Acronym gaquitxog Name great quasiterated hexeractihexacontatetrapeton Circumradius sqrt[(58-15 sqrt(2))/2] = 4.288753 Coordinates ((5 sqrt(2)-1)/2, (4 sqrt(2)-1)/2, (3 sqrt(2)-1)/2, (2 sqrt(2)-1)/2, (sqrt(2)-1)/2, 1/2)   & all permutations, all changes of sign

As abstract polypeton gaquitxog is isomorphic to gotaxog, thereby replacing the octagrams by octagons, resp. replacing quitco by girco and stop by op, resp. replacing gaquidpoth by gidpith, histodip by hodip, quitcope by gircope, and sistodip by sodip, resp. replacing gaquacint by gacnet, gaquidpothip by gidpithip, haquitco by hagirco, and stotoe by otoe.

Incidence matrix according to Dynkin symbol

```x3x3x3x3x4/3x

. . . . .   . | 46080 |     1     1     1     1     1     1 |    1     1     1     1     1    1     1     1     1    1     1     1    1     1    1 |    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1   1 |   1   1   1    1    1   1   1    1    1   1   1   1   1   1   1 |  1   1   1   1  1  1
--------------+-------+-------------------------------------+--------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------+-----------------------------------------------------------------+---------------------
x . . . .   . |     2 | 23040     *     *     *     *     * |    1     1     1     1     1    0     0     0     0    0     0     0    0     0    0 |    1    1    1    1    1    1    1    1    1    1    0    0    0    0    0    0    0    0    0   0 |   1   1   1    1    1   1   1    1    1   1   0   0   0   0   0 |  1   1   1   1  1  0
. x . . .   . |     2 |     * 23040     *     *     *     * |    1     0     0     0     0    1     1     1     1    0     0     0    0     0    0 |    1    1    1    1    0    0    0    0    0    0    1    1    1    1    1    1    0    0    0   0 |   1   1   1    1    1   1   0    0    0   0   1   1   1   1   0 |  1   1   1   1  0  1
. . x . .   . |     2 |     *     * 23040     *     *     * |    0     1     0     0     0    1     0     0     0    1     1     1    0     0    0 |    1    0    0    0    1    1    1    0    0    0    1    1    1    0    0    0    1    1    1   0 |   1   1   1    0    0   0   1    1    1   0   1   1   1   0   1 |  1   1   1   0  1  1
. . . x .   . |     2 |     *     *     * 23040     *     * |    0     0     1     0     0    0     1     0     0    1     0     0    1     1    0 |    0    1    0    0    1    0    0    1    1    0    1    0    0    1    1    0    1    1    0   1 |   1   0   0    1    1   0   1    1    0   1   1   1   0   1   1 |  1   1   0   1  1  1
. . . . x   . |     2 |     *     *     *     * 23040     * |    0     0     0     1     0    0     0     1     0    0     1     0    1     0    1 |    0    0    1    0    0    1    0    1    0    1    0    1    0    1    0    1    1    0    1   1 |   0   1   0    1    0   1   1    0    1   1   1   0   1   1   1 |  1   0   1   1  1  1
. . . . .   x |     2 |     *     *     *     *     * 23040 |    0     0     0     0     1    0     0     0     1    0     0     1    0     1    1 |    0    0    0    1    0    0    1    0    1    1    0    0    1    0    1    1    0    1    1   1 |   0   0   1    0    1   1   0    1    1   1   0   1   1   1   1 |  0   1   1   1  1  1
--------------+-------+-------------------------------------+--------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------+-----------------------------------------------------------------+---------------------
x3x . . .   . |     6 |     3     3     0     0     0     0 | 7680     *     *     *     *    *     *     *     *    *     *     *    *     *    * |    1    1    1    1    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0   0 |   1   1   1    1    1   1   0    0    0   0   0   0   0   0   0 |  1   1   1   1  0  0
x . x . .   . |     4 |     2     0     2     0     0     0 |    * 11520     *     *     *    *     *     *     *    *     *     *    *     *    * |    1    0    0    0    1    1    1    0    0    0    0    0    0    0    0    0    0    0    0   0 |   1   1   1    0    0   0   1    1    1   0   0   0   0   0   0 |  1   1   1   0  1  0
x . . x .   . |     4 |     2     0     0     2     0     0 |    *     * 11520     *     *    *     *     *     *    *     *     *    *     *    * |    0    1    0    0    1    0    0    1    1    0    0    0    0    0    0    0    0    0    0   0 |   1   0   0    1    1   0   1    1    0   1   0   0   0   0   0 |  1   1   0   1  1  0
x . . . x   . |     4 |     2     0     0     0     2     0 |    *     *     * 11520     *    *     *     *     *    *     *     *    *     *    * |    0    0    1    0    0    1    0    1    0    1    0    0    0    0    0    0    0    0    0   0 |   0   1   0    1    0   1   1    0    1   1   0   0   0   0   0 |  1   0   1   1  1  0
x . . . .   x |     4 |     2     0     0     0     0     2 |    *     *     *     * 11520    *     *     *     *    *     *     *    *     *    * |    0    0    0    1    0    0    1    0    1    1    0    0    0    0    0    0    0    0    0   0 |   0   0   1    0    1   1   0    1    1   1   0   0   0   0   0 |  0   1   1   1  1  0
. x3x . .   . |     6 |     0     3     3     0     0     0 |    *     *     *     *     * 7680     *     *     *    *     *     *    *     *    * |    1    0    0    0    0    0    0    0    0    0    1    1    1    0    0    0    0    0    0   0 |   1   1   1    0    0   0   0    0    0   0   1   1   1   0   0 |  1   1   1   0  0  1
. x . x .   . |     4 |     0     2     0     2     0     0 |    *     *     *     *     *    * 11520     *     *    *     *     *    *     *    * |    0    1    0    0    0    0    0    0    0    0    1    0    0    1    1    0    0    0    0   0 |   1   0   0    1    1   0   0    0    0   0   1   1   0   1   0 |  1   1   0   1  0  1
. x . . x   . |     4 |     0     2     0     0     2     0 |    *     *     *     *     *    *     * 11520     *    *     *     *    *     *    * |    0    0    1    0    0    0    0    0    0    0    0    1    0    1    0    1    0    0    0   0 |   0   1   0    1    0   1   0    0    0   0   1   0   1   1   0 |  1   0   1   1  0  1
. x . . .   x |     4 |     0     2     0     0     0     2 |    *     *     *     *     *    *     *     * 11520    *     *     *    *     *    * |    0    0    0    1    0    0    0    0    0    0    0    0    1    0    1    1    0    0    0   0 |   0   0   1    0    1   1   0    0    0   0   0   1   1   1   0 |  0   1   1   1  0  1
. . x3x .   . |     6 |     0     0     3     3     0     0 |    *     *     *     *     *    *     *     *     * 7680     *     *    *     *    * |    0    0    0    0    1    0    0    0    0    0    1    0    0    0    0    0    1    1    0   0 |   1   0   0    0    0   0   1    1    0   0   1   1   0   0   1 |  1   1   0   0  1  1
. . x . x   . |     4 |     0     0     2     0     2     0 |    *     *     *     *     *    *     *     *     *    * 11520     *    *     *    * |    0    0    0    0    0    1    0    0    0    0    0    1    0    0    0    0    1    0    1   0 |   0   1   0    0    0   0   1    0    1   0   1   0   1   0   1 |  1   0   1   0  1  1
. . x . .   x |     4 |     0     0     2     0     0     2 |    *     *     *     *     *    *     *     *     *    *     * 11520    *     *    * |    0    0    0    0    0    0    1    0    0    0    0    0    1    0    0    0    0    1    1   0 |   0   0   1    0    0   0   0    1    1   0   0   1   1   0   1 |  0   1   1   0  1  1
. . . x3x   . |     6 |     0     0     0     3     3     0 |    *     *     *     *     *    *     *     *     *    *     *     * 7680     *    * |    0    0    0    0    0    0    0    1    0    0    0    0    0    1    0    0    1    0    0   1 |   0   0   0    1    0   0   1    0    0   1   1   0   0   1   1 |  1   0   0   1  1  1
. . . x .   x |     4 |     0     0     0     2     0     2 |    *     *     *     *     *    *     *     *     *    *     *     *    * 11520    * |    0    0    0    0    0    0    0    0    1    0    0    0    0    0    1    0    0    1    0   1 |   0   0   0    0    1   0   0    1    0   1   0   1   0   1   1 |  0   1   0   1  1  1
. . . . x4/3x |     8 |     0     0     0     0     4     4 |    *     *     *     *     *    *     *     *     *    *     *     *    *     * 5760 |    0    0    0    0    0    0    0    0    0    1    0    0    0    0    0    1    0    0    1   1 |   0   0   0    0    0   1   0    0    1   1   0   0   1   1   1 |  0   0   1   1  1  1
--------------+-------+-------------------------------------+--------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------+-----------------------------------------------------------------+---------------------
x3x3x . .   . ♦    24 |    12    12    12     0     0     0 |    4     6     0     0     0    4     0     0     0    0     0     0    0     0    0 | 1920    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *   * |   1   1   1    0    0   0   0    0    0   0   0   0   0   0   0 |  1   1   1   0  0  0
x3x . x .   . ♦    12 |     6     6     0     6     0     0 |    2     0     3     0     0    0     3     0     0    0     0     0    0     0    0 |    * 3840    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *   * |   1   0   0    1    1   0   0    0    0   0   0   0   0   0   0 |  1   1   0   1  0  0
x3x . . x   . ♦    12 |     6     6     0     0     6     0 |    2     0     0     3     0    0     0     3     0    0     0     0    0     0    0 |    *    * 3840    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *   * |   0   1   0    1    0   1   0    0    0   0   0   0   0   0   0 |  1   0   1   1  0  0
x3x . . .   x ♦    12 |     6     6     0     0     0     6 |    2     0     0     0     3    0     0     0     3    0     0     0    0     0    0 |    *    *    * 3840    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *   * |   0   0   1    0    1   1   0    0    0   0   0   0   0   0   0 |  0   1   1   1  0  0
x . x3x .   . ♦    12 |     6     0     6     6     0     0 |    0     3     3     0     0    0     0     0     0    2     0     0    0     0    0 |    *    *    *    * 3840    *    *    *    *    *    *    *    *    *    *    *    *    *    *   * |   1   0   0    0    0   0   1    1    0   0   0   0   0   0   0 |  1   1   0   0  1  0
x . x . x   . ♦     8 |     4     0     4     0     4     0 |    0     2     0     2     0    0     0     0     0    0     2     0    0     0    0 |    *    *    *    *    * 5760    *    *    *    *    *    *    *    *    *    *    *    *    *   * |   0   1   0    0    0   0   1    0    1   0   0   0   0   0   0 |  1   0   1   0  1  0
x . x . .   x ♦     8 |     4     0     4     0     0     4 |    0     2     0     0     2    0     0     0     0    0     0     2    0     0    0 |    *    *    *    *    *    * 5760    *    *    *    *    *    *    *    *    *    *    *    *   * |   0   0   1    0    0   0   0    1    1   0   0   0   0   0   0 |  0   1   1   0  1  0
x . . x3x   . ♦    12 |     6     0     0     6     6     0 |    0     0     3     3     0    0     0     0     0    0     0     0    2     0    0 |    *    *    *    *    *    *    * 3840    *    *    *    *    *    *    *    *    *    *    *   * |   0   0   0    1    0   0   1    0    0   1   0   0   0   0   0 |  1   0   0   1  1  0
x . . x .   x ♦     8 |     4     0     0     4     0     4 |    0     0     2     0     2    0     0     0     0    0     0     0    0     2    0 |    *    *    *    *    *    *    *    * 5760    *    *    *    *    *    *    *    *    *    *   * |   0   0   0    0    1   0   0    1    0   1   0   0   0   0   0 |  0   1   0   1  1  0
x . . . x4/3x ♦    16 |     8     0     0     0     8     8 |    0     0     0     4     4    0     0     0     0    0     0     0    0     0    2 |    *    *    *    *    *    *    *    *    * 2880    *    *    *    *    *    *    *    *    *   * |   0   0   0    0    0   1   0    0    1   1   0   0   0   0   0 |  0   0   1   1  1  0
. x3x3x .   . ♦    24 |     0    12    12    12     0     0 |    0     0     0     0     0    4     6     0     0    4     0     0    0     0    0 |    *    *    *    *    *    *    *    *    *    * 1920    *    *    *    *    *    *    *    *   * |   1   0   0    0    0   0   0    0    0   0   1   1   0   0   0 |  1   1   0   0  0  1
. x3x . x   . ♦    12 |     0     6     6     0     6     0 |    0     0     0     0     0    2     0     3     0    0     3     0    0     0    0 |    *    *    *    *    *    *    *    *    *    *    * 3840    *    *    *    *    *    *    *   * |   0   1   0    0    0   0   0    0    0   0   1   0   1   0   0 |  1   0   1   0  0  1
. x3x . .   x ♦    12 |     0     6     6     0     0     6 |    0     0     0     0     0    2     0     0     3    0     0     3    0     0    0 |    *    *    *    *    *    *    *    *    *    *    *    * 3840    *    *    *    *    *    *   * |   0   0   1    0    0   0   0    0    0   0   0   1   1   0   0 |  0   1   1   0  0  1
. x . x3x   . ♦    12 |     0     6     0     6     6     0 |    0     0     0     0     0    0     3     3     0    0     0     0    2     0    0 |    *    *    *    *    *    *    *    *    *    *    *    *    * 3840    *    *    *    *    *   * |   0   0   0    1    0   0   0    0    0   0   1   0   0   1   0 |  1   0   0   1  0  1
. x . x .   x ♦     8 |     0     4     0     4     0     4 |    0     0     0     0     0    0     2     0     2    0     0     0    0     2    0 |    *    *    *    *    *    *    *    *    *    *    *    *    *    * 5760    *    *    *    *   * |   0   0   0    0    1   0   0    0    0   0   0   1   0   1   0 |  0   1   0   1  0  1
. x . . x4/3x ♦    16 |     0     8     0     0     8     8 |    0     0     0     0     0    0     0     4     4    0     0     0    0     0    2 |    *    *    *    *    *    *    *    *    *    *    *    *    *    *    * 2880    *    *    *   * |   0   0   0    0    0   1   0    0    0   0   0   0   1   1   0 |  0   0   1   1  0  1
. . x3x3x   . ♦    24 |     0     0    12    12    12     0 |    0     0     0     0     0    0     0     0     0    4     6     0    4     0    0 |    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *    * 1920    *    *   * |   0   0   0    0    0   0   1    0    0   0   1   0   0   0   1 |  1   0   0   0  1  1
. . x3x .   x ♦    12 |     0     0     6     6     0     6 |    0     0     0     0     0    0     0     0     0    2     0     3    0     3    0 |    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *    * 3840    *   * |   0   0   0    0    0   0   0    1    0   0   0   1   0   0   1 |  0   1   0   0  1  1
. . x . x4/3x ♦    16 |     0     0     8     0     8     8 |    0     0     0     0     0    0     0     0     0    0     4     4    0     0    2 |    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *    * 2880   * |   0   0   0    0    0   0   0    0    1   0   0   0   1   0   1 |  0   0   1   0  1  1
. . . x3x4/3x ♦    48 |     0     0     0    24    24    24 |    0     0     0     0     0    0     0     0     0    0     0     0    8    16    6 |    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *    *    * 960 |   0   0   0    0    0   0   0    0    0   1   0   0   0   1   1 |  0   0   0   1  1  1
--------------+-------+-------------------------------------+--------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------+-----------------------------------------------------------------+---------------------
x3x3x3x .   . ♦   120 |    60    60    60    60     0     0 |   20    30    30     0     0   20    30     0     0   20     0     0    0     0    0 |    5   10    0    0   10    0    0    0    0    0    5    0    0    0    0    0    0    0    0   0 | 384   *   *    *    *   *   *    *    *   *   *   *   *   *   * |  1   1   0   0  0  0
x3x3x . x   . ♦    48 |    24    24    24     0    24     0 |    8    12     0    12     0    8     0    12     0    0    12     0    0     0    0 |    2    0    4    0    0    6    0    0    0    0    0    4    0    0    0    0    0    0    0   0 |   * 960   *    *    *   *   *    *    *   *   *   *   *   *   * |  1   0   1   0  0  0
x3x3x . .   x ♦    48 |    24    24    24     0     0    24 |    8    16     0     0    12    8     0     0    12    0     0    12    0     0    0 |    2    0    0    4    0    0    6    0    0    0    0    0    4    0    0    0    0    0    0   0 |   *   * 960    *    *   *   *    *    *   *   *   *   *   *   * |  0   1   1   0  0  0
x3x . x3x   . ♦    36 |    18    18     0    18    18     0 |    6     0     9     9     0    0     9     9     0    0     0     0    6     0    0 |    0    3    3    0    0    0    0    3    0    0    0    0    0    3    0    0    0    0    0   0 |   *   *   * 1280    *   *   *    *    *   *   *   *   *   *   * |  1   0   0   1  0  0
x3x . x .   x ♦    24 |    12    12     0    12     0    12 |    4     0     6     0     6    0     6     0     6    0     0     0    0     6    0 |    0    2    0    2    0    0    0    0    3    0    0    0    0    0    3    0    0    0    0   0 |   *   *   *    * 1920   *   *    *    *   *   *   *   *   *   * |  0   1   0   1  0  0
x3x . . x4/3x ♦    48 |    24    24     0     0    24    24 |    8     0     0    12    12    0     0    12    12    0     0     0    0     0    6 |    0    0    4    4    0    0    0    0    0    3    0    0    0    0    0    3    0    0    0   0 |   *   *   *    *    * 960   *    *    *   *   *   *   *   *   * |  0   0   1   1  0  0
x . x3x3x   . ♦    48 |    24     0    24    24    24     0 |    0    12    12    12     0    0     0     0     0    8    12     0    8     0    0 |    0    0    0    0    4    6    0    4    0    0    0    0    0    0    0    0    2    0    0   0 |   *   *   *    *    *   * 960    *    *   *   *   *   *   *   * |  1   0   0   0  1  0
x . x3x .   x ♦    24 |    12     0    12    12     0    12 |    0     6     6     0     6    0     0     0     0    4     0     6    0     6    0 |    0    0    0    0    2    0    3    0    3    0    0    0    0    0    0    0    0    2    0   0 |   *   *   *    *    *   *   * 1920    *   *   *   *   *   *   * |  0   1   0   0  1  0
x . x . x4/3x ♦    32 |    16     0    16     0    16    16 |    0     8     0     8     8    0     0     0     0    0     8     8    0     0    4 |    0    0    0    0    0    4    4    0    0    2    0    0    0    0    0    0    0    0    2   0 |   *   *   *    *    *   *   *    * 1440   *   *   *   *   *   * |  0   0   1   0  1  0
x . . x3x4/3x ♦    96 |    48     0     0    48    48    48 |    0     0    24    24    24    0     0     0     0    0     0     0   16    32   12 |    0    0    0    0    0    0    0    8   12    6    0    0    0    0    0    0    0    0    0   2 |   *   *   *    *    *   *   *    *    * 480   *   *   *   *   * |  0   0   0   1  1  0
. x3x3x3x   . ♦   120 |     0    60    60    60    60     0 |    0     0     0     0     0   20    30    30     0   20    30     0   20     0    0 |    0    0    0    0    0    0    0    0    0    0    5   10    0   10    0    0    5    0    0   0 |   *   *   *    *    *   *   *    *    *   * 384   *   *   *   * |  1   0   0   0  0  1
. x3x3x .   x ♦    48 |     0    24    24    24     0    24 |    0     0     0     0     0    8    12     0    12    8     0    12    0    12    0 |    0    0    0    0    0    0    0    0    0    0    2    0    4    0    6    0    0    4    0   0 |   *   *   *    *    *   *   *    *    *   *   * 960   *   *   * |  0   1   0   0  0  1
. x3x . x4/3x ♦    48 |     0    24    24     0    24    24 |    0     0     0     0     0    8     0    12    12    0    12    12    0     0    6 |    0    0    0    0    0    0    0    0    0    0    0    4    4    0    0    3    0    0    3   0 |   *   *   *    *    *   *   *    *    *   *   *   * 960   *   * |  0   0   1   0  0  1
. x . x3x4/3x ♦    96 |     0    48     0    48    48    48 |    0     0     0     0     0    0    24    24    24    0     0     0   16    32   12 |    0    0    0    0    0    0    0    0    0    0    0    0    0    8   12    6    0    0    0   2 |   *   *   *    *    *   *   *    *    *   *   *   *   * 480   * |  0   0   0   1  0  1
. . x3x3x4/3x ♦   384 |     0     0   192   192   192   192 |    0     0     0     0     0    0     0     0     0   64    96    96   64    96   48 |    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0   16   32   24   8 |   *   *   *    *    *   *   *    *    *   *   *   *   *   * 120 |  0   0   0   0  1  1
--------------+-------+-------------------------------------+--------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------+-----------------------------------------------------------------+---------------------
x3x3x3x3x   . ♦   720 |   360   360   360   360   360     0 |  120   180   180   180     0  120   180   180     0  120   180     0  120     0    0 |   30   60   60    0   60   90    0   60    0    0   30   60    0   60    0    0   30    0    0   0 |   6  15   0   20    0   0  15    0    0   0   6   0   0   0   0 | 64   *   *   *  *  *
x3x3x3x .   x ♦   240 |   120   120   120   120     0   120 |   40    60    60     0    60   40    60     0    60   40     0    60    0    60    0 |   10   20    0   20   20    0   30    0   30    0   10    0   20    0   30    0    0   20    0   0 |   2   0   5    0   10   0   0   10    0   0   0   5   0   0   0 |  * 192   *   *  *  *
x3x3x . x4/3x ♦   192 |    96    96    96     0    96    96 |   32    48     0    48    48   32     0    48    48    0    48    48    0     0   24 |    8    0   16   16    0   24   24    0    0   12    0   16   16    0    0   12    0    0   12   0 |   0   4   4    0    0   4   0    0    6   0   0   0   4   0   0 |  *   * 240   *  *  *
x3x . x3x4/3x ♦   288 |   144   144     0   144   144   144 |   48     0    72    72    72    0    72    72    72    0     0     0   48    72   36 |    0   24   24   24    0    0    0   24   36   18    0    0    0   24   36   18    0    0    0   6 |   0   0   0    8   12   6   0    0    0   3   0   0   0   3   0 |  *   *   * 160  *  *
x . x3x3x4/3x ♦   768 |   384     0   384   384   384   384 |    0   192   192   192   192    0     0     0     0  128   192   192  128   192   96 |    0    0    0    0   64   96   96   64   96   48    0    0    0    0    0    0   32   64   48  16 |   0   0   0    0    0   0  16   32   24   8   0   0   0   0   2 |  *   *   *   * 60  *
. x3x3x3x4/3x ♦  3840 |     0  1920  1920  1920  1920  1920 |    0     0     0     0     0  640   960   960   960  640   960   960  640   960  480 |    0    0    0    0    0    0    0    0    0    0  160  320  320  320  480  240  160  320  240  80 |   0   0   0    0    0   0   0    0    0   0  32  80  80  40  10 |  *   *   *   *  * 12
```