Acronym crax (old: scrax)
Name (small) cellirhombated hexeract,
stericantellated hexeract
Circumradius sqrt[(13+6 sqrt(2))/2] = 3.277597
Coordinates ((1+2 sqrt(2))/2, (1+2 sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2)   & all permutations, all changes of sign
External
links
wikipedia

Incidence matrix according to Dynkin symbol

o3x3o3x3o4x

. . . . . . | 5760 |     4     4    2 |    2    2     8     8    2    2    4    1 |   1    4    4    4    4    4    8    4   1    2   2 |   2   2    2    4   2   2   4   2   4  1 |  1   2   1   2  2
------------+------+------------------+-------------------------------------------+-----------------------------------------------------+------------------------------------------+------------------
. x . . . . |    2 | 11520     *    * |    1    1     2     2    0    0    0    0 |   1    2    2    2    2    1    2    1   0    0   0 |   2   2    1    2   1   1   2   1   1  0 |  1   2   1   1  1
. . . x . . |    2 |     * 11520    * |    0    0     2     0    1    1    1    0 |   0    1    0    2    0    2    2    0   1    1   1 |   1   0    1    1   0   2   2   0   2  1 |  1   1   0   1  2
. . . . . x |    2 |     *     * 5760 |    0    0     0     4    0    0    2    1 |   0    0    2    0    2    0    4    4   0    1   2 |   0   1    0    2   2   0   2   2   4  1 |  0   1   1   2  2
------------+------+------------------+-------------------------------------------+-----------------------------------------------------+------------------------------------------+------------------
o3x . . . . |    3 |     3     0    0 | 3840    *     *     *    *    *    *    * |   1    2    2    0    0    0    0    0   0    0   0 |   2   2    1    2   1   0   0   0   0  0 |  1   2   1   1  0
. x3o . . . |    3 |     3     0    0 |    * 3840     *     *    *    *    *    * |   1    0    0    2    2    0    0    0   0    0   0 |   2   2    0    0   0   1   2   1   0  0 |  1   2   1   0  1
. x . x . . |    4 |     2     2    0 |    *    * 11520     *    *    *    *    * |   0    1    0    1    0    1    1    0   0    0   0 |   1   0    1    1   0   1   1   0   1  0 |  1   1   0   1  1
. x . . . x |    4 |     2     0    2 |    *    *     * 11520    *    *    *    * |   0    0    1    0    1    0    1    1   0    0   0 |   0   1    0    1   1   0   1   1   1  0 |  0   1   1   1  1
. . o3x . . |    3 |     0     3    0 |    *    *     *     * 3840    *    *    * |   0    0    0    2    0    0    0    0   1    1   0 |   1   0    0    0   0   2   2   0   0  1 |  1   1   0   0  2
. . . x3o . |    3 |     0     3    0 |    *    *     *     *    * 3840    *    * |   0    0    0    0    0    2    0    0   1    0   1 |   0   0    1    0   0   2   0   0   2  1 |  1   0   0   1  2
. . . x . x |    4 |     0     2    2 |    *    *     *     *    *    * 5760    * |   0    0    0    0    0    0    2    0   0    1   1 |   0   0    0    1   0   0   2   0   2  1 |  0   1   0   1  2
. . . . o4x |    4 |     0     0    4 |    *    *     *     *    *    *    * 1440 |   0    0    0    0    0    0    0    4   0    0   2 |   0   0    0    0   2   0   0   2   4  1 |  0   0   1   2  2
------------+------+------------------+-------------------------------------------+-----------------------------------------------------+------------------------------------------+------------------
o3x3o . . .     6 |    12     0    0 |    4    4     0     0    0    0    0    0 | 960    *    *    *    *    *    *    *   *    *   * |   2   2    0    0   0   0   0   0   0  0 |  1   2   1   0  0
o3x . x . .     6 |     6     3    0 |    2    0     3     0    0    0    0    0 |   * 3840    *    *    *    *    *    *   *    *   * |   1   0    1    1   0   0   0   0   0  0 |  1   1   0   1  0
o3x . . . x     6 |     6     0    3 |    2    0     0     3    0    0    0    0 |   *    * 3840    *    *    *    *    *   *    *   * |   0   1    0    1   1   0   0   0   0  0 |  0   1   1   1  0
. x3o3x . .    12 |    12    12    0 |    0    4     6     0    4    0    0    0 |   *    *    * 1920    *    *    *    *   *    *   * |   1   0    0    0   0   1   1   0   0  0 |  1   1   0   0  1
. x3o . . x     6 |     6     0    3 |    0    2     0     3    0    0    0    0 |   *    *    *    * 3840    *    *    *   *    *   * |   0   1    0    0   0   0   1   1   0  0 |  0   1   1   0  1
. x . x3o .     6 |     3     6    0 |    0    0     3     0    0    2    0    0 |   *    *    *    *    * 3840    *    *   *    *   * |   0   0    1    0   0   1   0   0   1  0 |  1   0   0   1  1
. x . x . x     8 |     4     4    4 |    0    0     2     2    0    0    2    0 |   *    *    *    *    *    * 5760    *   *    *   * |   0   0    0    1   0   0   1   0   1  0 |  0   1   0   1  1
. x . . o4x     8 |     4     0    8 |    0    0     0     4    0    0    0    2 |   *    *    *    *    *    *    * 2880   *    *   * |   0   0    0    0   1   0   0   1   1  0 |  0   0   1   1  1
. . o3x3o .     6 |     0    12    0 |    0    0     0     0    4    4    0    0 |   *    *    *    *    *    *    *    * 960    *   * |   0   0    0    0   0   2   0   0   0  1 |  1   0   0   0  2
. . o3x . x     6 |     0     6    3 |    0    0     0     0    2    0    3    0 |   *    *    *    *    *    *    *    *   * 1920   * |   0   0    0    0   0   0   2   0   0  1 |  0   1   0   0  2
. . . x3o4x    24 |     0    24   24 |    0    0     0     0    0    8   12    6 |   *    *    *    *    *    *    *    *   *    * 480 |   0   0    0    0   0   0   0   0   2  1 |  0   0   0   1  2
------------+------+------------------+-------------------------------------------+-----------------------------------------------------+------------------------------------------+------------------
o3x3o3x . .    30 |    60    30    0 |   20   20    30     0   10    0    0    0 |   5   10    0    5    0    0    0    0   0    0   0 | 384   *    *    *   *   *   *   *   *  * |  1   1   0   0  0
o3x3o . . x    12 |    24     0    6 |    8    8     0    12    0    0    0    0 |   2    0    4    0    4    0    0    0   0    0   0 |   * 960    *    *   *   *   *   *   *  * |  0   1   1   0  0
o3x . x3o .     9 |     9     9    0 |    3    0     9     0    0    3    0    0 |   0    3    0    0    0    3    0    0   0    0   0 |   *   * 1280    *   *   *   *   *   *  * |  1   0   0   1  0
o3x . x . x    12 |    12     6    6 |    4    0     6     6    0    0    3    0 |   0    2    2    0    0    0    3    0   0    0   0 |   *   *    * 1920   *   *   *   *   *  * |  0   1   0   1  0
o3x . . o4x    12 |    12     0   12 |    4    0     0    12    0    0    0    3 |   0    0    4    0    0    0    0    3   0    0   0 |   *   *    *    * 960   *   *   *   *  * |  0   0   1   1  0
. x3o3x3o .    30 |    30    60    0 |    0   10    30     0   20   20    0    0 |   0    0    0    5    0   10    0    0   5    0   0 |   *   *    *    *   * 384   *   *   *  * |  1   0   0   0  1
. x3o3x . x    24 |    24    24   12 |    0    8    12    12    8    0   12    0 |   0    0    0    2    4    0    6    0   0    4   0 |   *   *    *    *   *   * 960   *   *  * |  0   1   0   0  1
. x3o . o4x    12 |    12     0   12 |    0    4     0    12    0    0    0    3 |   0    0    0    0    4    0    0    3   0    0   0 |   *   *    *    *   *   *   * 960   *  * |  0   0   1   0  1
. x . x3o4x    48 |    24    48   48 |    0    0    24    24    0   16   24   12 |   0    0    0    0    0    8   12    6   0    0   2 |   *   *    *    *   *   *   *   * 480  * |  0   0   0   1  1
. . o3x3o4x    96 |     0   192   96 |    0    0     0     0   64   64   96   24 |   0    0    0    0    0    0    0    0  16   32   8 |   *   *    *    *   *   *   *   *   * 60 |  0   0   0   0  2
------------+------+------------------+-------------------------------------------+-----------------------------------------------------+------------------------------------------+------------------
o3x3o3x3o .    90 |   180   180    0 |   60   60   180     0   60   60    0    0 |  15   60    0   30    0   60    0    0  15    0   0 |   6   0   20    0   0   6   0   0   0  0 | 64   *   *   *  *
o3x3o3x . x    60 |   120    60   30 |   40   40    60    60   20    0   30    0 |  10   20   20   10   20    0   30    0   0   10   0 |   2   5    0   10   0   0   5   0   0  0 |  * 192   *   *  *
o3x3o . o4x    24 |    48     0   24 |   16   16     0    48    0    0    0    6 |   4    0   16    0   16    0    0   12   0    0   0 |   0   4    0    0   4   0   0   4   0  0 |  *   * 240   *  *
o3x . x3o4x    72 |    72    72   72 |   24    0    72    72    0   24   36   18 |   0   24   24    0    0   24   36   18   0    0   3 |   0   0    8   12   6   0   0   0   3  0 |  *   *   * 160  *
. x3o3x3o4x   960 |   960  1920  960 |    0  320   960   960  640  640  960  240 |   0    0    0  160  320  320  480  240 160  320  80 |   0   0    0    0   0  32  80  80  40 10 |  *   *   *   * 12

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