Acronym potax
Name prismatotruncated hexeract,
runcitruncated hexeract
Circumradius sqrt[(17+8 sqrt(2))/2] = 3.762560
Coordinates ((1+2 sqrt(2))/2, (1+2 sqrt(2))/2, (1+2 sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, 1/2)   & all permutations, all changes of sign
External
links
wikipedia   polytopewiki  

As abstract polytope potax is isomorphic to quoptax, thereby replacing octagons by octagrams, resp. tic by quith and op by stop, resp. proh by quiproh and todip by tistodip, resp pattin by quiptin and otet by stotet.


Incidence matrix according to Dynkin symbol

o3o3x3o3x4x

. . . . . . | 3840 |     6    2    1 |    6    3    3    3    1   2 |    2    3    6    6   3    3    6   1 |   1   2   2   3   3   6  3 |  1   1   2  3
------------+------+-----------------+------------------------------+---------------------------------------+----------------------------+--------------
. . x . . . |    2 | 11520    *    * |    2    1    1    1    0   0 |    1    2    2    2   1    1    1   0 |   1   1   1   2   2   2  1 |  1   1   1  2
. . . . x . |    2 |     * 3840    * |    0    0    3    0    1   1 |    0    0    3    0   3    0    3   1 |   0   1   0   3   0   3  3 |  1   0   1  3
. . . . . x |    2 |     *    * 1920 |    0    0    0    6    0   2 |    0    0    0    6   0    3    6   1 |   0   0   2   0   3   6  3 |  0   1   2  3
------------+------+-----------------+------------------------------+---------------------------------------+----------------------------+--------------
. o3x . . . |    3 |     3    0    0 | 7680    *    *    *    *   * |    1    1    1    1   0    0    0   0 |   1   1   1   1   1   1  0 |  1   1   1  1
. . x3o . . |    3 |     3    0    0 |    * 3840    *    *    *   * |    0    2    0    0   1    1    0   0 |   1   0   0   2   2   0  1 |  1   1   0  2
. . x . x . |    4 |     2    2    0 |    *    * 5760    *    *   * |    0    0    2    0   1    0    1   0 |   0   1   0   2   0   2  1 |  1   0   1  2
. . x . . x |    4 |     2    0    2 |    *    *    * 5760    *   * |    0    0    0    2   0    1    1   0 |   0   0   1   0   2   2  1 |  0   1   1  2
. . . o3x . |    3 |     0    3    0 |    *    *    *    * 1280   * |    0    0    0    0   3    0    0   1 |   0   0   0   3   0   0  3 |  1   0   0  3
. . . . x4x |    8 |     0    4    4 |    *    *    *    *    * 960 |    0    0    0    0   0    0    3   1 |   0   0   0   0   0   3  3 |  0   0   1  3
------------+------+-----------------+------------------------------+---------------------------------------+----------------------------+--------------
o3o3x . . .     4 |     6    0    0 |    4    0    0    0    0   0 | 1920    *    *    *   *    *    *   * |   1   1   1   0   0   0  0 |  1   1   1  0
. o3x3o . .     6 |    12    0    0 |    4    4    0    0    0   0 |    * 1920    *    *   *    *    *   * |   1   0   0   1   1   0  0 |  1   1   0  1
. o3x . x .     6 |     6    3    0 |    2    0    3    0    0   0 |    *    * 3840    *   *    *    *   * |   0   1   0   1   0   1  0 |  1   0   1  1
. o3x . . x     6 |     6    0    3 |    2    0    0    3    0   0 |    *    *    * 3840   *    *    *   * |   0   0   1   0   1   1  0 |  0   1   1  1
. . x3o3x .    12 |    12   12    0 |    0    4    6    0    4   0 |    *    *    *    * 960    *    *   * |   0   0   0   2   0   0  1 |  1   0   0  2
. . x3o . x     6 |     6    0    3 |    0    2    0    3    0   0 |    *    *    *    *   * 1920    *   * |   0   0   0   0   2   0  1 |  0   1   0  2
. . x . x4x    16 |     8    8    8 |    0    0    4    4    0   2 |    *    *    *    *   *    * 1440   * |   0   0   0   0   0   2  1 |  0   0   1  2
. . . o3x4x    24 |     0   24   12 |    0    0    0    0    8   6 |    *    *    *    *   *    *    * 160 |   0   0   0   0   0   0  3 |  0   0   0  3
------------+------+-----------------+------------------------------+---------------------------------------+----------------------------+--------------
o3o3x3o . .    10 |    30    0    0 |   20   10    0    0    0   0 |    5    5    0    0   0    0    0   0 | 384   *   *   *   *   *  * |  1   1   0  0
o3o3x . x .     8 |    12    4    0 |    8    0    6    0    0   0 |    2    0    4    0   0    0    0   0 |   * 960   *   *   *   *  * |  1   0   1  0
o3o3x . . x     8 |    12    0    4 |    8    0    0    6    0   0 |    2    0    0    4   0    0    0   0 |   *   * 960   *   *   *  * |  0   1   1  0
. o3x3o3x .    30 |    60   30    0 |   20   20   30    0   10   0 |    0    5   10    0   5    0    0   0 |   *   *   * 384   *   *  * |  1   0   0  1
. o3x3o . x    12 |    24    0    6 |    8    8    0   12    0   0 |    0    2    0    4   0    4    0   0 |   *   *   *   * 960   *  * |  0   1   0  1
. o3x . x4x    24 |    24   12   12 |    8    0   12   12    0   3 |    0    0    4    4   0    0    3   0 |   *   *   *   *   * 960  * |  0   0   1  1
. . x3o3x4x   192 |   192  192   96 |    0   64   96   96   64  48 |    0    0    0    0  16   32   24   8 |   *   *   *   *   *   * 60 |  0   0   0  2
------------+------+-----------------+------------------------------+---------------------------------------+----------------------------+--------------
o3o3x3o3x .    60 |   180   60    0 |  120   60   90    0   20   0 |   30   30   60    0  15    0    0   0 |   6  15   0   6   0   0  0 | 64   *   *  *
o3o3x3o . x    20 |    60    0   10 |   40   20    0   30    0   0 |   10   10    0   20   0   10    0   0 |   2   0   5   0   5   0  0 |  * 192   *  *
o3o3x . x4x    32 |    48   16   16 |   32    0   24   24    0   4 |    8    0   16   16   0    0    6   0 |   0   4   4   0   0   4  0 |  *   * 240  *
. o3x3o3x4x   960 |  1920  960  480 |  640  640  960  960  320 240 |    0  160  320  320 160  320  240  40 |   0   0   0  32  80  80 10 |  *   *   * 12

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