Acronym ren
Name rectified enneract,
rectified octadecayotton
Circumradius 2
Coordinates (1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0)   & all permutations, all changes of sign

Incidence matrix according to Dynkin symbol

o3o3o3o3o3o3o3x4o

. . . . . . . . . | 2304 |    16 |    56    8 |   112   28 |   140   56 |   112   70 |    56  56 |   16  28 |   2  8
------------------+------+-------+------------+------------+------------+------------+-----------+----------+-------
. . . . . . . x . |    2 | 18432 |     7    1 |    21    7 |    35   21 |    35   35 |    21  35 |    7  21 |   1  7
------------------+------+-------+------------+------------+------------+------------+-----------+----------+-------
. . . . . . o3x . |    3 |     3 | 43008    * |     6    1 |    15    6 |    20   15 |    15  20 |    6  15 |   1  6
. . . . . . . x4o |    4 |     4 |     * 4608      0    7 |     0   21 |     0   35 |     0  35 |    0  21 |   0  7
------------------+------+-------+------------+------------+------------+------------+-----------+----------+-------
. . . . . o3o3x .     4 |     6 |     4    0 | 64512    * |     5    1 |    10    5 |    10  10 |    5  10 |   1  5
. . . . . . o3x4o    12 |    24 |     8    6 |     * 5376      0    6 |     0   15 |     0  20 |    0  15 |   0  6
------------------+------+-------+------------+------------+------------+------------+-----------+----------+-------
. . . . o3o3o3x .     5 |    10 |    10    0 |     5    0 | 64512    * |     4    1 |     6   4 |    4   6 |   1  4
. . . . . o3o3x4o    32 |    96 |    64   24 |    16    8 |     * 4032      0    5 |     0  10 |    0  10 |   0  5
------------------+------+-------+------------+------------+------------+------------+-----------+----------+-------
. . . o3o3o3o3x .     6 |    15 |    20    0 |    15    0 |     6    0 | 43008    * |     3   1 |    3   3 |   1  3
. . . . o3o3o3x4o    80 |   320 |   320   80 |   160   40 |    32   10 |     * 2016      0   4 |    0   6 |   0  4
------------------+------+-------+------------+------------+------------+------------+-----------+----------+-------
. . o3o3o3o3o3x .     7 |    21 |    35    0 |    35    0 |    21    0 |     7    0 | 18432   * |    2   1 |   1  2
. . . o3o3o3o3x4o   192 |   960 |  1280  240 |   960  160 |   384   60 |    64   12 |     * 672 |    0   3 |   0  3
------------------+------+-------+------------+------------+------------+------------+-----------+----------+-------
. o3o3o3o3o3o3x .     8 |    28 |    56    0 |    70    0 |    56    0 |    28    0 |     8   0 | 4608   * |   1  1
. . o3o3o3o3o3x4o   448 |  2688 |  4480  672 |  4480  560 |  2688  280 |   896   84 |   128  14 |    * 144 |   0  2
------------------+------+-------+------------+------------+------------+------------+-----------+----------+-------
o3o3o3o3o3o3o3x .     9 |    36 |    84    0 |   126    0 |   126    0 |    84    0 |    36   0 |    9   0 | 512  *
. o3o3o3o3o3o3x4o  1024 |  7168 | 14336 1792 | 17920 1792 | 14336 1120 |  7168  448 |  2048 112 |  256  16 |   * 18

x3o3x *b3o3o3o3o3o3o

. . .    . . . . . . | 2304 |    8    8 |    28    8    28 |   28    56    56 |   56    70    70 |   70    56    56 |  56   28   28 |  28    8    8 |  8   1   1
---------------------+------+-----------+------------------+------------------+------------------+------------------+---------------+---------------+-----------
x . .    . . . . . . |    2 | 9216    * |     7    1     0 |    7    21     0 |   21    35     0 |   35    35     0 |  35   21    0 |  21    7    0 |  7   1   0
. . x    . . . . . . |    2 |    * 9216 |     0    1     7 |    7     0    21 |   21     0    35 |   35     0    35 |  35    0   21 |  21    0    7 |  7   0   1
---------------------+------+-----------+------------------+------------------+------------------+------------------+---------------+---------------+-----------
x3o .    . . . . . . |    3 |    3    0 | 21504    *     * |    1     6     0 |    6    15     0 |   15    20     0 |  20   15    0 |  15    6    0 |  6   1   0
x . x    . . . . . . |    4 |    2    2 |     * 4608     *     7     0     0 |   21     0     0 |   35     0     0 |  35    0    0 |  21    0    0 |  7   0   0
. o3x    . . . . . . |    3 |    0    3 |     *    * 21504 |    1     0     6 |    6     0    15 |   15     0    20 |  20    0   15 |  15    0    6 |  6   0   1
---------------------+------+-----------+------------------+------------------+------------------+------------------+---------------+---------------+-----------
x3o3x    . . . . . .    12 |   12   12 |     4    6     4 | 5376     *     *     6     0     0 |   15     0     0 |  20    0    0 |  15    0    0 |  6   0   0
x3o . *b3o . . . . .     4 |    6    0 |     4    0     0 |    * 32256     * |    1     5     0 |    5    10     0 |  10   10    0 |  10    5    0 |  5   1   0
. o3x *b3o . . . . .     4 |    0    6 |     0    0     4 |    *     * 32256 |    1     0     5 |    5     0    10 |  10    0   10 |  10    0    5 |  5   0   1
---------------------+------+-----------+------------------+------------------+------------------+------------------+---------------+---------------+-----------
x3o3x *b3o . . . . .    32 |   48   48 |    32   24    32 |    8     8     8 | 4032     *     *     5     0     0 |  10    0    0 |  10    0    0 |  5   0   0
x3o . *b3o3o . . . .     5 |   10    0 |    10    0     0 |    0     5     0 |    * 32256     * |    1     4     0 |   4    6    0 |   6    4    0 |  4   1   0
. o3x *b3o3o . . . .     5 |    0   10 |     0    0    10 |    0     0     5 |    *     * 32256 |    1     0     4 |   4    0    6 |   6    0    4 |  4   0   1
---------------------+------+-----------+------------------+------------------+------------------+------------------+---------------+---------------+-----------
x3o3x *b3o3o . . . .    80 |  160  160 |   160   80   160 |   40    80    80 |   10    16    16 | 2016     *     * |   4    0    0 |   6    0    0   4   0   0
x3o . *b3o3o3o . . .     6 |   15    0 |    20    0     0 |    0    15     0 |    0     6     0 |    * 21504     * |   1    3    0 |   3    3    0 |  3   1   0
. o3x *b3o3o3o . . .     6 |    0   15 |     0    0    20 |    0     0    15 |    0     0     6 |    *     * 21504 |   1    0    3 |   3    0    3 |  3   0   1
---------------------+------+-----------+------------------+------------------+------------------+------------------+---------------+---------------+-----------
x3o3x *b3o3o3o . . .   192 |  480  480 |   640  240   640 |  160   480   480 |   60   192   192 |   12    32    32 | 672    *    * |   3    0    0 |  3   0   0
x3o . *b3o3o3o3o . .     7 |   21    0 |    35    0     0 |    0    35     0 |    0    21     0 |    0     7     0 |   * 9216    * |   1    2    0 |  2   1   0
. o3x *b3o3o3o3o . .     7 |    0   21 |     0    0    35 |    0     0    35 |    0     0    21 |    0     0     7 |   *    * 9216 |   1    0    2 |  2   0   1
---------------------+------+-----------+------------------+------------------+------------------+------------------+---------------+---------------+-----------
x3o3x *b3o3o3o3o . .   448 | 1344 1344 |  2240  672  2240 |  560  2240  2240 |  280  1344  1344 |   84   448   448 |  14   64   64 | 144    *    * |  2   0   0
x3o . *b3o3o3o3o3o .     8 |   28    0 |    56    0     0 |    0    70     0 |    0    56     0 |    0    28     0 |   0    8    0 |   * 2304    * |  1   1   0
. o3x *b3o3o3o3o3o .     8 |    0   28 |     0    0    56 |    0     0    70 |    0     0    56 |    0     0    28 |   0    0    8 |   *    * 2304 |  1   0   1
---------------------+------+-----------+------------------+------------------+------------------+------------------+---------------+---------------+-----------
x3o3x *b3o3o3o3o3o .  1024 | 3584 3584 |  7168 1792  7168 | 1792  8960  8960 | 1120  7168  7168 |  448  3584  3584 | 112 1024 1024 |  16  128  128 | 18   *   *
x3o . *b3o3o3o3o3o3o     9 |   36    0 |    84    0     0 |    0   126     0 |    0   126     0 |    0    84     0 |   0   36    0 |   0    9    0 |  * 256   *
. o3x *b3o3o3o3o3o3o     9 |    0   36 |     0    0    84 |    0     0   126 |    0     0   126 |    0     0    84 |   0    0   36 |   0    0    9 |  *   * 256

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