Acronym tapox (old: stapox)
Name teriprismated hexeract,
penticantellated hexacross
Circumradius 2+sqrt(1/2) = 2.707107
Coordinates ((1+2 sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
External
links
wikipedia

Incidence matrix according to Dynkin symbol

x3o3x3o3o4x

. . . . . . | 3840 |    2     6    3 |    1    6    6    3    6    12    3 |   3    3    6   12    6    3    6    2    6    6   1 |   3   6   3   2    6    6   2   1   3   3   2 |  1   3   3   1  2  1
------------+------+-----------------+-------------------------------------+------------------------------------------------------+-----------------------------------------------+---------------------
x . . . . . |    2 | 3840     *    * |    1    3    3    0    0     0    0 |   3    3    3    6    3    0    0    0    0    0   0 |   3   6   3   1    3    3   1   0   0   0   0 |  1   3   3   1  1  0
. . x . . . |    2 |    * 11520    * |    0    1    0    1    2     2    0 |   1    0    2    2    0    2    2    1    2    1   0 |   2   2   0   1    2    1   0   1   2   1   1 |  1   2   1   0  1  1
. . . . . x |    2 |    *     * 5760 |    0    0    2    0    0     4    2 |   0    1    0    4    4    0    2    0    2    4   1 |   0   2   2   0    2    4   2   0   1   2   2 |  0   1   2   1  2  1
------------+------+-----------------+-------------------------------------+------------------------------------------------------+-----------------------------------------------+---------------------
x3o . . . . |    3 |    3     0    0 | 1280    *    *    *    *     *    * |   3    3    0    0    0    0    0    0    0    0   0 |   3   6   3   0    0    0   0   0   0   0   0 |  1   3   3   1  0  0
x . x . . . |    4 |    2     2    0 |    * 5760    *    *    *     *    * |   1    0    2    2    0    0    0    0    0    0   0 |   2   2   0   1    2    1   0   0   0   0   0 |  1   2   1   0  1  0
x . . . . x |    4 |    2     0    2 |    *    * 5760    *    *     *    * |   0    1    0    2    2    0    0    0    0    0   0 |   0   2   2   0    1    2   1   0   0   0   0 |  0   1   2   1  1  0
. o3x . . . |    3 |    0     3    0 |    *    *    * 3840    *     *    * |   1    0    0    0    0    2    2    0    0    0   0 |   2   2   0   0    0    0   0   1   2   1   0 |  1   2   1   0  0  1
. . x3o . . |    3 |    0     3    0 |    *    *    *    * 7680     *    * |   0    0    1    0    0    1    0    1    1    0   0 |   1   0   0   1    1    0   0   1   1   0   1 |  1   1   0   0  1  1
. . x . . x |    4 |    0     2    2 |    *    *    *    *    * 11520    * |   0    0    0    1    0    0    1    0    1    1   0 |   0   1   0   0    1    1   0   0   1   1   1 |  0   1   1   0  1  1
. . . . o4x |    4 |    0     0    4 |    *    *    *    *    *     * 2880 |   0    0    0    0    2    0    0    0    0    2   1 |   0   0   1   0    0    2   2   0   0   1   2 |  0   0   1   1  2  1
------------+------+-----------------+-------------------------------------+------------------------------------------------------+-----------------------------------------------+---------------------
x3o3x . . .    12 |   12    12    0 |    4    6    0    4    0     0    0 | 960    *    *    *    *    *    *    *    *    *   * |   2   2   0   0    0    0   0   0   0   0   0 |  1   2   1   0  0  0
x3o . . . x     6 |    6     0    3 |    2    0    3    0    0     0    0 |   * 1920    *    *    *    *    *    *    *    *   * |   0   2   2   0    0    0   0   0   0   0   0 |  0   1   2   1  0  0
x . x3o . .     6 |    3     6    0 |    0    3    0    0    2     0    0 |   *    * 3840    *    *    *    *    *    *    *   * |   1   0   0   1    1    0   0   0   0   0   0 |  1   1   0   0  1  0
x . x . . x     8 |    4     4    4 |    0    2    2    0    0     2    0 |   *    *    * 5760    *    *    *    *    *    *   * |   0   1   0   0    1    1   0   0   0   0   0 |  0   1   1   0  1  0
x . . . o4x     8 |    4     0    8 |    0    0    4    0    0     0    2 |   *    *    *    * 2880    *    *    *    *    *   * |   0   0   1   0    0    1   1   0   0   0   0 |  0   0   1   1  1  0
. o3x3o . .     6 |    0    12    0 |    0    0    0    4    4     0    0 |   *    *    *    *    * 1920    *    *    *    *   * |   1   0   0   0    0    0   0   1   1   0   0 |  1   1   0   0  0  1
. o3x . . x     6 |    0     6    3 |    0    0    0    2    0     3    0 |   *    *    *    *    *    * 3840    *    *    *   * |   0   1   0   0    0    0   0   0   1   1   0 |  0   1   1   0  0  1
. . x3o3o .     4 |    0     6    0 |    0    0    0    0    4     0    0 |   *    *    *    *    *    *    * 1920    *    *   * |   0   0   0   1    0    0   0   1   0   0   1 |  1   0   0   0  1  1
. . x3o . x     6 |    0     6    3 |    0    0    0    0    2     3    0 |   *    *    *    *    *    *    *    * 3840    *   * |   0   0   0   0    1    0   0   0   1   0   1 |  0   1   0   0  1  1
. . x . o4x     8 |    0     4    8 |    0    0    0    0    0     4    2 |   *    *    *    *    *    *    *    *    * 2880   * |   0   0   0   0    0    1   0   0   0   1   1 |  0   0   1   0  1  1
. . . o3o4x     8 |    0     0   12 |    0    0    0    0    0     0    6 |   *    *    *    *    *    *    *    *    *    * 480 |   0   0   0   0    0    0   2   0   0   0   2 |  0   0   0   1  2  1
------------+------+-----------------+-------------------------------------+------------------------------------------------------+-----------------------------------------------+---------------------
x3o3x3o . .    30 |   30    60    0 |   10   30    0   20   20     0    0 |   5    0   10    0    0    5    0    0    0    0   0 | 384   *   *   *    *    *   *   *   *   *   * |  1   1   0   0  0  0
x3o3x . . x    24 |   24    24   12 |    8   12   12    8    0    12    0 |   2    4    0    6    0    0    4    0    0    0   0 |   * 960   *   *    *    *   *   *   *   *   * |  0   1   1   0  0  0
x3o . . o4x    12 |   12     0   12 |    4    0   12    0    0     0    3 |   0    4    0    0    3    0    0    0    0    0   0 |   *   * 960   *    *    *   *   *   *   *   * |  0   0   1   1  0  0
x . x3o3o .     8 |    4    12    0 |    0    6    0    0    8     0    0 |   0    0    4    0    0    0    0    2    0    0   0 |   *   *   * 960    *    *   *   *   *   *   * |  1   0   0   0  1  0
x . x3o . x    12 |    6    12    6 |    0    6    3    0    4     6    0 |   0    0    2    3    0    0    0    0    2    0   0 |   *   *   *   * 1920    *   *   *   *   *   * |  0   1   0   0  1  0
x . x . o4x    16 |    8     8   16 |    0    4    8    0    0     8    4 |   0    0    0    4    2    0    0    0    0    2   0 |   *   *   *   *    * 1440   *   *   *   *   * |  0   0   1   0  1  0
x . . o3o4x    16 |    8     0   24 |    0    0   12    0    0     0   12 |   0    0    0    0    6    0    0    0    0    0   2 |   *   *   *   *    *    * 480   *   *   *   * |  0   0   0   1  1  0
. o3x3o3o .    10 |    0    30    0 |    0    0    0   10   20     0    0 |   0    0    0    0    0    5    0    5    0    0   0 |   *   *   *   *    *    *   * 384   *   *   * |  1   0   0   0  0  1
. o3x3o . x    12 |    0    24    6 |    0    0    0    8    8    12    0 |   0    0    0    0    0    2    4    0    4    0   0 |   *   *   *   *    *    *   *   * 960   *   * |  0   1   0   0  0  1
. o3x . o4x    12 |    0    12   12 |    0    0    0    4    0    12    3 |   0    0    0    0    0    0    4    0    0    3   0 |   *   *   *   *    *    *   *   *   * 960   * |  0   0   1   0  0  1
. . x3o3o4x    64 |    0    96   96 |    0    0    0    0   64    96   48 |   0    0    0    0    0    0    0   16   32   24   8 |   *   *   *   *    *    *   *   *   *   * 120 |  0   0   0   0  1  1
------------+------+-----------------+-------------------------------------+------------------------------------------------------+-----------------------------------------------+---------------------
x3o3x3o3o .    60 |   60   180    0 |   20   90    0   60  120     0    0 |  15    0   60    0    0   30    0   30    0    0   0 |   6   0   0  15    0    0   0   6   0   0   0 | 64   *   *   *  *  *
x3o3x3o . x    60 |   60   120   30 |   20   60   30   40   40    60    0 |  10   10   20   30    0   10   20    0   20    0   0 |   2   5   0   0   10    0   0   0   5   0   0 |  * 192   *   *  *  *
x3o3x . o4x    48 |   48    48   48 |   16   24   48   16    0    48   12 |   4   16    0   24   12    0   16    0    0   12   0 |   0   4   4   0    0    6   0   0   0   4   0 |  *   * 240   *  *  *
x3o . o3o4x    24 |   24     0   36 |    8    0   36    0    0     0   18 |   0   12    0    0   18    0    0    0    0    0   3 |   0   0   6   0    0    0   3   0   0   0   0 |  *   *   * 160  *  *
x . x3o3o4x   128 |   64   192  192 |    0   96   96    0  128   192   96 |   0    0   64   96   48    0    0   32   64   48  16 |   0   0   0  16   32   24   8   0   0   0   2 |  *   *   *   * 60  *
. o3x3o3o4x   320 |    0   960  480 |    0    0    0  320  640   960  240 |   0    0    0    0    0  160  320  160  320  240  40 |   0   0   0   0    0    0   0  32  80  80  10 |  *   *   *   *  * 12

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