *   * |  1   0   0   0   0   2   0   0 |  2   0  0  1
. x3o    . x .     6 |    0    6    3 |    0    0    2    0    3    0    0 |   *   *    *   *   *   * 1920   *    *   * |  0   1   0   0   0   1   1   0 |  1   1  0  1
. x . *b3o3x .    12 |    0   12   12 |    0    0    0    4    6    4    0 |   *   *    *   *   *   *    * 960    *   * |  0   0   1   0   0   1   0   1 |  1   0  1  1
. x .    . x3o     6 |    0    3    6 |    0    0    0    0    3    0    2 |   *   *    *   *   *   *    *   * 1920   * |  0   0   0   1   0   0   1   1 |  0   1  1  1
. . .    o3x3o     6 |    0    0   12 |    0    0    0    0    0    4    4 |   *   *    *   *   *   *    *   *    * 480 |  0   0   0   0   1   0   0   2 |  0   0  2  1
---------------+------+----------------+------------------------------------+--------------------------------------------+--------------------------------+-------------
x3x3o *b3o . .    48 |   24   96    0 |   32    0   32   32    0    0    0 |   8   8    0   0   0   8    0   0    0   0 | 60   *   *   *   *   *   *   * |  2   0  0  0
x3x3o    . x .    24 |   12   24   12 |    8    6    8    0   12    0    0 |   2   0    4   0   0   0    4   0    0   0 |  * 480   *   *   *   *   *   * |  1   1  0  0
x3x . *b3o3x .    60 |   30   60   60 |   20   30    0   20   30   20    0 |   0   5   10  10   0   0    0   5    0   0 |  *   * 192   *   *   *   *   * |  1   0  1  0
x3x .    . x3o    18 |    9    9   18 |    3    9    0    0    9    0    6 |   0   0    3   0   3   0    0   0    3   0 |  *   *   * 640   *   *   *   * |  0   1  1  0
x . .    o3x3o    12 |    6    0   24 |    0   12    0    0    0    8    8 |   0   0    0   4   4   0    0   0    0   2 |  *   *   *   * 240   *   *   * |  0   0  2  0
. x3o *b3o3x .    30 |    0   60   30 |    0    0   20   20   30   10    0 |   0   0    0   0   0   5   10   5    0   0 |  *   *   *   *   * 192   *   * |  1   0  0  1
. x3o    . x3o     9 |    0    9    9 |    0    0    3    0    9    0    3 |   0   0    0   0   0   0    3   0    3   0 |  *   *   *   *   *   * 640   * |  0   1  0  1
. x . *b3o3x3o    30 |    0   30   60 |    0    0    0   10   30   20   20 |   0   0    0   0   0   0    0   5   10   5 |  *   *   *   *   *   *   * 192 |  0   0  1  1
---------------+------+----------------+------------------------------------+--------------------------------------------+--------------------------------+-------------
x3x3o *b3o3x .   480 |  240  960  480 |  320  240  320  320  480  160    0 |  80  80  160  80   0  80  160  80    0   0 | 10  40  16   0   0  16   0   0 | 12   *  *  *
x3x3o    . x3o    36 |   18   36   36 |   12   18   12    0   36    0   12 |   3   0   12   0   6   0   12   0   12   0 |  0   3   0   4   0   0   4   0 |  * 160  *  *
x3x . *b3o3x3o   180 |   90  180  360 |   60  180    0   60  180  120  120 |   0  15   60  60  60   0    0  30   60  30 |  0   0   6  20  15   0   0   6 |  *   * 32  *
. x3o *b3o3x3o    90 |    0  180  180 |    0    0   60   60  180   60   60 |   0   0    0   0   0  15   60  30   60  15 |  0   0   0   0   0   6  20   6 |  *   *  * 32

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