Acronym gabach
Name great bicellihexadecaexon
Circumradius sqrt(15) = 3.872983
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Incidence matrix according to Dynkin symbol

o3x3x3x3x3x3o

. . . . . . .    | 10080 |     4     2    1 |    2    4     4     4     4    2    1 |    2    2    2    4    4    4    8    4    4   1 |   2   2    4    2    4    4    1   4    8    4 |  2   4   4   2   4   1  4 |  4   2  1
-----------------+-------+------------------+---------------------------------------+--------------------------------------------------+------------------------------------------------+---------------------------+----------
. x . . . . .  & |     2 | 20160     *    * |    1    1     1     1     2    0    0 |    1    1    1    3    1    1    4    1    2   0 |   1   1    3    1    3    3    1   1    4    2 |  1   3   3   2   3   1  2 |  3   2  1
. . x . . . .  & |     2 |     * 10080    * |    0    2     0     2     0    1    1 |    1    0    1    0    2    4    4    2    0   1 |   1   2    2    1    0    2    0   4    4    4 |  2   2   4   1   2   0  4 |  4   1  1
. . . x . . .    |     2 |     *     * 5040 |    0    0     4     0     0    2    0 |    0    2    0    0    4    0    0    4    4   1 |   2   0    0    2    4    0    0   4    8    0 |  2   4   0   0   4   1  4 |  4   2  0
-----------------+-------+------------------+---------------------------------------+--------------------------------------------------+------------------------------------------------+---------------------------+----------
o3x . . . . .  & |     3 |     3     0    0 | 6720    *     *     *     *    *    * |    1    1    1    2    0    0    0    0    0   0 |   1   1    2    1    2    2    1   0    0    0 |  1   2   2   2   2   1  0 |  2   2  1
. x3x . . . .  & |     6 |     3     3    0 |    * 6720     *     *     *    *    * |    1    0    0    0    1    1    2    0    0   0 |   1   1    2    0    0    1    0   1    2    2 |  1   2   3   1   1   0  2 |  3   1  1
. x . x . . .  & |     4 |     2     0    2 |    *    * 10080     *     *    *    * |    0    1    0    0    1    0    0    1    2   0 |   1   0    0    1    3    0    0   1    4    0 |  1   3   0   0   3   1  2 |  3   2  0
. x . . x . .  & |     4 |     2     2    0 |    *    *     * 10080     *    *    * |    0    0    1    0    0    1    2    1    0   0 |   0   1    1    1    0    2    0   1    2    2 |  1   1   3   1   2   0  2 |  3   1  1
. x . . . x .    |     4 |     4     0    0 |    *    *     *     * 10080    *    * |    0    0    0    2    0    0    2    0    1   0 |   0   0    2    0    2    2    1   0    2    1 |  0   2   2   2   2   1  1 |  2   2  1
. . x3x . . .  & |     6 |     0     3    3 |    *    *     *     *     * 3360    * |    0    0    0    0    2    0    0    2    0   1 |   1   0    0    1    0    0    0   4    4    0 |  2   2   0   0   2   0  4 |  4   1  0
. . x . x . .    |     4 |     0     4    0 |    *    *     *     *     *    * 2520 |    0    0    0    0    0    4    0    0    0   1 |   0   2    0    0    0    0    0   4    0    4 |  2   0   4   0   0   0  4 |  4   0  1
-----------------+-------+------------------+---------------------------------------+--------------------------------------------------+------------------------------------------------+---------------------------+----------
o3x3x . . . .  &     12 |    12     6    0 |    4    4     0     0     0    0    0 | 1680    *    *    *    *    *    *    *    *   * |   1   1    2    0    0    0    0   0    0    0 |  1   2   2   1   0   0  0 |  2   1  1
o3x . x . . .  &      6 |     6     0    3 |    2    0     3     0     0    0    0 |    * 3360    *    *    *    *    *    *    *   * |   1   0    0    1    2    0    0   0    0    0 |  1   2   0   0   2   1  0 |  2   2  0
o3x . . x . .  &      6 |     6     3    0 |    2    0     0     3     0    0    0 |    *    * 3360    *    *    *    *    *    *   * |   0   1    0    1    0    2    0   0    0    0 |  1   0   2   1   2   0  0 |  2   1  1
o3x . . . x .  &      6 |     9     0    0 |    2    0     0     0     3    0    0 |    *    *    * 6720    *    *    *    *    *   * |   0   0    1    0    1    1    1   0    0    0 |  0   1   1   2   1   1  0 |  1   2  1
. x3x3x . . .  &     24 |    12    12   12 |    0    4     6     0     0    4    0 |    *    *    *    * 1680    *    *    *    *   * |   1   0    0    0    0    0    0   1    2    0 |  1   2   0   0   1   0  2 |  3   1  0
. x3x . x . .  &     12 |     6    12    0 |    0    2     0     3     0    0    3 |    *    *    *    *    * 3360    *    *    *   * |   0   1    0    0    0    0    0   1    0    2 |  1   0   3   0   0   0  2 |  3   0  1
. x3x . . x .  &     12 |    12     6    0 |    0    2     0     3     3    0    0 |    *    *    *    *    *    * 6720    *    *   * |   0   0    1    0    0    1    0   0    1    1 |  0   1   2   1   1   0  1 |  2   1  1
. x . x3x . .  &     12 |     6     6    6 |    0    0     3     3     0    2    0 |    *    *    *    *    *    *    * 3360    *   * |   0   0    0    1    0    0    0   1    2    0 |  1   1   0   0   2   0  2 |  3   1  0
. x . x . x .         8 |     8     0    4 |    0    0     4     0     2    0    0 |    *    *    *    *    *    *    *    * 5040   * |   0   0    0    0    2    0    0   0    2    0 |  0   2   0   0   2   1  1 |  2   2  0
. . x3x3x . .        24 |     0    24   12 |    0    0     0     0     0    8    6 |    *    *    *    *    *    *    *    *    * 420 |   0   0    0    0    0    0    0   4    0    0 |  2   0   0   0   0   0  4 |  4   0  0
-----------------+-------+------------------+---------------------------------------+--------------------------------------------------+------------------------------------------------+---------------------------+----------
o3x3x3x . . .  &     60 |    60    30   30 |   20   20    30     0     0   10    0 |    5   10    0    0    5    0    0    0    0   0 | 336   *    *    *    *    *    *   *    *    * |  1   2   0   0   0   0  0 |  2   1  0
o3x3x . x . .  &     24 |    24    24    0 |    8    8     0    12     0    0    6 |    2    0    4    0    0    4    0    0    0   0 |   * 840    *    *    *    *    *   *    *    * |  1   0   2   0   0   0  0 |  2   0  1
o3x3x . . x .  &     24 |    36    12    0 |    8    8     0     6    12    0    0 |    2    0    0    4    0    0    4    0    0   0 |   *   * 1680    *    *    *    *   *    *    * |  0   1   1   1   0   0  0 |  1   1  1
o3x . x3x . .  &     18 |    18     9    9 |    6    0     9     9     0    3    0 |    0    3    3    0    0    0    0    3    0   0 |   *   *    * 1120    *    *    *   *    *    * |  1   0   0   0   2   0  0 |  2   1  0
o3x . x . x .  &     12 |    18     0    6 |    4    0     9     0     6    0    0 |    0    2    0    2    0    0    0    0    3   0 |   *   *    *    * 3360    *    *   *    *    * |  0   1   0   0   1   1  0 |  1   2  0
o3x . . x3x .  &     18 |    27     9    0 |    6    3     0     9     9    0    0 |    0    0    3    3    0    0    3    0    0   0 |   *   *    *    *    * 2240    *   *    *    * |  0   0   1   1   1   0  0 |  1   1  1
o3x . . . x3o         9 |    18     0    0 |    6    0     0     0     9    0    0 |    0    0    0    6    0    0    0    0    0   0 |   *   *    *    *    *    * 1120   *    *    * |  0   0   0   2   0   1  0 |  0   2  1
. x3x3x3x . .  &    120 |    60   120   60 |    0   20    30    30     0   40   30 |    0    0    0    0    5   10    0   10    0   5 |   *   *    *    *    *    *    * 336    *    * |  1   0   0   0   0   0  2 |  3   0  0
. x3x3x . x .  &     48 |    48    24   24 |    0    8    24    12    12    8    0 |    0    0    0    0    2    0    4    4    6   0 |   *   *    *    *    *    *    *   * 1680    * |  0   1   0   0   1   0  1 |  2   1  0
. x3x . x3x .        36 |    36    36    0 |    0   12     0    18     9    0    9 |    0    0    0    0    0    6    6    0    0   0 |   *   *    *    *    *    *    *   *    * 1120 |  0   0   2   0   0   0  1 |  2   0  1
-----------------+-------+------------------+---------------------------------------+--------------------------------------------------+------------------------------------------------+---------------------------+----------
o3x3x3x3x . .  &    360 |   360   360  180 |  120  120   180   180     0  120   90 |   30   60   60    0   30   60    0   60    0  15 |   6  15    0   20    0    0    0   6    0    0 | 56   *   *   *   *   *  * |  2   0  0
o3x3x3x . x .  &    120 |   180    60   60 |   40   40    90    30    60   20    0 |   10   20    0   20   10    0   20   10   30   0 |   2   0    5    0   10    0    0   0    5    0 |  * 336   *   *   *   *  * |  1   1  0
o3x3x . x3x .  &     72 |   108    72    0 |   24   36     0    54    36    0   18 |    6    0   12   12    0   18   24    0    0   0 |   0   3    3    0    0    4    0   0    0    4 |  *   * 560   *   *   *  * |  1   0  1
o3x3x . . x3o  &     36 |    72    18    0 |   24   12     0    18    36    0    0 |    3    0    6   24    0    0   12    0    0   0 |   0   0    3    0    0    4    4   0    0    0 |  *   *   * 560   *   *  * |  0   1  1
o3x . x3x3x .  &     72 |   108    36   36 |   24   12    54    36    36   12    0 |    0   12   12   12    3    0   12   12   18   0 |   0   0    0    4    6    4    0   0    3    0 |  *   *   *   * 560   *  * |  1   1  0
o3x . x . x3o        18 |    36     0    9 |   12    0    18     0    18    0    0 |    0    6    0   12    0    0    0    0    9   0 |   0   0    0    0    6    0    2   0    0    0 |  *   *   *   *   * 560  * |  0   2  0
. x3x3x3x3x .       720 |   720   720  360 |    0  240   360   360   180  240  180 |    0    0    0    0   60  120  120  120   90  30 |   0   0    0    0    0    0    0  12   30   20 |  *   *   *   *   *   * 56 |  2   0  0
-----------------+-------+------------------+---------------------------------------+--------------------------------------------------+------------------------------------------------+---------------------------+----------
o3x3x3x3x3x .  &   2520 |  3780  2520 1260 |  840 1260  1890  1890  1260  840  630 |  210  420  420  420  315  630  840  630  630 105 |  42 105  105  140  210  140    0  63  210  140 |  7  21  35   0  35   0  7 | 16   *  *
o3x3x3x . x3o  &    180 |   360    90   90 |  120   60   180    90   180   30    0 |   15   60   30  120   15    0   60   30   90   0 |   3   0   15   10   60   20   20   0   15    0 |  0   3   0   5   5  10  0 |  * 112  *
o3x3x . x3x3o       144 |   288   144    0 |   96   96     0   144   144    0   36 |   24    0   48   96    0   48   96    0    0   0 |   0  12   24    0    0   32   16   0    0   16 |  0   0   8   8   0   0  0 |  *   * 70

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