Acronym quaxoke Name quasi-exiocteracti-diacosipentacontahexazetton Circumradius sqrt[(5-sqrt(2))/2] = 1.338990 Coordinates ((sqrt(2)-1)/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign

As abstract polytope quaxoke is isomorphic to saxoke.

Incidence matrix according to Dynkin symbol

x3o3o3o3o3o3o4/3x

. . . . . . .   . | 2048 |    7    7 |    21    42    21 |    35   105   105   35 |    35   140   210   140   35 |   21   105   210   210  105   21 |    7   42   105  140  105   42   7 |   1    7   21   35   35  21   7  1
------------------+------+-----------+-------------------+------------------------+------------------------------+----------------------------------+------------------------------------+-----------------------------------
x . . . . . .   . |    2 | 7168    * |     6     6     0 |    15    30    15    0 |    20    60    60    20    0 |   15    60    90    60   15    0 |    6   30    60   60   30    6   0 |   1    6   15   20   15   6   1  0
. . . . . . .   x |    2 |    * 7168 |     0     6     6 |     0    15    30   15 |     0    20    60    60   20 |    0    15    60    90   60   15 |    0    6    30   60   60   30   6 |   0    1    6   15   20  15   6  1
------------------+------+-----------+-------------------+------------------------+------------------------------+----------------------------------+------------------------------------+-----------------------------------
x3o . . . . .   . |    3 |    3    0 | 14336     *     * |     5     5     0    0 |    10    20    10     0    0 |   10    30    30    10    0    0 |    5   20    30   20    5    0   0 |   1    5   10   10    5   1   0  0
x . . . . . .   x |    4 |    2    2 |     * 21504     * |     0     5     5    0 |     0    10    20    10    0 |    0    10    30    30   10    0 |    0    5    20   30   20    5   0 |   0    1    5   10   10   5   1  0
. . . . . . o4/3x |    4 |    0    4 |     *     * 10752 |     0     0     5    5 |     0     0    10    20   10 |    0     0    10    30   30   10 |    0    0     5   20   30   20   5 |   0    0    1    5   10  10   5  1
------------------+------+-----------+-------------------+------------------------+------------------------------+----------------------------------+------------------------------------+-----------------------------------
x3o3o . . . .   .     4 |    6    0 |     4     0     0 | 17920     *     *    * |     4     4     0     0    0 |    6    12     6     0    0    0 |    4   12    12    4    0    0   0 |   1    4    6    4    1   0   0  0
x3o . . . . .   x     6 |    6    3 |     2     3     0 |     * 35840     *    * |     0     4     4     0    0 |    0     6    12     6    0    0 |    0    4    12   12    4    0   0 |   0    1    4    6    4   1   0  0
x . . . . . o4/3x     8 |    4    8 |     0     4     2 |     *     * 26880    * |     0     0     4     4    0 |    0     0     6    12    6    0 |    0    0     4   12   12    4   0 |   0    0    1    4    6   4   1  0
. . . . . o3o4/3x     8 |    0   12 |     0     0     6 |     *     *     * 8960 |     0     0     0     4    4 |    0     0     0     6   12    6 |    0    0     0    4   12   12   4 |   0    0    0    1    4   6   4  1
------------------+------+-----------+-------------------+------------------------+------------------------------+----------------------------------+------------------------------------+-----------------------------------
x3o3o3o . . .   .     5 |   10    0 |    10     0     0 |     5     0     0    0 | 14336     *     *     *    * |    3     3     0     0    0    0 |    3    6     3    0    0    0   0 |   1    3    3    1    0   0   0  0
x3o3o . . . .   x     8 |   12    4 |     8     6     0 |     2     4     0    0 |     * 35840     *     *    * |    0     3     3     0    0    0 |    0    3     6    3    0    0   0 |   0    1    3    3    1   0   0  0
x3o . . . . o4/3x    12 |   12   12 |     4    12     3 |     0     4     3    0 |     *     * 35840     *    * |    0     0     3     3    0    0 |    0    0     3    6    3    0   0 |   0    0    1    3    3   1   0  0
x . . . . o3o4/3x    16 |    8   24 |     0    12    12 |     0     0     6    2 |     *     *     * 17920    * |    0     0     0     3    3    0 |    0    0     0    3    6    3   0 |   0    0    0    1    3   3   1  0
. . . . o3o3o4/3x    16 |    0   32 |     0     0    24 |     0     0     0    8 |     *     *     *     * 4480 |    0     0     0     0    3    3 |    0    0     0    0    3    6   3 |   0    0    0    0    1   3   3  1
------------------+------+-----------+-------------------+------------------------+------------------------------+----------------------------------+------------------------------------+-----------------------------------
x3o3o3o3o . .   .     6 |   15    0 |    20     0     0 |    15     0     0    0 |     6     0     0     0    0 | 7168     *     *     *    *    * |    2    2     0    0    0    0   0 |   1    2    1    0    0   0   0  0
x3o3o3o . . .   x    10 |   20    5 |    20    10     0 |    10    10     0    0 |     2     5     0     0    0 |    * 21504     *     *    *    * |    0    2     2    0    0    0   0 |   0    1    2    1    0   0   0  0
x3o3o . . . o4/3x    16 |   24   16 |    16    24     4 |     4    16     6    0 |     0     4     4     0    0 |    *     * 26880     *    *    * |    0    0     2    2    0    0   0 |   0    0    1    2    1   0   0  0
x3o . . . o3o4/3x    24 |   24   36 |     8    36    18 |     0    12    18    3 |     0     0     6     3    0 |    *     *     * 17920    *    * |    0    0     0    2    2    0   0 |   0    0    0    1    2   1   0  0
x . . . o3o3o4/3x    32 |   16   64 |     0    32    48 |     0     0    24   16 |     0     0     0     8    2 |    *     *     *     * 6720    * |    0    0     0    0    2    2   0 |   0    0    0    0    1   2   1  0
. . . o3o3o3o4/3x    32 |    0   80 |     0     0    80 |     0     0     0   40 |     0     0     0     0   10 |    *     *     *     *    * 1344 |    0    0     0    0    0    2   2 |   0    0    0    0    0   1   2  1
------------------+------+-----------+-------------------+------------------------+------------------------------+----------------------------------+------------------------------------+-----------------------------------
x3o3o3o3o3o .   .     7 |   21    0 |    35     0     0 |    35     0     0    0 |    21     0     0     0    0 |    7     0     0     0    0    0 | 2048    *     *    *    *    *   * |   1    1    0    0    0   0   0  0
x3o3o3o3o . .   x    12 |   30    6 |    40    15     0 |    30    20     0    0 |    12    15     0     0    0 |    2     6     0     0    0    0 |    * 7168     *    *    *    *   * |   0    1    1    0    0   0   0  0
x3o3o3o . . o4/3x    20 |   40   20 |    40    40     5 |    20    40    10    0 |     4    20    10     0    0 |    0     4     5     0    0    0 |    *    * 10752    *    *    *   * |   0    0    1    1    0   0   0  0
x3o3o . . o3o4/3x    32 |   48   48 |    32    72    24 |     8    48    36    4 |     0    12    24     6    0 |    0     0     6     4    0    0 |    *    *     * 8960    *    *   * |   0    0    0    1    1   0   0  0
x3o . . o3o3o4/3x    48 |   48   96 |    16    96    72 |     0    32    72   24 |     0     0    24    24    3 |    0     0     0     8    3    0 |    *    *     *    * 4480    *   * |   0    0    0    0    1   1   0  0
x . . o3o3o3o4/3x    64 |   32  160 |     0    80   160 |     0     0    80   80 |     0     0     0    40   20 |    0     0     0     0   10    2 |    *    *     *    *    * 1344   * |   0    0    0    0    0   1   1  0
. . o3o3o3o3o4/3x    64 |    0  192 |     0     0   240 |     0     0     0  160 |     0     0     0     0   60 |    0     0     0     0    0   12 |    *    *     *    *    *    * 224 |   0    0    0    0    0   0   1  1
------------------+------+-----------+-------------------+------------------------+------------------------------+----------------------------------+------------------------------------+-----------------------------------
x3o3o3o3o3o3o   .     8 |   28    0 |    56     0     0 |    70     0     0    0 |    56     0     0     0    0 |   28     0     0     0    0    0 |    8    0     0    0    0    0   0 | 256    *    *    *    *   *   *  *
x3o3o3o3o3o .   x    14 |   42    7 |    70    21     0 |    70    35     0    0 |    42    35     0     0    0 |   14    21     0     0    0    0 |    2    7     0    0    0    0   0 |   * 1024    *    *    *   *   *  *
x3o3o3o3o . o4/3x    24 |   60   24 |    80    60     6 |    60    80    15    0 |    24    60    20     0    0 |    4    24    15     0    0    0 |    0    4     6    0    0    0   0 |   *    * 1792    *    *   *   *  *
x3o3o3o . o3o4/3x    40 |   80   60 |    80   120    30 |    40   120    60    5 |     8    60    60    10    0 |    0    12    30    10    0    0 |    0    0     6    5    0    0   0 |   *    *    * 1792    *   *   *  *
x3o3o . o3o3o4/3x    64 |   96  128 |    64   192    96 |    16   128   144   32 |     0    32    96    48    4 |    0     0    24    32    6    0 |    0    0     0    8    4    0   0 |   *    *    *    * 1120   *   *  *
x3o . o3o3o3o4/3x    96 |   96  240 |    32   240   240 |     0    80   240  120 |     0     0    80   120   30 |    0     0     0    40   30    3 |    0    0     0    0   10    3   0 |   *    *    *    *    * 448   *  *
x . o3o3o3o3o4/3x   128 |   64  384 |     0   192   480 |     0     0   240  320 |     0     0     0   160  120 |    0     0     0     0   60   24 |    0    0     0    0    0   12   2 |   *    *    *    *    *   * 112  *
. o3o3o3o3o3o4/3x   128 |    0  448 |     0     0   672 |     0     0     0  560 |     0     0     0     0  280 |    0     0     0     0    0   84 |    0    0     0    0    0    0  14 |   *    *    *    *    *   *   * 16