Acronym takus
Name teriskewed hepteract
Circumradius sqrt(11)/2 = 1.658312

As abstract polytope takus is isomorphic to ratkus, thereby replacing octagrams by octagons, resp. stop by op and gocco by socco, resp. tistodip by todip, goccope by soccope, and gittith by steth, resp stotet by otet, tragocco by trasocco, gittithip by stethip, and ginnont by sinnont, resp. stoxog by quitoxog, stopen by open, tetgocco by tetsocco, tragittith by trasteth, ginnontip by sinnontip, and goxaxog by soxaxog.


Incidence matrix according to Dynkin symbol

x3o3o3o3o3x4/3x4*e

. . . . . .   .    | 5376 |     5     5     5 |    10    20    20    10    10    5 |    10    30    30    30    30   20    10   10   10 |    5    20    20    30    30   30    20   20   30    5    5  10 |   1    5    5   10   10   20   10   10   30    5   5  20   1   1   5 |   1  1   5  10  10  5  1
-------------------+------+-------------------+------------------------------------+----------------------------------------------------+-----------------------------------------------------------------+----------------------------------------------------------------------+-------------------------
x . . . . .   .    |    2 | 13440     *     * |     4     4     4     0     0    0 |     6    12    12     6     6    4     0    0    0 |    4    12    12    12    12   12     4    4    6    0    0   0 |   1    4    4    6    6   12    4    4   12    1   1   4   0   0   0 |   1  1   4   6   4  1  0
. . . . . x   .    |    2 |     * 13440     * |     0     4     0     4     0    1 |     0     6     0    12     0    4     6    0    4 |    0     4     0    12     0    6    12    0   12    4    0   6 |   0    1    0    4    0    4    6    0   12    4   0  12   1   0   4 |   1  0   1   4   6  4  1
. . . . . .   x    |    2 |     *     * 13440 |     0     0     4     0     4    1 |     0     0     6     0    12    4     0    6    4 |    0     0     4     0    12    6     0   12   12    0    4   6 |   0    0    1    0    4    4    0    6   12    0   4  12   0   1   4 |   0  1   1   4   6  4  1
-------------------+------+-------------------+------------------------------------+----------------------------------------------------+-----------------------------------------------------------------+----------------------------------------------------------------------+-------------------------
x3o . . . .   .    |    3 |     3     0     0 | 17920     *     *     *     *    * |     3     3     3     0     0    0     0    0    0 |    3     6     6     3     3    3     0    0    0    0    0   0 |   1    3    3    3    3    6    1    1    3    0   0   0   0   0   0 |   1  1   3   3   1  0  0
x . . . . x   .    |    4 |     2     2     0 |     * 26880     *     *     *    * |     0     3     0     3     0    1     0    0    0 |    0     3     0     6     0    3     3    0    3    0    0   0 |   0    1    0    3    0    3    3    0    6    1   0   3   0   0   0 |   1  0   1   3   3  1  0
x . . . . .   x    |    4 |     2     0     2 |     *     * 26880     *     *    * |     0     0     3     0     3    1     0    0    0 |    0     0     3     0     6    3     0    3    3    0    0   0 |   0    0    1    0    3    3    0    3    6    0   1   3   0   0   0 |   0  1   1   3   3  1  0
. . . . o3x   .    |    3 |     0     3     0 |     *     *     * 17920     *    * |     0     0     0     3     0    0     3    0    1 |    0     0     0     3     0    0     6    0    3    3    0   3 |   0    0    0    1    0    0    3    0    3    3   0   6   1   0   3 |   1  0   0   1   3  3  1
. . . . o .   x4*e |    4 |     0     0     4 |     *     *     *     * 13440    * |     0     0     0     0     3    0     0    3    1 |    0     0     0     0     3    0     0    6    3    0    3   3 |   0    0    0    0    1    0    0    3    3    0   3   6   0   1   3 |   0  1   0   1   3  3  1
. . . . . x4/3x    |    8 |     0     4     4 |     *     *     *     *     * 3360 |     0     0     0     0     0    4     0    0    4 |    0     0     0     0     0    6     0    0   12    0    0   6 |   0    0    0    0    0    4    0    0   12    0   0  12   0   0   4 |   0  0   1   4   6  4  1
-------------------+------+-------------------+------------------------------------+----------------------------------------------------+-----------------------------------------------------------------+----------------------------------------------------------------------+-------------------------
x3o3o . . .   .        4 |     6     0     0 |     4     0     0     0     0    0 | 13440     *     *     *     *    *     *    *    * |    2     2     2     0     0    0     0    0    0    0    0   0 |   1    2    2    1    1    2    0    0    0    0   0   0   0   0   0 |   1  1   2   1   0  0  0
x3o . . . x   .        6 |     6     3     0 |     2     3     0     0     0    0 |     * 26880     *     *     *    *     *    *    * |    0     2     0     2     0    1     0    0    0    0    0   0 |   0    1    0    2    0    2    1    0    2    0   0   0   0   0   0 |   1  0   1   2   1  0  0
x3o . . . .   x        6 |     6     0     3 |     2     0     3     0     0    0 |     *     * 26880     *     *    *     *    *    * |    0     0     2     0     2    1     0    0    0    0    0   0 |   0    0    1    0    2    2    0    1    2    0   0   0   0   0   0 |   0  1   1   2   1  0  0
x . . . o3x   .        6 |     3     6     0 |     0     3     0     2     0    0 |     *     *     * 26880     *    *     *    *    * |    0     0     0     2     0    0     2    0    1    0    0   0 |   0    0    0    1    0    0    2    0    2    1   0   2   0   0   0 |   1  0   0   1   2  1  0
x . . . o .   x4*e     8 |     4     0     8 |     0     0     4     0     2    0 |     *     *     *     * 20160    *     *    *    * |    0     0     0     0     2    0     0    2    1    0    0   0 |   0    0    0    0    1    0    0    2    2    0   1   2   0   0   0 |   0  1   0   1   2  1  0
x . . . . x4/3x       16 |     8     8     8 |     0     4     4     0     0    2 |     *     *     *     *     * 6720     *    *    * |    0     0     0     0     0    3     0    0    3    0    0   0 |   0    0    0    0    0    3    0    0    6    0   0   3   0   0   0 |   0  0   1   3   3  1  0
. . . o3o3x   .        4 |     0     6     0 |     0     0     0     4     0    0 |     *     *     *     *     *    * 13440    *    * |    0     0     0     0     0    0     2    0    0    2    0   1 |   0    0    0    0    0    0    1    0    0    2   0   2   1   0   2 |   1  0   0   0   1  2  1
. . . o3o .   x4*e     8 |     0     0    12 |     0     0     0     0     6    0 |     *     *     *     *     *    *     * 6720    * |    0     0     0     0     0    0     0    2    0    0    2   1 |   0    0    0    0    0    0    0    1    0    0   2   2   0   1   2 |   0  1   0   0   1  2  1
. . . . o3x4/3x4*e    24 |     0    24    24 |     0     0     0     8     6    6 |     *     *     *     *     *    *     *    * 2240 |    0     0     0     0     0    0     0    0    3    0    0   3 |   0    0    0    0    0    0    0    0    3    0   0   6   0   0   3 |   0  0   0   1   3  3  1
-------------------+------+-------------------+------------------------------------+----------------------------------------------------+-----------------------------------------------------------------+----------------------------------------------------------------------+-------------------------
x3o3o3o . .   .        5 |    10     0     0 |    10     0     0     0     0    0 |     5     0     0     0     0    0     0    0    0 | 5376     *     *     *     *    *     *    *    *    *    *   * |   1    1    1    0    0    0    0    0    0    0   0   0   0   0   0 |   1  1   1   0   0  0  0
x3o3o . . x   .        8 |    12     4     0 |     8     6     0     0     0    0 |     2     4     0     0     0    0     0    0    0 |    * 13440     *     *     *    *     *    *    *    *    *   * |   0    1    0    1    0    1    0    0    0    0   0   0   0   0   0 |   1  0   1   1   0  0  0
x3o3o . . .   x        8 |    12     0     4 |     8     0     6     0     0    0 |     2     0     4     0     0    0     0    0    0 |    *     * 13440     *     *    *     *    *    *    *    *   * |   0    0    1    0    1    1    0    0    0    0   0   0   0   0   0 |   0  1   1   1   0  0  0
x3o . . o3x   .        9 |     9     9     0 |     3     9     0     3     0    0 |     0     3     0     3     0    0     0    0    0 |    *     *     * 17920     *    *     *    *    *    *    *   * |   0    0    0    1    0    0    1    0    1    0   0   0   0   0   0 |   1  0   0   1   1  0  0
x3o . . o .   x4*e    12 |    12     0    12 |     4     0    12     0     3    0 |     0     0     4     0     3    0     0    0    0 |    *     *     *     * 13440    *     *    *    *    *    *   * |   0    0    0    0    1    0    0    1    1    0   0   0   0   0   0 |   0  1   0   1   1  0  0
x3o . . . x4/3x       24 |    24    12    12 |     8    12    12     0     0    3 |     0     4     4     0     0    3     0    0    0 |    *     *     *     *     * 6720     *    *    *    *    *   * |   0    0    0    0    0    2    0    0    2    0   0   0   0   0   0 |   0  0   1   2   1  0  0
x . . o3o3x   .        8 |     4    12     0 |     0     6     0     8     0    0 |     0     0     0     4     0    0     2    0    0 |    *     *     *     *     *    * 13440    *    *    *    *   * |   0    0    0    0    0    0    1    0    0    1   0   1   0   0   0 |   1  0   0   0   1  1  0
x . . o3o .   x4*e    16 |     8     0    24 |     0     0    12     0    12    0 |     0     0     0     0     6    0     0    2    0 |    *     *     *     *     *    *     * 6720    *    *    *   * |   0    0    0    0    0    0    0    1    0    0   1   1   0   0   0 |   0  1   0   0   1  1  0
x . . . o3x4/3x4*e    48 |    24    48    48 |     0    24    24    16    12   12 |     0     0     0     8     6    6     0    0    2 |    *     *     *     *     *    *     *    * 3360    *    *   * |   0    0    0    0    0    0    0    0    2    0   0   2   0   0   0 |   0  0   0   1   2  1  0
. . o3o3o3x   .        5 |     0    10     0 |     0     0     0    10     0    0 |     0     0     0     0     0    0     5    0    0 |    *     *     *     *     *    *     *    *    * 5376    *   * |   0    0    0    0    0    0    0    0    0    1   0   0   1   0   1 |   1  0   0   0   0  1  1
. . o3o3o .   x4*e    16 |     0     0    32 |     0     0     0     0    24    0 |     0     0     0     0     0    0     0    8    0 |    *     *     *     *     *    *     *    *    *    * 1680   * |   0    0    0    0    0    0    0    0    0    0   1   0   0   1   1 |   0  1   0   0   0  1  1
. . . o3o3x4/3x4*e    64 |     0    96    96 |     0     0     0    64    48   24 |     0     0     0     0     0    0    16    8    8 |    *     *     *     *     *    *     *    *    *    *    * 840 |   0    0    0    0    0    0    0    0    0    0   0   2   0   0   2 |   0  0   0   0   1  2  1
-------------------+------+-------------------+------------------------------------+----------------------------------------------------+-----------------------------------------------------------------+----------------------------------------------------------------------+-------------------------
x3o3o3o3o .   .        6 |    15     0     0 |    20     0     0     0     0    0 |    15     0     0     0     0    0     0    0    0 |    6     0     0     0     0    0     0    0    0    0    0   0 | 896    *    *    *    *    *    *    *    *    *   *   *   *   *   * |   1  1   0   0   0  0  0
x3o3o3o . x   .       10 |    20     5     0 |    20    10     0     0     0    0 |    10    10     0     0     0    0     0    0    0 |    2     5     0     0     0    0     0    0    0    0    0   0 |   * 2688    *    *    *    *    *    *    *    *   *   *   *   *   * |   1  0   1   0   0  0  0
x3o3o3o . .   x       10 |    20     0     5 |    20     0    10     0     0    0 |    10     0    10     0     0    0     0    0    0 |    2     0     5     0     0    0     0    0    0    0    0   0 |   *    * 2688    *    *    *    *    *    *    *   *   *   *   *   * |   0  1   1   0   0  0  0
x3o3o . o3x   .       12 |    18    12     0 |    12    18     0     4     0    0 |     3    12     0     6     0    0     0    0    0 |    0     3     0     4     0    0     0    0    0    0    0   0 |   *    *    * 4480    *    *    *    *    *    *   *   *   *   *   * |   1  0   0   1   0  0  0
x3o3o . o .   x4*e    16 |    24     0    16 |    16     0    24     0     4    0 |     4     0    16     0     6    0     0    0    0 |    0     0     4     0     4    0     0    0    0    0    0   0 |   *    *    *    * 3360    *    *    *    *    *   *   *   *   *   * |   0  1   0   1   0  0  0
x3o3o . . x4/3x       32 |    48    16    16 |    32    24    24     0     0    4 |     8    16    16     0     0    6     0    0    0 |    0     4     4     0     0    4     0    0    0    0    0   0 |   *    *    *    *    * 3360    *    *    *    *   *   *   *   *   * |   0  0   1   1   0  0  0
x3o . o3o3x   .       12 |    12    18     0 |     4    18     0    12     0    0 |     0     6     0    12     0    0     3    0    0 |    0     0     0     4     0    0     3    0    0    0    0   0 |   *    *    *    *    *    * 4480    *    *    *   *   *   *   *   * |   1  0   0   0   1  0  0
x3o . o3o .   x4*e    24 |    24     0    36 |     8     0    36     0    18    0 |     0     0    12     0    18    0     0    3    0 |    0     0     0     0     6    0     0    3    0    0    0   0 |   *    *    *    *    *    *    * 2240    *    *   *   *   *   *   * |   0  1   0   0   1  0  0
x3o . . o3x4/3x4*e    72 |    72    72    72 |    24    72    72    24    18   18 |     0    24    24    24    18   18     0    0    3 |    0     0     0     8     6    6     0    0    3    0    0   0 |   *    *    *    *    *    *    *    * 2240    *   *   *   *   *   * |   0  0   0   1   1  0  0
x . o3o3o3x   .       10 |     5    20     0 |     0    10     0    20     0    0 |     0     0     0    10     0    0    10    0    0 |    0     0     0     0     0    0     5    0    0    2    0   0 |   *    *    *    *    *    *    *    *    * 2688   *   *   *   *   * |   1  0   0   0   0  1  0
x . o3o3o .   x4*e    32 |    16     0    64 |     0     0    32     0    48    0 |     0     0     0     0    24    0     0   16    0 |    0     0     0     0     0    0     0    8    0    0    2   0 |   *    *    *    *    *    *    *    *    *    * 840   *   *   *   * |   0  1   0   0   0  1  0
x . . o3o3x4/3x4*e   128 |    64   192   192 |     0    96    96   128    96   48 |     0     0     0    64    48   24    32   16   16 |    0     0     0     0     0    0    16    8    8    0    0   2 |   *    *    *    *    *    *    *    *    *    *   * 840   *   *   * |   0  0   0   0   1  1  0
. o3o3o3o3x   .        6 |     0    15     0 |     0     0     0    20     0    0 |     0     0     0     0     0    0    15    0    0 |    0     0     0     0     0    0     0    0    0    6    0   0 |   *    *    *    *    *    *    *    *    *    *   *   * 896   *   * |   1  0   0   0   0  0  1
. o3o3o3o .   x4*e    32 |     0     0    80 |     0     0     0     0    80    0 |     0     0     0     0     0    0     0   40    0 |    0     0     0     0     0    0     0    0    0    0   10   0 |   *    *    *    *    *    *    *    *    *    *   *   *   * 168   * |   0  1   0   0   0  0  1
. . o3o3o3x4/3x4*e   160 |     0   320   320 |     0     0     0   320   240   80 |     0     0     0     0     0    0   160   80   40 |    0     0     0     0     0    0     0    0    0   32   10  10 |   *    *    *    *    *    *    *    *    *    *   *   *   *   * 168 |   0  0   0   0   0  1  1
-------------------+------+-------------------+------------------------------------+----------------------------------------------------+-----------------------------------------------------------------+----------------------------------------------------------------------+-------------------------
x3o3o3o3o3x   .       42 |   105   105     0 |   140   210     0   140     0    0 |   105   210     0   210     0    0   105    0    0 |   42   105     0   140     0    0   105    0    0   42    0   0 |   7   21    0   35    0    0   35    0    0   21   0   0   7   0   0 | 128  *   *   *   *  *  *
x3o3o3o3o .   x4*e   384 |   960     0   960 |  1280     0  1920     0   960    0 |   960     0  1920     0  1440    0     0  480    0 |  384     0   960     0   960    0     0  480    0    0  120   0 |  64    0  192    0  240    0    0  160    0    0  60   0   0  12   0 |   * 14   *   *   *  *  *
x3o3o3o . x4/3x       40 |    80    20    20 |    80    40    40     0     0    5 |    40    40    40     0     0   10     0    0    0 |    8    20    20     0     0   10     0    0    0    0    0   0 |   0    4    4    0    0    5    0    0    0    0   0   0   0   0   0 |   *  * 672   *   *  *  *
x3o3o . o3x4/3x4*e    96 |   144    96    96 |    96   144   144    32    24   24 |    24    96    96    48    36   36     0    0    4 |    0    24    24    32    24   24     0    0    6    0    0   0 |   0    0    0    8    6    6    0    0    4    0   0   0   0   0   0 |   *  *   * 560   *  *  *
x3o . o3o3x4/3x4*e   192 |   192   288   288 |    64   288   288   192   144   72 |     0    96    96   192   144   72    48   24   24 |    0     0     0    64    48   24    48   24   24    0    0   3 |   0    0    0    0    0    0   16    8    8    0   0   3   0   0   0 |   *  *   *   * 280  *  *
x . o3o3o3x4/3x4*e   320 |   160   640   640 |     0   320   320   640   480  160 |     0     0     0   320   240   80   320  160   80 |    0     0     0     0     0    0   160   80   40   64   20  20 |   0    0    0    0    0    0    0    0    0   32  10  10   0   0   2 |   *  *   *   *   * 84  *
. o3o3o3o3x4/3x4*e   384 |     0   960   960 |     0     0     0  1280   960  240 |     0     0     0     0     0    0   960  480  160 |    0     0     0     0     0    0     0    0    0  384  120  60 |   0    0    0    0    0    0    0    0    0    0   0   0  64  12  12 |   *  *   *   *   *  * 14

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