Acronym berlin (old: shabrilq)
Name birhombated pentacontihexahecatonicosihexaexon
(small demibirhombated pentacontihexapentacosiheptacontihexaexon)
Circumradius sqrt(51)/2 = 3.570714

Incidence matrix according to Dynkin symbol

o3x3o3o *c3x3o3o

. . . .    . . . | 40320 |      6      9 |     3     6     18      9      9 |     3     9     2    18     18     3     9     3 |    1     9     9    6    18     6     3     3 |   3    9     3    6    6    4 |  3   3   2
-----------------+-------+---------------+----------------------------------+--------------------------------------------------+-----------------------------------------------+-------------------------------+-----------
. x . .    . . . |     2 | 120960      * |     1     2      3      0      0 |     2     3     1     6      3     0     0     0 |    1     6     3    3     6     1     0     0 |   3    6     1    3    2    0 |  3   2   1
. . . .    x . . |     2 |      * 181440 |     0     0      2      2      2 |     0     1     0     4      4     1     4     1 |    0     2     2    2     8     2     2     2 |   1    4     1    4    4    1 |  2   2   2
-----------------+-------+---------------+----------------------------------+--------------------------------------------------+-----------------------------------------------+-------------------------------+-----------
o3x . .    . . . |     3 |      3      0 | 40320     *      *      *      * |     2     3     0     0      0     0     0     0 |    1     6     3    0     0     0     0     0 |   3    6     1    0    0    0 |  3   2   0
. x3o .    . . . |     3 |      3      0 |     * 80640      *      *      * |     1     0     1     3      0     0     0     0 |    1     3     0    3     3     0     0     0 |   3    3     0    3    1    0 |  3   1   1
. x . .    x . . |     4 |      2      2 |     *     * 181440      *      * |     0     1     0     2      2     0     0     0 |    0     2     2    1     4     1     0     0 |   1    4     1    2    2    0 |  2   2   1
. . o . *c3x . . |     3 |      0      3 |     *     *      * 120960      * |     0     0     0     2      0     1     2     0 |    0     1     0    2     4     0     2     1 |   1    2     0    4    2    1 |  2   1   2
. . . .    x3o . |     3 |      0      3 |     *     *      *      * 120960 |     0     0     0     0      2     0     2     1 |    0     0     1    0     4     2     1     2 |   0    2     1    2    4    1 |  1   2   2
-----------------+-------+---------------+----------------------------------+--------------------------------------------------+-----------------------------------------------+-------------------------------+-----------
o3x3o .    . . .      6 |     12      0 |     4     4      0      0      0 | 20160     *     *     *      *     *     *     * |    1     3     0    0     0     0     0     0 |   3    3     0    0    0    0 |  3   1   0
o3x . .    x . .      6 |      6      3 |     2     0      3      0      0 |     * 60480     *     *      *     *     *     * |    0     2     2    0     0     0     0     0 |   1    4     1    0    0    0 |  2   2   0
. x3o3o    . . .      4 |      6      0 |     0     4      0      0      0 |     *     * 20160     *      *     *     *     * |    1     0     0    3     0     0     0     0 |   3    0     0    3    0    0 |  3   0   1
. x3o . *c3x . .     12 |     12     12 |     0     4      6      4      0 |     *     *     * 60480      *     *     *     * |    0     1     0    1     2     0     0     0 |   1    2     0    2    1    0 |  2   1   1
. x . .    x3o .      6 |      3      6 |     0     0      3      0      2 |     *     *     *     * 120960     *     *     * |    0     0     1    0     2     1     0     0 |   0    2     1    1    2    0 |  1   2   1
. . o3o *c3x . .      4 |      0      6 |     0     0      0      4      0 |     *     *     *     *      * 30240     *     * |    0     0     0    2     0     0     2     0 |   1    0     0    4    0    1 |  2   0   2
. . o . *c3x3o .      6 |      0     12 |     0     0      0      4      4 |     *     *     *     *      *     * 60480     * |    0     0     0    0     2     0     1     1 |   0    1     0    2    2    1 |  1   1   2
. . . .    x3o3o      4 |      0      6 |     0     0      0      0      4 |     *     *     *     *      *     *     * 30240 |    0     0     0    0     0     2     0     2 |   0    0     1    0    4    1 |  0   2   2
-----------------+-------+---------------+----------------------------------+--------------------------------------------------+-----------------------------------------------+-------------------------------+-----------
o3x3o3o    . . .     10 |     30      0 |    10    20      0      0      0 |     5     0     5     0      0     0     0     0 | 4032     *     *    *     *     *     *     * |   3    0     0    0    0    0 |  3   0   0
o3x3o . *c3x . .     30 |     60     30 |    20    20     30     10      0 |     5    10     0     5      0     0     0     0 |    * 12096     *    *     *     *     *     * |   1    2     0    0    0    0 |  2   1   0
o3x . .    x3o .      9 |      9      9 |     3     0      9      0      3 |     0     3     0     0      3     0     0     0 |    *     * 40320    *     *     *     *     * |   0    2     1    0    0    0 |  1   2   0
. x3o3o *c3x . .     32 |     48     48 |     0    32     24     32      0 |     0     0     8     8      0     8     0     0 |    *     *     * 7560     *     *     *     * |   1    0     0    2    0    0 |  2   0   1
. x3o . *c3x3o .     30 |     30     60 |     0    10     30     20     20 |     0     0     0     5     10     0     5     0 |    *     *     *    * 24192     *     *     * |   0    1     0    1    1    0 |  1   1   1
. x . .    x3o3o      8 |      4     12 |     0     0      6      0      8 |     0     0     0     0      4     0     0     2 |    *     *     *    *     * 30240     *     * |   0    0     1    0    2    0 |  0   2   1
. . o3o *c3x3o .     10 |      0     30 |     0     0      0     20     10 |     0     0     0     0      0     5     5     0 |    *     *     *    *     *     * 12096     * |   0    0     0    2    0    1 |  1   0   2
. . o . *c3x3o3o     10 |      0     30 |     0     0      0     10     20 |     0     0     0     0      0     0     5     5 |    *     *     *    *     *     *     * 12096 |   0    0     0    0    2    1 |  0   1   2
-----------------+-------+---------------+----------------------------------+--------------------------------------------------+-----------------------------------------------+-------------------------------+-----------
o3x3o3o *c3x . .    160 |    480    240 |   160   320    240    160      0 |    80    80    80    80      0    40     0     0 |   16    16     0   10     0     0     0     0 | 756    *     *    *    *    * |  2   0   0
o3x3o . *c3x3o .     90 |    180    180 |    60    60    180     60     60 |    15    60     0    30     60     0    15     0 |    0     6    20    0     6     0     0     0 |   * 4032     *    *    *    * |  1   1   0
o3x . .    x3o3o     12 |     12     18 |     4     0     18      0     12 |     0     6     0     0     12     0     0     3 |    0     0     4    0     0     3     0     0 |   *    * 10080    *    *    * |  0   2   0
. x3o3o *c3x3o .    160 |    240    480 |     0   160    240    320    160 |     0     0    40    80     80    80    80     0 |    0     0     0   10    16     0    16     0 |   *    *     * 1512    *    * |  1   0   1
. x3o . *c3x3o3o     60 |     60    180 |     0    20     90     60    120 |     0     0     0    15     60     0    30    30 |    0     0     0    0     6    15     0     6 |   *    *     *    * 4032    * |  0   1   1
. . o3o *c3x3o3o     20 |      0     90 |     0     0      0     60     60 |     0     0     0     0      0    15    30    15 |    0     0     0    0     0     0     6     6 |   *    *     *    *    * 2016 |  0   0   2
-----------------+-------+---------------+----------------------------------+--------------------------------------------------+-----------------------------------------------+-------------------------------+-----------
o3x3o3o *c3x3o .   2160 |   6480   6480 |  2160  4320   6480   4320   2160 |  1080  2160  1080  2160   2160  1080  1080     0 |  216   432   720  270   432     0   216     0 |  27   72     0   27    0    0 | 56   *   *
o3x3o . *c3x3o3o    210 |    420    630 |   140   140    630    210    420 |    35   210     0   105    420     0   105   105 |    0    21   140    0    42   105     0    21 |   0    7    35    0    7    0 |  * 576   *
. x3o3o *c3x3o3o    640 |    960   2880 |     0   640   1440   1920   1920 |     0     0   160   480    960   480   960   480 |    0     0     0   60   192   240   192   192 |   0    0     0   12   32   32 |  *   * 126

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