Acronym prox
Name prismatorhombated hexeract,
runcicantellated hexeract
Circumradius sqrt([16+7 sqrt(2)]/2) = 3.598576
Coordinates ((1+2 sqrt(2))/2, (1+2 sqrt(2))/2, (1+2 sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2)   & all permutations, all changes of sign
External
links
wikipedia   polytopewiki  

Incidence matrix according to Dynkin symbol

o3o3x3x3o4x

o3o3o3o3o4o | 3840 |    3    2    2 |    3    6    6    1    2   1 |   1    6    6   3    6    3   1 |   2   2   3   6   3  3 |  1   2   1  3
------------+------+----------------+------------------------------+---------------------------------+------------------------+--------------
. . x . . . |    2 | 5760    *    * |    2    2    2    0    0   0 |   1    4    4   1    2    1   0 |   2   2   2   4   2  1 |  1   2   1  2
. . . x . . |    2 |    * 3840    * |    0    3    0    1    1   0 |   0    3    0   3    3    0   1 |   1   0   3   3   0  3 |  1   1   0  3
. . . . . x |    2 |    *    * 3840 |    0    0    3    0    1   1 |   0    0    3   0    3    3   1 |   0   1   0   3   3  3 |  0   1   1  3
------------+------+----------------+------------------------------+---------------------------------+------------------------+--------------
. o3x . . . |    3 |    3    0    0 | 3840    *    *    *    *   * |   1    2    2   0    0    0   0 |   2   2   1   2   1  0 |  1   2   1  1
. . x3x . . |    6 |    3    3    0 |    * 3840    *    *    *   * |   0    2    0   1    1    0   0 |   1   0   2   2   0  1 |  1   1   0  2
. . x . . x |    4 |    2    0    2 |    *    * 5760    *    *   * |   0    0    2   0    1    1   0 |   0   1   0   2   2  1 |  0   1   1  2
. . . x3o . |    3 |    0    3    0 |    *    *    * 1280    *   * |   0    0    0   3    0    0   1 |   0   0   3   0   0  3 |  1   0   0  3
. . . x . x |    4 |    0    2    2 |    *    *    *    * 1920   * |   0    0    0   0    3    0   1 |   0   0   0   3   0  3 |  0   1   0  3
. . . . o4x |    4 |    0    0    4 |    *    *    *    *    * 960 |   0    0    0   0    0    3   1 |   0   0   0   0   3  3 |  0   0   1  3
------------+------+----------------+------------------------------+---------------------------------+------------------------+--------------
o3o3x . . .     4 |    6    0    0 |    4    0    0    0    0   0 | 960    *    *   *    *    *   * |   2   2   0   0   0  0 |  1   2   1  0
. o3x3x . .    12 |   12    6    0 |    4    4    0    0    0   0 |   * 1920    *   *    *    *   * |   1   0   1   1   0  0 |  1   1   0  1
. o3x . . x     6 |    6    0    3 |    2    0    3    0    0   0 |   *    * 3840   *    *    *   * |   0   1   0   1   1  0 |  0   1   1  1
. . x3x3o .    12 |    6   12    0 |    0    4    0    4    0   0 |   *    *    * 960    *    *   * |   0   0   2   0   0  1 |  1   0   0  2
. . x3x . x    12 |    6    6    6 |    0    2    3    0    3   0 |   *    *    *   * 1920    *   * |   0   0   0   2   0  1 |  0   1   0  2
. . x . o4x     8 |    4    0    8 |    0    0    4    0    0   2 |   *    *    *   *    * 1440   * |   0   0   0   0   2  1 |  0   0   1  2
. . . x3o4x    24 |    0   24   24 |    0    0    0    8   12   6 |   *    *    *   *    *    * 160 |   0   0   0   0   0  3 |  0   0   0  3
------------+------+----------------+------------------------------+---------------------------------+------------------------+--------------
o3o3x3x . .    20 |   30   10    0 |   20   10    0    0    0   0 |   5    5    0   0    0    0   0 | 384   *   *   *   *  * |  1   1   0  0
o3o3x . . x     8 |   12    0    4 |    8    0    6    0    0   0 |   2    0    4   0    0    0   0 |   * 960   *   *   *  * |  0   1   1  0
. o3x3x3o .    30 |   30   30    0 |   10   20    0   10    0   0 |   0    5    0   5    0    0   0 |   *   * 384   *   *  * |  1   0   0  1
. o3x3x . x    24 |   24   12   12 |    8    8   12    0    6   0 |   0    2    4   0    4    0   0 |   *   *   * 960   *  * |  0   1   0  1
. o3x . o4x    12 |   12    0   12 |    4    0   12    0    0   3 |   0    0    4   0    0    3   0 |   *   *   *   * 960  * |  0   0   1  1
. . x3x3o4x   192 |   96  192  192 |    0   64   96   64   96  48 |   0    0    0  16   32   24   8 |   *   *   *   *   * 60 |  0   0   0  2
------------+------+----------------+------------------------------+---------------------------------+------------------------+--------------
o3o3x3x3o .    60 |   90   60    0 |   60   60    0   20    0   0 |  15   30    0  15    0    0   0 |   6   0   6   0   0  0 | 64   *   *  *
o3o3x3x . x    40 |   60   20   20 |   40   20   30    0   10   0 |  10   10   20   0   10    0   0 |   2   5   0   5   0  0 |  * 192   *  *
o3o3x . o4x    16 |   24    0   16 |   16    0   24    0    0   4 |   4    0   16   0    0    6   0 |   0   4   0   0   4  0 |  *   * 240  *
. o3x3x3o4x   960 |  960  960  960 |  320  640  960  320  480 240 |   0  160  320 160  320  240  40 |   0   0  32  80  80 10 |  *   *   * 12

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