Acronym scox
Name small cellihexeract,
stericated hexeract
Circumradius sqrt[sqrt(2)+5/2] = 1.978437
Coordinates ((1+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

o3x3o3o3o4x

. . . . . . | 960 |    8    4 |    4   12   24    6 |   6   12    8   24   24   4 |   4  12  12   2   8  12   8  1 |  1   4   6   4  2
------------+-----+-----------+---------------------+-----------------------------+--------------------------------+------------------
. x . . . . |   2 | 3840    * |    1    3    3    0 |   3    3    3    6    3   0 |   3   6   3   1   3   3   1  0 |  1   3   3   1  1
. . . . . x |   2 |    * 1920 |    0    0    6    3 |   0    3    0    6   12   3 |   0   3   6   0   2   6   6  1 |  0   1   3   3  2
------------+-----+-----------+---------------------+-----------------------------+--------------------------------+------------------
o3x . . . . |   3 |    3    0 | 1280    *    *    * |   3    3    0    0    0   0 |   3   6   3   0   0   0   0  0 |  1   3   3   1  0
. x3o . . . |   3 |    3    0 |    * 3840    *    * |   1    0    2    2    0   0 |   2   2   0   1   2   1   0  0 |  1   2   1   0  1
. x . . . x |   4 |    2    2 |    *    * 5760    * |   0    1    0    2    2   0 |   0   2   2   0   1   2   1  0 |  0   1   2   1  1
. . . . o4x |   4 |    0    4 |    *    *    * 1440 |   0    0    0    0    4   2 |   0   0   2   0   0   2   4  1 |  0   0   1   2  2
------------+-----+-----------+---------------------+-----------------------------+--------------------------------+------------------
o3x3o . . .    6 |   12    0 |    4    4    0    0 | 960    *    *    *    *   * |   2   2   0   0   0   0   0  0 |  1   2   1   0  0
o3x . . . x    6 |    6    3 |    2    0    3    0 |   * 1920    *    *    *   * |   0   2   2   0   0   0   0  0 |  0   1   2   1  0
. x3o3o . .    4 |    6    0 |    0    4    0    0 |   *    * 1920    *    *   * |   1   0   0   1   1   0   0  0 |  1   1   0   0  1
. x3o . . x    6 |    6    3 |    0    2    3    0 |   *    *    * 3840    *   * |   0   1   0   0   1   1   0  0 |  0   1   1   0  1
. x . . o4x    8 |    4    8 |    0    0    4    2 |   *    *    *    * 2880   * |   0   0   1   0   0   1   1  0 |  0   0   1   1  1
. . . o3o4x    8 |    0   12 |    0    0    0    6 |   *    *    *    *    * 480 |   0   0   0   0   0   0   2  1 |  0   0   0   1  2
------------+-----+-----------+---------------------+-----------------------------+--------------------------------+------------------
o3x3o3o . .   10 |   30    0 |   10   20    0    0 |   5    0    5    0    0   0 | 384   *   *   *   *   *   *  * |  1   1   0   0  0
o3x3o . . x   12 |   24    6 |    8    8   12    0 |   2    4    0    4    0   0 |   * 960   *   *   *   *   *  * |  0   1   1   0  0
o3x . . o4x   12 |   12   12 |    4    0   12    3 |   0    4    0    0    3   0 |   *   * 960   *   *   *   *  * |  0   0   1   1  0
. x3o3o3o .    5 |   10    0 |    0   10    0    0 |   0    0    5    0    0   0 |   *   *   * 384   *   *   *  * |  1   0   0   0  1
. x3o3o . x    8 |   12    4 |    0    8    6    0 |   0    0    2    4    0   0 |   *   *   *   * 960   *   *  * |  0   1   0   0  1
. x3o . o4x   12 |   12   12 |    0    4   12    3 |   0    0    0    4    3   0 |   *   *   *   *   * 960   *  * |  0   0   1   0  1
. x . o3o4x   16 |    8   24 |    0    0   12   12 |   0    0    0    0    6   2 |   *   *   *   *   *   * 480  * |  0   0   0   1  1
. . o3o3o4x   16 |    0   32 |    0    0    0   24 |   0    0    0    0    0   8 |   *   *   *   *   *   *   * 60 |  0   0   0   0  2
------------+-----+-----------+---------------------+-----------------------------+--------------------------------+------------------
o3x3o3o3o .   15 |   60    0 |   20   60    0    0 |  15    0   30    0    0   0 |   6   0   0   6   0   0   0  0 | 64   *   *   *  *
o3x3o3o . x   20 |   60   10 |   20   40   30    0 |  10   10   10   20    0   0 |   2   5   0   0   5   0   0  0 |  * 192   *   *  *
o3x3o . o4x   24 |   48   24 |   16   16   48    6 |   4   16    0   16   12   0 |   0   4   4   0   0   4   0  0 |  *   * 240   *  *
o3x . o3o4x   24 |   24   36 |    8    0   36   18 |   0   12    0    0   18   3 |   0   0   6   0   0   0   3  0 |  *   *   * 160  *
. x3o3o3o4x  160 |  320  320 |    0  320  480  240 |   0    0  160  320  240  80 |   0   0   0  32  80  80  40 10 |  *   *   *   * 12

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