Acronym tocrax (old: stocrax)
Name (small) tericellirhombated hexeract,
pentiruncitruncated hexacontitetrapeton
Circumradius sqrt[(18+7 sqrt(2))/2] = 3.734936
Coordinates ((1+3 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
Face vector 11520, 51840, 77760, 48480, 11768, 728
Confer
general polytopal classes:
Wythoffian polypeta   lace simplices  
External
links
wikipedia   polytopewiki  

Incidence matrix according to Dynkin symbol

x3x3o3x3o4x

. . . . . . | 11520 |    1     2     4     2 |    2     4    2    1     4     4    2    2     4    1 |   1    4    4    2    2    4    1    2    2    2    4    2    1    2   2 |   2   2    2    4   2   1    2   2   1   2   1   2   1 |  1   2   1   2  1  1
------------+-------+------------------------+-------------------------------------------------------+--------------------------------------------------------------------------+--------------------------------------------------------+---------------------
x . . . . . |     2 | 5760     *     *     * |    2     4    2    0     0     0    0    0     0    0 |   1    4    4    2    2    4    1    0    0    0    0    0    0    0   0 |   2   2    2    4   2   1    2   2   0   0   0   0   0 |  1   2   1   2  1  0
. x . . . . |     2 |    * 11520     *     * |    1     0    0    1     2     2    0    0     0    0 |   1    2    2    0    0    0    0    2    2    1    2    1    0    0   0 |   2   2    1    2   1   0    0   0   1   2   1   1   0 |  1   2   1   1  0  1
. . . x . . |     2 |    *     * 23040     * |    0     1    0    0     1     0    1    1     1    0 |   0    1    0    1    1    1    0    1    0    1    1    0    1    1   1 |   1   0    1    1   0   1    1   1   1   1   0   1   1 |  1   1   0   1  1  1
. . . . . x |     2 |    *     *     * 11520 |    0     0    1    0     0     2    0    0     2    1 |   0    0    2    0    0    2    1    0    1    0    2    2    0    1   2 |   0   1    0    2   2   0    1   2   0   1   1   2   1 |  0   1   1   2  1  1
------------+-------+------------------------+-------------------------------------------------------+--------------------------------------------------------------------------+--------------------------------------------------------+---------------------
x3x . . . . |     6 |    3     3     0     0 | 3840     *    *    *     *     *    *    *     *    * |   1    2    2    0    0    0    0    0    0    0    0    0    0    0   0 |   2   2    1    2   1   0    0   0   0   0   0   0   0 |  1   2   1   1  0  0
x . . x . . |     4 |    2     0     2     0 |    * 11520    *    *     *     *    *    *     *    * |   0    1    0    1    1    1    0    0    0    0    0    0    0    0   0 |   1   0    1    1   0   1    1   1   0   0   0   0   0 |  1   1   0   1  1  0
x . . . . x |     4 |    2     0     0     2 |    *     * 5760    *     *     *    *    *     *    * |   0    0    2    0    0    2    1    0    0    0    0    0    0    0   0 |   0   1    0    2   2   0    1   2   0   0   0   0   0 |  0   1   1   2  1  0
. x3o . . . |     3 |    0     3     0     0 |    *     *    * 3840     *     *    *    *     *    * |   1    0    0    0    0    0    0    2    2    0    0    0    0    0   0 |   2   2    0    0   0   0    0   0   1   2   1   0   0 |  1   2   1   0  0  1
. x . x . . |     4 |    0     2     2     0 |    *     *    *    * 11520     *    *    *     *    * |   0    1    0    0    0    0    0    1    0    1    1    0    0    0   0 |   1   0    1    1   0   0    0   0   1   1   0   1   0 |  1   1   0   1  0  1
. x . . . x |     4 |    0     2     0     2 |    *     *    *    *     * 11520    *    *     *    * |   0    0    1    0    0    0    0    0    1    0    1    1    0    0   0 |   0   1    0    1   1   0    0   0   0   1   1   1   0 |  0   1   1   1  0  1
. . o3x . . |     3 |    0     0     3     0 |    *     *    *    *     *     * 7680    *     *    * |   0    0    0    1    0    0    0    1    0    0    0    0    1    1   0 |   1   0    0    0   0   1    1   0   1   1   0   0   1 |  1   1   0   0  1  1
. . . x3o . |     3 |    0     0     3     0 |    *     *    *    *     *     *    * 7680     *    * |   0    0    0    0    1    0    0    0    0    1    0    0    1    0   1 |   0   0    1    0   0   1    0   1   1   0   0   1   1 |  1   0   0   1  1  1
. . . x . x |     4 |    0     0     2     2 |    *     *    *    *     *     *    *    * 11520    * |   0    0    0    0    0    1    0    0    0    0    1    0    0    1   1 |   0   0    0    1   0   0    1   1   0   1   0   1   1 |  0   1   0   1  1  1
. . . . o4x |     4 |    0     0     0     4 |    *     *    *    *     *     *    *    *     * 2880 |   0    0    0    0    0    0    1    0    0    0    0    2    0    0   2 |   0   0    0    0   2   0    0   2   0   0   1   2   1 |  0   0   1   2  1  1
------------+-------+------------------------+-------------------------------------------------------+--------------------------------------------------------------------------+--------------------------------------------------------+---------------------
x3x3o . . .     12 |    6    12     0     0 |    4     0    0    4     0     0    0    0     0    0 | 960    *    *    *    *    *    *    *    *    *    *    *    *    *   * |   2   2    0    0   0   0    0   0   0   0   0   0   0 |  1   2   1   0  0  0
x3x . x . .     12 |    6     6     6     0 |    2     3    0    0     3     0    0    0     0    0 |   * 3840    *    *    *    *    *    *    *    *    *    *    *    *   * |   1   0    1    1   0   0    0   0   0   0   0   0   0 |  1   1   0   1  0  0
x3x . . . x     12 |    6     6     0     6 |    2     0    3    0     0     3    0    0     0    0 |   *    * 3840    *    *    *    *    *    *    *    *    *    *    *   * |   0   1    0    1   1   0    0   0   0   0   0   0   0 |  0   1   1   1  0  0
x . o3x . .      6 |    3     0     6     0 |    0     3    0    0     0     0    2    0     0    0 |   *    *    * 3840    *    *    *    *    *    *    *    *    *    *   * |   1   0    0    0   0   1    1   0   0   0   0   0   0 |  1   1   0   0  1  0
x . . x3o .      6 |    3     0     6     0 |    0     3    0    0     0     0    0    2     0    0 |   *    *    *    * 3840    *    *    *    *    *    *    *    *    *   * |   0   0    1    0   0   1    0   1   0   0   0   0   0 |  1   0   0   1  1  0
x . . x . x      8 |    4     0     4     4 |    0     2    2    0     0     0    0    0     2    0 |   *    *    *    *    * 5760    *    *    *    *    *    *    *    *   * |   0   0    0    1   0   0    1   1   0   0   0   0   0 |  0   1   0   1  1  0
x . . . o4x      8 |    4     0     0     8 |    0     0    4    0     0     0    0    0     0    2 |   *    *    *    *    *    * 1440    *    *    *    *    *    *    *   * |   0   0    0    0   2   0    0   2   0   0   0   0   0 |  0   0   1   2  1  0
. x3o3x . .     12 |    0    12    12     0 |    0     0    0    4     6     0    4    0     0    0 |   *    *    *    *    *    *    * 1920    *    *    *    *    *    *   * |   1   0    0    0   0   0    0   0   1   1   0   0   0 |  1   1   0   0  0  1
. x3o . . x      6 |    0     6     0     3 |    0     0    0    2     0     3    0    0     0    0 |   *    *    *    *    *    *    *    * 3840    *    *    *    *    *   * |   0   1    0    0   0   0    0   0   0   1   1   0   0 |  0   1   1   0  0  1
. x . x3o .      6 |    0     3     6     0 |    0     0    0    0     3     0    0    2     0    0 |   *    *    *    *    *    *    *    *    * 3840    *    *    *    *   * |   0   0    1    0   0   0    0   0   1   0   0   1   0 |  1   0   0   1  0  1
. x . x . x      8 |    0     4     4     4 |    0     0    0    0     2     2    0    0     2    0 |   *    *    *    *    *    *    *    *    *    * 5760    *    *    *   * |   0   0    0    1   0   0    0   0   0   1   0   1   0 |  0   1   0   1  0  1
. x . . o4x      8 |    0     4     0     8 |    0     0    0    0     0     4    0    0     0    2 |   *    *    *    *    *    *    *    *    *    *    * 2880    *    *   * |   0   0    0    0   1   0    0   0   0   0   1   1   0 |  0   0   1   1  0  1
. . o3x3o .      6 |    0     0    12     0 |    0     0    0    0     0     0    4    4     0    0 |   *    *    *    *    *    *    *    *    *    *    *    * 1920    *   * |   0   0    0    0   0   1    0   0   1   0   0   0   1 |  1   0   0   0  1  1
. . o3x . x      6 |    0     0     6     3 |    0     0    0    0     0     0    2    0     3    0 |   *    *    *    *    *    *    *    *    *    *    *    *    * 3840   * |   0   0    0    0   0   0    1   0   0   1   0   0   1 |  0   1   0   0  1  1
. . . x3o4x     24 |    0     0    24    24 |    0     0    0    0     0     0    0    8    12    6 |   *    *    *    *    *    *    *    *    *    *    *    *    *    * 960 |   0   0    0    0   0   0    0   1   0   0   0   1   1 |  0   0   0   1  1  1
------------+-------+------------------------+-------------------------------------------------------+--------------------------------------------------------------------------+--------------------------------------------------------+---------------------
x3x3o3x . .     60 |   30    60    60     0 |   20    30    0   20    30     0   20    0     0    0 |   5   10    0   10    0    0    0    5    0    0    0    0    0    0   0 | 384   *    *    *   *   *    *   *   *   *   *   *   * |  1   1   0   0  0  0
x3x3o . . x     24 |   12    24     0    12 |    8     0    6    8     0    12    0    0     0    0 |   2    0    4    0    0    0    0    0    4    0    0    0    0    0   0 |   * 960    *    *   *   *    *   *   *   *   *   *   * |  0   1   1   0  0  0
x3x . x3o .     18 |    9     9    18     0 |    3     9    0    0     9     0    0    6     0    0 |   0    3    0    0    3    0    0    0    0    3    0    0    0    0   0 |   *   * 1280    *   *   *    *   *   *   *   *   *   * |  1   0   0   1  0  0
x3x . x . x     24 |   12    12    12    12 |    4     6    6    0     6     6    0    0     6    0 |   0    2    2    0    0    3    0    0    0    0    3    0    0    0   0 |   *   *    * 1920   *   *    *   *   *   *   *   *   * |  0   1   0   1  0  0
x3x . . o4x     24 |   12    12     0    24 |    4     0   12    0     0    12    0    0     0    6 |   0    0    4    0    0    0    3    0    0    0    0    3    0    0   0 |   *   *    *    * 960   *    *   *   *   *   *   *   * |  0   0   1   1  0  0
x . o3x3o .     12 |    6     0    24     0 |    0    12    0    0     0     0    8    8     0    0 |   0    0    0    4    4    0    0    0    0    0    0    0    2    0   0 |   *   *    *    *   * 960    *   *   *   *   *   *   * |  1   0   0   0  1  0
x . o3x . x     12 |    6     0    12     6 |    0     6    3    0     0     0    4    0     6    0 |   0    0    0    2    0    3    0    0    0    0    0    0    0    2   0 |   *   *    *    *   *   * 1920   *   *   *   *   *   * |  0   1   0   0  1  0
x . . x3o4x     48 |   24     0    48    48 |    0    24   24    0     0     0    0   16    24   12 |   0    0    0    0    8   12    6    0    0    0    0    0    0    0   2 |   *   *    *    *   *   *    * 480   *   *   *   *   * |  0   0   0   1  1  0
. x3o3x3o .     30 |    0    30    60     0 |    0     0    0   10    30     0   20   20     0    0 |   0    0    0    0    0    0    0    5    0   10    0    0    5    0   0 |   *   *    *    *   *   *    *   * 384   *   *   *   * |  1   0   0   0  0  1
. x3o3x . x     24 |    0    24    24    12 |    0     0    0    8    12    12    8    0    12    0 |   0    0    0    0    0    0    0    2    4    0    6    0    0    4   0 |   *   *    *    *   *   *    *   *   * 960   *   *   * |  0   1   0   0  0  1
. x3o . o4x     12 |    0    12     0    12 |    0     0    0    4     0    12    0    0     0    3 |   0    0    0    0    0    0    0    0    4    0    0    3    0    0   0 |   *   *    *    *   *   *    *   *   *   * 960   *   * |  0   0   1   0  0  1
. x . x3o4x     48 |    0    24    48    48 |    0     0    0    0    24    24    0   16    24   12 |   0    0    0    0    0    0    0    0    0    8   12    6    0    0   2 |   *   *    *    *   *   *    *   *   *   *   * 480   * |  0   0   0   1  0  1
. . o3x3o4x     96 |    0     0   192    96 |    0     0    0    0     0     0   64   64    96   24 |   0    0    0    0    0    0    0    0    0    0    0    0   16   32   8 |   *   *    *    *   *   *    *   *   *   *   *   * 120 |  0   0   0   0  1  1
------------+-------+------------------------+-------------------------------------------------------+--------------------------------------------------------------------------+--------------------------------------------------------+---------------------
x3x3o3x3o .    180 |   90   180   360     0 |   60   180    0   60   180     0  120  120     0    0 |  15   60    0   60   60    0    0   30    0   60    0    0   30    0   0 |   6   0   20    0   0  15    0   0   6   0   0   0   0 | 64   *   *   *  *  *
x3x3o3x . x    120 |   60   120   120    60 |   40    60   30   40    60    60   40    0    60    0 |  10   20   20   20    0   30    0   10   20    0   30    0    0   20   0 |   2   5    0   10   0   0   10   0   0   5   0   0   0 |  * 192   *   *  *  *
x3x3o . o4x     48 |   24    48     0    48 |   16     0   24   16     0    48    0    0     0   12 |   4    0   16    0    0    0    6    0   16    0    0   12    0    0   0 |   0   4    0    0   4   0    0   0   0   0   4   0   0 |  *   * 240   *  *  *
x3x . x3o4x    144 |   72    72   144   144 |   24    72   72    0    72    72    0   48    72   36 |   0   24   24    0   24   36   18    0    0   24   36   18    0    0   6 |   0   0    8   12   6   0    0   3   0   0   0   3   0 |  *   *   * 160  *  *
x . o3x3o4x    192 |   96     0   384   192 |    0   192   96    0     0     0  128  128   192   48 |   0    0    0   64   64   96   24    0    0    0    0    0   32   64  16 |   0   0    0    0   0  16   32   8   0   0   0   0   2 |  *   *   *   * 60  *
. x3o3x3o4x    960 |    0   960  1920   960 |    0     0    0  320   960   960  640  640   960  240 |   0    0    0    0    0    0    0  160  320  320  480  240  160  320  80 |   0   0    0    0   0   0    0   0  32  80  80  40  10 |  *   *   *   *  * 12

snubbed forms: x3x3o3x3o4s

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