Acronym catax
Name cellitruncated hexeract
Circumradius sqrt[(14+7 sqrt(2))/2] = 3.456841
Coordinates ((1+2 sqrt(2))/2, (1+2 sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, 1/2)   & all permutations, all changes of sign
External
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Incidence matrix according to Dynkin symbol

o3x3o3o3x4x

. . . . . . | 3840 |     6    3    1 |    3    6    12    6    3    3 |    3    6    3    2    6    6    6   12   1   3 |   1   3   3    3   6   2   2   6   6  1 |  1   1   3   3  2
------------+------+-----------------+--------------------------------+-------------------------------------------------+-----------------------------------------+------------------
. x . . . . |    2 | 11520    *    * |    1    2     2    1    0    0 |    2    2    1    1    2    2    1    2   0   0 |   1   2   2    1   2   1   1   2   1  0 |  1   1   2   1  1
. . . . x . |    2 |     * 5760    * |    0    0     4    0    2    1 |    0    2    0    0    2    0    4    4   1   2 |   0   1   0    2   2   2   0   2   4  1 |  1   0   1   2  2
. . . . . x |    2 |     *    * 1920 |    0    0     0    6    0    3 |    0    0    3    0    0    6    0   12   0   4 |   0   0   3    0   6   0   2   6   6  1 |  0   1   3   3  2
------------+------+-----------------+--------------------------------+-------------------------------------------------+-----------------------------------------+------------------
o3x . . . . |    3 |     3    0    0 | 3840    *     *    *    *    * |    2    2    1    0    0    0    0    0   0   0 |   1   2   2    1   2   0   0   0   0  0 |  1   1   2   1  0
. x3o . . . |    3 |     3    0    0 |    * 7680     *    *    *    * |    1    0    0    1    1    1    0    0   0   0 |   1   1   1    0   0   1   1   1   0  0 |  1   1   1   0  1
. x . . x . |    4 |     2    2    0 |    *    * 11520    *    *    * |    0    1    0    0    1    0    1    1   0   0 |   0   1   0    1   1   1   0   1   1  0 |  1   0   1   1  1
. x . . . x |    4 |     2    0    2 |    *    *     * 5760    *    * |    0    0    1    0    0    2    0    2   0   0 |   0   0   2    0   2   0   1   2   1  0 |  0   1   2   1  1
. . . o3x . |    3 |     0    3    0 |    *    *     *    * 3840    * |    0    0    0    0    0    0    2    0   1   1 |   0   0   0    1   0   2   0   0   2  1 |  1   0   0   1  2
. . . . x4x |    8 |     0    4    4 |    *    *     *    *    * 1440 |    0    0    0    0    0    0    0    4   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 | 1920    *    *    *    *    *    *    *   *   * |   1   1   1    0   0   0   0   0   0  0 |  1   1   1   0  0
o3x . . x .     6 |     6    3    0 |    2    0     3    0    0    0 |    * 3840    *    *    *    *    *    *   *   * |   0   1   0    1   1   0   0   0   0  0 |  1   0   1   1  0
o3x . . . x     6 |     6    0    3 |    2    0     0    3    0    0 |    *    * 1920    *    *    *    *    *   *   * |   0   0   2    0   2   0   0   0   0  0 |  0   1   2   1  0
. x3o3o . .     4 |     6    0    0 |    0    4     0    0    0    0 |    *    *    * 1920    *    *    *    *   *   * |   1   0   0    0   0   1   1   0   0  0 |  1   1   0   0  1
. x3o . x .     6 |     6    3    0 |    0    2     3    0    0    0 |    *    *    *    * 3840    *    *    *   *   * |   0   1   0    0   0   1   0   1   0  0 |  1   0   1   0  1
. x3o . . x     6 |     6    0    3 |    0    2     0    3    0    0 |    *    *    *    *    * 3840    *    *   *   * |   0   0   1    0   0   0   1   1   0  0 |  0   1   1   0  1
. x . o3x .     6 |     3    6    0 |    0    0     3    0    2    0 |    *    *    *    *    *    * 3840    *   *   * |   0   0   0    1   0   1   0   0   1  0 |  1   0   0   1  1
. x . . x4x    16 |     8    8    8 |    0    0     4    4    0    2 |    *    *    *    *    *    *    * 2880   *   * |   0   0   0    0   1   0   0   1   1  0 |  0   0   1   1  1
. . o3o3x .     4 |     0    6    0 |    0    0     0    0    4    0 |    *    *    *    *    *    *    *    * 960   * |   0   0   0    0   0   2   0   0   0  1 |  1   0   0   0  2
. . . o3x4x    24 |     0   24   12 |    0    0     0    0    8    6 |    *    *    *    *    *    *    *    *   * 480 |   0   0   0    0   0   0   0   0   2  1 |  0   0   0   1  2
------------+------+-----------------+--------------------------------+-------------------------------------------------+-----------------------------------------+------------------
o3x3o3o . .    10 |    30    0    0 |   10   20     0    0    0    0 |    5    0    0    5    0    0    0    0   0   0 | 384   *   *    *   *   *   *   *   *  * |  1   1   0   0  0
o3x3o . x .    12 |    24    6    0 |    8    8    12    0    0    0 |    2    4    0    0    4    0    0    0   0   0 |   * 960   *    *   *   *   *   *   *  * |  1   0   1   0  0
o3x3o . . x    12 |    24    0    6 |    8    8     0   12    0    0 |    2    0    4    0    0    4    0    0   0   0 |   *   * 960    *   *   *   *   *   *  * |  0   1   1   0  0
o3x . o3x .     9 |     9    9    0 |    3    0     9    0    3    0 |    0    3    0    0    0    0    3    0   0   0 |   *   *   * 1280   *   *   *   *   *  * |  1   0   0   1  0
o3x . . x4x    24 |    24   12   12 |    8    0    12   12    0    3 |    0    4    4    0    0    0    0    3   0   0 |   *   *   *    * 960   *   *   *   *  * |  0   0   1   1  0
. x3o3o3x .    20 |    30   30    0 |    0   20    30    0   20    0 |    0    0    0    5   10    0   10    0   5   0 |   *   *   *    *   * 384   *   *   *  * |  1   0   0   0  1
. x3o3o . x     8 |    12    0    4 |    0    8     0    6    0    0 |    0    0    0    2    0    4    0    0   0   0 |   *   *   *    *   *   * 960   *   *  * |  0   1   0   0  1
. x3o . x4x    24 |    24   12   12 |    0    8    12   12    0    3 |    0    0    0    0    4    4    0    3   0   0 |   *   *   *    *   *   *   * 960   *  * |  0   0   1   0  1
. x . o3x4x    48 |    24   48   24 |    0    0    24   12   16   12 |    0    0    0    0    0    0    8    6   0   2 |   *   *   *    *   *   *   *   * 480  * |  0   0   0   1  1
. . o3o3x4x    64 |     0   96   32 |    0    0     0    0   64   24 |    0    0    0    0    0    0    0    0  16   8 |   *   *   *    *   *   *   *   *   * 60 |  0   0   0   0  2
------------+------+-----------------+--------------------------------+-------------------------------------------------+-----------------------------------------+------------------
o3x3o3o3x .    60 |   180   90    0 |   60  120   180    0   60    0 |   30   60    0   30   60    0   60    0  15   0 |   6  15   0   20   0   6   0   0   0  0 | 64   *   *   *  *
o3x3o3o . x    20 |    60    0   10 |   20   40     0   30    0    0 |   10    0   10   10    0   20    0    0   0   0 |   2   0   5    0   0   0   5   0   0  0 |  * 192   *   *  *
o3x3o . x4x    48 |    96   24   24 |   32   32    48   48    0    6 |    8   16   16    0   16   16    0   12   0   0 |   0   4   4    0   4   0   0   4   0  0 |  *   * 240   *  *
o3x . o3x4x    72 |    72   72   36 |   24    0    72   36   24   18 |    0   24   12    0    0    0   24   18   0   3 |   0   0   0    8   6   0   0   0   3  0 |  *   *   * 160  *
. x3o3o3x4x   640 |   960  960  320 |    0  640   960  480  640  240 |    0    0    0  160  320  320  320  240 160  80 |   0   0   0    0   0  32  80  80  40 10 |  *   *   *   * 12

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