Acronym gook
Name great octeractiocteractidiacosipentacontahexazetton
Circumradius sqrt[(5-sqrt(2))/2] = 1.338990
Coordinates ((sqrt(2)-1)/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign

Incidence matrix according to Dynkin symbol

o3o3o3o3o3o3x4/3x4*f

. . . . . . .   .    | 2048 |    7    7 |    21    21    7 |    35   35   21 |    35   35   35 |   21   21  35 |    7   7  21 |   1  1  7
---------------------+------+-----------+------------------+-----------------+-----------------+---------------+--------------+----------
. . . . . . x   .    |    2 | 7168    * |     6     0    1 |    15    0    6 |    20    0   15 |   15    0  20 |    6   0  15 |   1  0  6
. . . . . . .   x    |    2 |    * 7168 |     0     6    1 |     0   15    6 |     0   20   15 |    0   15  20 |    0   6  15 |   0  1  6
---------------------+------+-----------+------------------+-----------------+-----------------+---------------+--------------+----------
. . . . . o3x   .    |    3 |    3    0 | 14336     *    * |     5    0    1 |    10    0    5 |   10    0  10 |    5   0  10 |   1  0  5
. . . . . o .   x4*f |    4 |    0    4 |     * 10752    * |     0    5    1 |     0   10    5 |    0   10  10 |    0   5  10 |   0  1  5
. . . . . . x4/3x    |    8 |    4    4 |     *     * 1792      0    0    6 |     0    0   15 |    0    0  20 |    0   0  15 |   0  0  6
---------------------+------+-----------+------------------+-----------------+-----------------+---------------+--------------+----------
. . . . o3o3x   .        4 |    6    0 |     4     0    0 | 17920    *    * |     4    0    1 |    6    0   4 |    4   0   6 |   1  0  4
. . . . o3o .   x4*f     8 |    0   12 |     0     6    0 |     * 8960    * |     0    4    1 |    0    6   4 |    0   4   6 |   0  1  4
. . . . . o3x4/3x4*f    24 |   24   24 |     8     6    6 |     *    * 1792      0    0    5 |    0    0  10 |    0   0  10 |   0  0  5
---------------------+------+-----------+------------------+-----------------+-----------------+---------------+--------------+----------
. . . o3o3o3x   .        5 |   10    0 |    10     0    0 |     5    0    0 | 14336    *    * |    3    0   1 |    3   0   3 |   1  0  3
. . . o3o3o .   x4*f    16 |    0   32 |     0    24    0 |     0    8    0 |     * 4480    * |    0    3   1 |    0   3   3 |   0  1  3
. . . . o3o3x4/3x4*f    64 |   96   96 |    64    48   24 |    16    8    8 |     *    * 1120     0    0   4 |    0   0   6 |   0  0  4
---------------------+------+-----------+------------------+-----------------+-----------------+---------------+--------------+----------
. . o3o3o3o3x   .        6 |   15    0 |    20     0    0 |    15    0    0 |     6    0    0 | 7168    *   * |    2   0   1 |   1  0  2
. . o3o3o3o .   x4*f    32 |    0   80 |     0    80    0 |     0   40    0 |     0   10    0 |    * 1344   * |    0   2   1 |   0  1  2
. . . o3o3o3x4/3x4*f   160 |  320  320 |   320   240   80 |   160   80   40 |    32   10   10 |    *    * 448 |    0   0   3 |   0  0  3
---------------------+------+-----------+------------------+-----------------+-----------------+---------------+--------------+----------
. o3o3o3o3o3x   .        7 |   21    0 |    35     0    0 |    35    0    0 |    21    0    0 |    7    0   0 | 2048   *   * |   1  0  1
. o3o3o3o3o .   x4*f    64 |    0  192 |     0   240    0 |     0  160    0 |     0   60    0 |    0   12   0 |    * 224   * |   0  1  1
. . o3o3o3o3x4/3x4*f   384 |  960  960 |  1280   960  240 |   960  480  160 |   384  120   60 |   64   12  12 |    *   * 112 |   0  0  2
---------------------+------+-----------+------------------+-----------------+-----------------+---------------+--------------+----------
o3o3o3o3o3o3x   .        8 |   28    0 |    56     0    0 |    70    0    0 |    56    0    0 |   28    0   0 |    8   0   0 | 256  *  *
o3o3o3o3o3o .   x4*f   128 |    0  448 |     0   672    0 |     0  560    0 |     0  280    0 |    0   84   0 |    0  14   0 |   * 16  *
. o3o3o3o3o3x4/3x4*f   896 | 2688 2688 |  4480  3360  672 |  4480 2240  560 |  2688  840  280 |  896  168  84 |  128  14  14 |   *  * 16

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