Acronym tacox
Name tericellated hexeract,
pentitruncated hexacross
Circumradius sqrt[16+6 sqrt(2)]/2 = 2.474130
Coordinates ((1+2 sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
External
links
wikipedia

Incidence matrix according to Dynkin symbol

x3x3o3o3o4x

. . . . . . | 1920 |   1    4    4 |    4    4    6   12    6 |   6   12    6    4   12   12   4 |   4  12  12   4   1   4   6   4   1 |  1   4   6   4  1  1
------------+------+---------------+--------------------------+----------------------------------+-------------------------------------+---------------------
x . . . . . |    2 | 960    *    * |    4    4    0    0    0 |   6   12    6    0    0    0   0 |   4  12  12   4   0   0   0   0   0 |  1   4   6   4  1  0
. x . . . . |    2 |   * 3840    * |    1    0    3    3    0 |   3    3    0    3    6    3   0 |   3   6   3   0   1   3   3   1   0 |  1   3   3   1  0  1
. . . . . x |    2 |   *    * 3840 |    0    1    0    3    3 |   0    3    3    0    3    6   3 |   0   3   6   3   0   1   3   3   1 |  0   1   3   3  1  1
------------+------+---------------+--------------------------+----------------------------------+-------------------------------------+---------------------
x3x . . . . |    6 |   3    3    0 | 1280    *    *    *    * |   3    3    0    0    0    0   0 |   3   6   3   0   0   0   0   0   0 |  1   3   3   1  0  0
x . . . . x |    4 |   2    0    2 |    * 1920    *    *    * |   0    3    3    0    0    0   0 |   0   3   6   3   0   0   0   0   0 |  0   1   3   3  1  0
. x3o . . . |    3 |   0    3    0 |    *    * 3840    *    * |   1    0    0    2    2    0   0 |   2   2   0   0   1   2   1   0   0 |  1   2   1   0  0  1
. x . . . x |    4 |   0    2    2 |    *    *    * 5760    * |   0    1    0    0    2    2   0 |   0   2   2   0   0   1   2   1   0 |  0   1   2   1  0  1
. . . . o4x |    4 |   0    0    4 |    *    *    *    * 2880 |   0    0    1    0    0    2   2 |   0   0   2   2   0   0   1   2   1 |  0   0   1   2  1  1
------------+------+---------------+--------------------------+----------------------------------+-------------------------------------+---------------------
x3x3o . . .    12 |   6   12    0 |    4    0    4    0    0 | 960    *    *    *    *    *   * |   2   2   0   0   0   0   0   0   0 |  1   2   1   0  0  0
x3x . . . x    12 |   6    6    6 |    2    3    0    3    0 |   * 1920    *    *    *    *   * |   0   2   2   0   0   0   0   0   0 |  0   1   2   1  0  0
x .     o4x     8 |   4    0    8 |    0    4    0    0    2 |   *    * 1440    *    *    *   * |   0   0   2   2   0   0   0   0   0 |  0   0   1   2  1  0
. x3o3o . .     4 |   0    6    0 |    0    0    4    0    0 |   *    *    * 1920    *    *   * |   1   0   0   0   1   1   0   0   0 |  1   1   0   0  0  1
. x3o . . x     6 |   0    6    3 |    0    0    2    3    0 |   *    *    *    * 3840    *   * |   0   1   0   0   0   1   1   0   0 |  0   1   1   0  0  1
. x . . o4x     8 |   0    4    8 |    0    0    0    4    2 |   *    *    *    *    * 2880   * |   0   0   1   0   0   0   1   1   0 |  0   0   1   1  0  1
. . . o3o4x     8 |   0    0   12 |    0    0    0    0    6 |   *    *    *    *    *    * 960 |   0   0   0   1   0   0   0   1   1 |  0   0   0   1  1  1
------------+------+---------------+--------------------------+----------------------------------+-------------------------------------+---------------------
x3x3o3o . .    20 |  10   30    0 |   10    0   20    0    0 |   5    0    0    5    0    0   0 | 384   *   *   *   *   *   *   *   * |  1   1   0   0  0  0
x3x3o . . x    24 |  12   24   12 |    8    6    8   12    0 |   2    4    0    0    4    0   0 |   * 960   *   *   *   *   *   *   * |  0   1   1   0  0  0
x3x . . o4x    24 |  12   12   24 |    4   12    0   12    6 |   0    4    3    0    0    3   0 |   *   * 960   *   *   *   *   *   * |  0   0   1   1  0  0
x . . o3o4x    16 |   8    0   24 |    0   12    0    0   12 |   0    0    6    0    0    0   2 |   *   *   * 480   *   *   *   *   * |  0   0   0   1  1  0
. x3o3o3o .     5 |   0   10    0 |    0    0   10    0    0 |   0    0    0    5    0    0   0 |   *   *   *   * 384   *   *   *   * |  1   0   0   0  0  1
. x3o3o . x     8 |   0   12    4 |    0    0    8    6    0 |   0    0    0    2    4    0   0 |   *   *   *   *   * 960   *   *   * |  0   1   0   0  0  1
. x3o . o4x    12 |   0   12   12 |    0    0    4   12    3 |   0    0    0    0    4    3   0 |   *   *   *   *   *   * 960   *   * |  0   0   1   0  0  1
. x . o3o4x    16 |   0    8   24 |    0    0    0   12   12 |   0    0    0    0    0    6   2 |   *   *   *   *   *   *   * 480   * |  0   0   0   1  0  1
. . o3o3o4x    16 |   0    0   32 |    0    0    0    0   24 |   0    0    0    0    0    0   8 |   *   *   *   *   *   *   *   * 120 |  0   0   0   0  1  1
------------+------+---------------+--------------------------+----------------------------------+-------------------------------------+---------------------
x3x3o3o3o .    30 |  15   60    0 |   20    0   60    0    0 |  15    0    0   30    0    0   0 |   6   0   0   0   6   0   0   0   0 | 64   *   *   *  *  *
x3x3o3o . x    40 |  20   60   20 |   20   10   40   30    0 |  10   10    0   10   20    0   0 |   2   5   0   0   0   5   0   0   0 |  * 192   *   *  *  *
x3x3o . o4x    48 |  24   48   48 |   16   24   16   48   12 |   4   16    6    0   16   12   0 |   0   4   4   0   0   0   4   0   0 |  *   * 240   *  *  *
x3x . o3o4x    48 |  24   24   72 |    8   36    0   36   36 |   0   12   18    0    0   18   6 |   0   0   6   3   0   0   0   3   0 |  *   *   * 160  *  *
x . o3o3o4x    32 |  16    0   64 |    0   32    0    0   48 |   0    0   24    0    0    0  16 |   0   0   0   8   0   0   0   0   2 |  *   *   *   * 60  *
. x3o3o3o4x   160 |   0  320  320 |    0    0  320  480  240 |   0    0    0  160  320  240  80 |   0   0   0   0  32  80  80  40  10 |  *   *   *   *  * 12

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