Acronym sotho
Name small terated hemiocteract,
hexic octeract
Circumradius sqrt(3) = 1.732051
Coordinates (3/sqrt(8), 3/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8))   & all permutations, all even changes of sign

Incidence matrix according to Dynkin symbol

x3o3o *b3o3o3o3x3o

o3o3o *b3o3o3o3o3o | 3584 |    15    12 |    60    120    30    6 |    20    60    360    180    60    40   15 |   15   120    30    240    360   180   120    90    30   20 |    6    60   120    60    6    60   120   120   120   180    30    60   12   15 |   1   12   30   30   40   60   12   30   60   60   15    2    6 |  2   6   15   20   6   1
-------------------+------+-------------+-------------------------+--------------------------------------------+-------------------------------------------------------------+---------------------------------------------------------------------------------+-----------------------------------------------------------------+-------------------------
x . .    . . . . . |    2 | 26880     * |     8      8     0    0 |     4    12     48     12     4     0    0 |    6    24     8     48     48    24     8     6     0    0 |    4    24    24    12    2    16    24    24    16    24     2     4    0    0 |   1    8   12   12    8   12    4    8   12    8    1    0    0 |  2   4    6    4   2   0
. . .    . . . x . |    2 |     * 21504 |     0     10     5    1 |     0     0     30     30    10    10    5 |    0    10     0     20     60    30    30    30    10   10 |    0     5    20    10    0     5    20    20    30    60    10    30    5   10 |   0    1    5    5   10   20    5    5   20   30   10    1    5 |  1   1    5   10   5   1
-------------------+------+-------------+-------------------------+--------------------------------------------+-------------------------------------------------------------+---------------------------------------------------------------------------------+-----------------------------------------------------------------+-------------------------
x3o .    . . . . . |    3 |     3     0 | 71680      *     *    * |     1     3      6      0     0     0    0 |    3     6     3     12      6     3     0     0     0    0 |    3    12     6     3    1     6     6     6     2     3     0     0    0    0 |   1    6    6    6    2    3    2    3    3    1    0    0    0 |  2   3    3    1   1   0
x . .    . . . x . |    4 |     2     2 |     * 107520     *    * |     0     0      6      3     1     0    0 |    0     3     0      6     12     6     3     3     0    0 |    0     3     6     3    0     2     6     6     6    12     1     3    0    0 |   0    1    3    3    3    6    2    2    6    6    1    0    0 |  1   1    3    3   2   0
. . .    . . o3x . |    3 |     0     3 |     *      * 35840    * |     0     0      0      6     0     4    1 |    0     0     0      0     12     0    12     6     6    4 |    0     0     4     0    0     0     4     0    12    12     6    12    4    6 |   0    0    1    0    4    4    4    0    4   12    6    1    4 |  1   0    1    4   4   1
. . .    . . . x3o |    3 |     0     3 |     *      *     * 7168 |     0     0      0      0    10     0    5 |    0     0     0      0      0    30     0    30     0   10 |    0     0     0    10    0     0     0    20     0    60     0    30    0   10 |   0    0    0    5    0   20    0    5   20   30   10    0    5 |  0   1    5   10   5   1
-------------------+------+-------------+-------------------------+--------------------------------------------+-------------------------------------------------------------+---------------------------------------------------------------------------------+-----------------------------------------------------------------+-------------------------
x3o3o    . . . . .     4 |     6     0 |     4      0     0    0 | 17920     *      *      *     *     *    * |    3     6     0      0      0     0     0     0     0    0 |    3    12     6     3    0     0     0     0     0     0     0     0    0    0 |   1    6    6    6    2    3    0    0    0    0    0    0    0 |  2   3    3    1   0   0
x3o . *b3o . . . .     4 |     6     0 |     4      0     0    0 |     * 53760      *      *     *     *    * |    1     0     2      4      0     0     0     0     0    0 |    2     4     0     0    1     4     2     2     0     0     0     0    0    0 |   1    4    2    2    0    0    2    2    1    0    0    0    0 |  2   2    1    0   1   0
x3o .    . . . x .     6 |     6     3 |     2      3     0    0 |     *     * 215040      *     *     *    * |    0     1     0      2      2     1     0     0     0    0 |    0     2     2     1    0     1     2     2     1     2     0     0    0    0 |   0    1    2    2    1    2    1    1    2    1    0    0    0 |  1   1    2    1   1   0
x . .    . . o3x .     6 |     3     6 |     0      3     2    0 |     *     *      * 107520     *     *    * |    0     0     0      0      4     0     2     1     0    0 |    0     0     2     0    0     0     2     0     4     4     1     2    0    0 |   0    0    1    0    2    2    2    0    2    4    1    0    0 |  1   0    1    2   2   0
x . .    . . . x3o     6 |     3     6 |     0      3     0    2 |     *     *      *      * 35840     *    * |    0     0     0      0      0     6     0     3     0    0 |    0     0     0     3    0     0     0     6     0    12     0     3    0    0 |   0    0    0    3    0    6    0    2    6    6    1    0    0 |  0   1    3    3   2   0
. . .    . o3o3x .     4 |     0     6 |     0      0     4    0 |     *     *      *      *     * 35840    * |    0     0     0      0      0     0     3     0     3    1 |    0     0     0     0    0     0     0     0     3     0     3     3    3    3 |   0    0    0    0    1    0    3    0    0    3    3    1    3 |  1   0    0    1   3   1
. . .    . . o3x3o     6 |     0    12 |     0      0     4    4 |     *     *      *      *     *     * 8960 |    0     0     0      0      0     0     0     6     0    4 |    0     0     0     0    0     0     0     0     0    12     0    12    0    6 |   0    0    0    0    0    4    0    0    4   12    6    0    4 |  0   0    1    4   4   1
-------------------+------+-------------+-------------------------+--------------------------------------------+-------------------------------------------------------------+---------------------------------------------------------------------------------+-----------------------------------------------------------------+-------------------------
x3o3o *b3o . . . .     8 |    24     0 |    32      0     0    0 |     8     8      0      0     0     0    0 | 6720     *     *      *      *     *     *     *     *    * |    2     4     0     0    0     0     0     0     0     0     0     0    0    0 |   1    4    2    2    0    0    0    0    0    0    0    0    0 |  2   2    1    0   0   0
x3o3o    . . . x .     8 |    12     4 |     8      6     0    0 |     2     0      4      0     0     0    0 |    * 53760     *      *      *     *     *     *     *    * |    0     2     2     1    0     0     0     0     0     0     0     0    0    0 |   0    1    2    2    1    2    0    0    0    0    0    0    0 |  1   1    2    1   0   0
x3o . *b3o3o . . .     5 |    10     0 |    10      0     0    0 |     0     5      0      0     0     0    0 |    *     * 21504      *      *     *     *     *     *    * |    1     0     0     0    1     2     0     0     0     0     0     0    0    0 |   1    2    0    0    0    0    2    1    0    0    0    0    0 |  2   1    0    0   1   0
x3o . *b3o . . x .     8 |    12     4 |     8      6     0    0 |     0     2      4      0     0     0    0 |    *     *     * 107520      *     *     *     *     *    * |    0     1     0     0    0     1     1     1     0     0     0     0    0    0 |   0    1    1    1    0    0    1    1    1    0    0    0    0 |  1   1    1    0   1   0
x3o .    . . o3x .     9 |     9     9 |     3      9     3    0 |     0     0      3      3     0     0    0 |    *     *     *      * 143360     *     *     *     *    * |    0     0     1     0    0     0     1     0     1     1     0     0    0    0 |   0    0    1    0    1    1    1    0    1    1    0    0    0 |  1   0    1    1   1   0
x3o .    . . . x3o     9 |     9     9 |     3      9     0    3 |     0     0      3      0     3     0    0 |    *     *     *      *      * 71680     *     *     *    * |    0     0     0     1    0     0     0     2     0     2     0     0    0    0 |   0    0    0    2    0    2    0    1    2    1    0    0    0 |  0   1    2    1   1   0
x . .    . o3o3x .     8 |     4    12 |     0      6     8    0 |     0     0      0      4     0     2    0 |    *     *     *      *      *     * 53760     *     *    * |    0     0     0     0    0     0     0     0     2     0     1     1    0    0 |   0    0    0    0    1    0    2    0    0    2    1    0    0 |  1   0    0    1   2   0
x . .    . . o3x3o    12 |     6    24 |     0     12     8    8 |     0     0      0      4     4     0    2 |    *     *     *      *      *     *     * 26880     *    * |    0     0     0     0    0     0     0     0     0     4     0     2    0    0 |   0    0    0    0    0    2    0    0    2    4    1    0    0 |  0   0    1    2   2   0
. . .    o3o3o3x .     5 |     0    10 |     0      0    10    0 |     0     0      0      0     0     5    0 |    *     *     *      *      *     *     *     * 21504    * |    0     0     0     0    0     0     0     0     0     0     1     0    2    1 |   0    0    0    0    0    0    2    0    0    0    1    1    2 |  1   0    0    0   2   1
. . .    . o3o3x3o    10 |     0    30 |     0      0    20   10 |     0     0      0      0     0     5    5 |    *     *     *      *      *     *     *     *     * 7168 |    0     0     0     0    0     0     0     0     0     0     0     3    0    3 |   0    0    0    0    0    0    0    0    0    3    3    0    3 |  0   0    0    1   3   1
-------------------+------+-------------+-------------------------+--------------------------------------------+-------------------------------------------------------------+---------------------------------------------------------------------------------+-----------------------------------------------------------------+-------------------------
x3o3o *b3o3o . . .    16 |    80     0 |   160      0     0    0 |    40    80      0      0     0     0    0 |   10     0    16      0      0     0     0     0     0    0 | 1344     *     *     *    *     *     *     *     *     *     *     *    *    * |   1    2    0    0    0    0    0    0    0    0    0    0    0 |  2   1    0    0   0   0
x3o3o *b3o . . x .    16 |    48     8 |    64     24     0    0 |    16    16     32      0     0     0    0 |    2     8     0      8      0     0     0     0     0    0 |    * 13440     *     *    *     *     *     *     *     *     *     *    *    * |   0    1    1    1    0    0    0    0    0    0    0    0    0 |  1   1    1    0   0   0
x3o3o    . . o3x .    12 |    18    12 |    12     18     4    0 |     3     0     12      6     0     0    0 |    0     3     0      0      4     0     0     0     0    0 |    *     * 35840     *    *     *     *     *     *     *     *     *    *    * |   0    0    1    0    1    1    0    0    0    0    0    0    0 |  1   0    1    1   0   0
x3o3o    . . . x3o    12 |    18    12 |    12     18     0    4 |     3     0     12      0     6     0    0 |    0     3     0      0      0     4     0     0     0    0 |    *     *     * 17920    *     *     *     *     *     *     *     *    *    * |   0    0    0    2    0    2    0    0    0    0    0    0    0 |  0   1    2    1   0   0
x3o . *b3o3o3o . .     6 |    15     0 |    20      0     0    0 |     0    15      0      0     0     0    0 |    0     0     6      0      0     0     0     0     0    0 |    *     *     *     * 3584     *     *     *     *     *     *     *    *    * |   1    0    0    0    0    0    2    0    0    0    0    0    0 |  2   0    0    0   1   0
x3o . *b3o3o . x .    10 |    20     5 |    20     10     0    0 |     0    10     10      0     0     0    0 |    0     0     2      5      0     0     0     0     0    0 |    *     *     *     *    * 21504     *     *     *     *     *     *    *    * |   0    1    0    0    0    0    1    1    0    0    0    0    0 |  1   1    0    0   1   0
x3o . *b3o . o3x .    12 |    18    12 |    12     18     4    0 |     0     3     12      6     0     0    0 |    0     0     0      3      4     0     0     0     0    0 |    *     *     *     *    *     * 35840     *     *     *     *     *    *    * |   0    0    1    0    0    0    1    0    1    0    0    0    0 |  1   0    1    0   1   0
x3o . *b3o . . x3o    12 |    18    12 |    12     18     0    4 |     0     3     12      0     6     0    0 |    0     0     0      3      0     4     0     0     0    0 |    *     *     *     *    *     *     * 35840     *     *     *     *    *    * |   0    0    0    1    0    0    0    1    1    0    0    0    0 |  0   1    1    0   1   0
x3o .    . o3o3x .    12 |    12    18 |     4     18    12    0 |     0     0      6     12     0     3    0 |    0     0     0      0      4     0     3     0     0    0 |    *     *     *     *    *     *     *     * 35840     *     *     *    *    * |   0    0    0    0    1    0    1    0    0    1    0    0    0 |  1   0    0    1   1   0
x3o .    . . o3x3o    18 |    18    36 |     6     36    12   12 |     0     0     12     12    12     0    3 |    0     0     0      0      4     4     0     3     0    0 |    *     *     *     *    *     *     *     *     * 35840     *     *    *    * |   0    0    0    0    0    1    0    0    1    1    0    0    0 |  0   0    1    1   1   0
x . .    o3o3o3x .    10 |     5    20 |     0     10    20    0 |     0     0      0     10     0    10    0 |    0     0     0      0      0     0     5     0     2    0 |    *     *     *     *    *     *     *     *     *     * 10752     *    *    * |   0    0    0    0    0    0    2    0    0    0    1    0    0 |  1   0    0    0   2   0
x . .    . o3o3x3o    20 |    10    60 |     0     30    40   20 |     0     0      0     20    10    10   10 |    0     0     0      0      0     0     5     5     0    2 |    *     *     *     *    *     *     *     *     *     *     * 10752    *    * |   0    0    0    0    0    0    0    0    0    2    1    0    0 |  0   0    0    1   2   0
. o . *b3o3o3o3x .     6 |     0    15 |     0      0    20    0 |     0     0      0      0     0    15    0 |    0     0     0      0      0     0     0     0     6    0 |    *     *     *     *    *     *     *     *     *     *     *     * 7168    * |   0    0    0    0    0    0    1    0    0    0    0    1    1 |  1   0    0    0   1   1
. . .    o3o3o3x3o    15 |     0    60 |     0      0    60   20 |     0     0      0      0     0    30   15 |    0     0     0      0      0     0     0     0     6    6 |    *     *     *     *    *     *     *     *     *     *     *     *    * 3584 |   0    0    0    0    0    0    0    0    0    0    1    0    2 |  0   0    0    0   2   1
-------------------+------+-------------+-------------------------+--------------------------------------------+-------------------------------------------------------------+---------------------------------------------------------------------------------+-----------------------------------------------------------------+-------------------------
x3o3o *b3o3o3o . .    32 |   240     0 |   640      0     0    0 |   160   480      0      0     0     0    0 |   60     0   192      0      0     0     0     0     0    0 |   12     0     0     0   32     0     0     0     0     0     0     0    0    0 | 112    *    *    *    *    *    *    *    *    *    *    *    * |  2   0    0    0   0   0
x3o3o *b3o3o . x .    32 |   160    16 |   320     80     0    0 |    80   160    160      0     0     0    0 |   20    40    32     80      0     0     0     0     0    0 |    2    10     0     0    0    16     0     0     0     0     0     0    0    0 |   * 1344    *    *    *    *    *    *    *    *    *    *    * |  1   1    0    0   0   0
x3o3o *b3o . o3x .    24 |    72    24 |    96     72     8    0 |    24    24     96     24     0     0    0 |    3    24     0     24     32     0     0     0     0    0 |    0     3     8     0    0     0     8     0     0     0     0     0    0    0 |   *    * 4480    *    *    *    *    *    *    *    *    *    * |  1   0    1    0   0   0
x3o3o *b3o . . x3o    24 |    72    24 |    96     72     0    8 |    24    24     96      0    24     0    0 |    3    24     0     24      0    32     0     0     0    0 |    0     3     0     8    0     0     0     8     0     0     0     0    0    0 |   *    *    * 4480    *    *    *    *    *    *    *    *    * |  0   1    1    0   0   0
x3o3o    . o3o3x .    16 |    24    24 |    16     36    16    0 |     4     0     24     24     0     4    0 |    0     6     0      0     16     0     6     0     0    0 |    0     0     4     0    0     0     0     0     4     0     0     0    0    0 |   *    *    *    * 8960    *    *    *    *    *    *    *    * |  1   0    0    1   0   0
x3o3o    . . o3x3o    24 |    36    48 |    24     72    16   16 |     6     0     48     24    24     0    4 |    0    12     0      0     16    16     0     6     0    0 |    0     0     4     4    0     0     0     0     0     4     0     0    0    0 |   *    *    *    *    * 8960    *    *    *    *    *    *    * |  0   0    1    1   0   0
x3o . *b3o3o3o3x .    42 |   105   105 |   140    210   140    0 |     0   105    210    210     0   105    0 |    0     0    42    105    140     0   105     0    42    0 |    0     0     0     0    7    21    35     0    35     0    21     0    7    0 |   *    *    *    *    *    * 1024    *    *    *    *    *    * |  1   0    0    0   1   0
x3o . *b3o3o . x3o    15 |    30    15 |    30     30     0    5 |     0    15     30      0    10     0    0 |    0     0     3     15      0    10     0     0     0    0 |    0     0     0     0    0     3     0     5     0     0     0     0    0    0 |   *    *    *    *    *    *    * 7168    *    *    *    *    * |  0   1    0    0   1   0
x3o . *b3o . o3x3o    24 |    36    48 |    24     72    16   16 |     0     6     48     24    24     0    4 |    0     0     0     12     16    16     0     6     0    0 |    0     0     0     0    0     0     4     4     0     4     0     0    0    0 |   *    *    *    *    *    *    *    * 8960    *    *    *    * |  0   0    1    0   1   0
x3o .    . o3o3x3o    30 |    30    90 |    10     90    60   30 |     0     0     30     60    30    15   15 |    0     0     0      0     20    10    15    15     0    3 |    0     0     0     0    0     0     0     0     5     5     0     3    0    0 |   *    *    *    *    *    *    *    *    * 7168    *    *    * |  0   0    0    1   1   0
x . .    o3o3o3x3o    30 |    15   120 |     0     60   120   40 |     0     0      0     60    20    60   30 |    0     0     0      0      0     0    30    15    12   12 |    0     0     0     0    0     0     0     0     0     0     6     6    0    2 |   *    *    *    *    *    *    *    *    *    * 1792    *    * |  0   0    0    0   2   0
. o3o *b3o3o3o3x .     7 |     0    21 |     0      0    35    0 |     0     0      0      0     0    35    0 |    0     0     0      0      0     0     0     0    21    0 |    0     0     0     0    0     0     0     0     0     0     0     0    7    0 |   *    *    *    *    *    *    *    *    *    *    * 1024    * |  1   0    0    0   0   1
. o . *b3o3o3o3x3o    21 |     0   105 |     0      0   140   35 |     0     0      0      0     0   105   35 |    0     0     0      0      0     0     0     0    42   21 |    0     0     0     0    0     0     0     0     0     0     0     0    7    7 |   *    *    *    *    *    *    *    *    *    *    *    * 1024 |  0   0    0    0   1   1
-------------------+------+-------------+-------------------------+--------------------------------------------+-------------------------------------------------------------+---------------------------------------------------------------------------------+-----------------------------------------------------------------+-------------------------
x3o3o *b3o3o3o3x .   448 |  3360  1344 |  8960   6720  2240    0 |  2240  6720  13440   6720     0  2240    0 |  840  3360  2688   6720   8960     0  3360     0  1344    0 |  168   840  2240     0  448  1344  2240     0  2240     0   672     0  448    0 |  14   84  280    0  560    0   64    0    0    0    0   64    0 | 16   *    *    *   *   *
x3o3o *b3o3o . x3o    48 |   240    48 |   480    240     0   16 |   120   240    480      0    80     0    0 |   30   120    48    240      0   160     0     0     0    0 |    3    30     0    40    0    48     0    80     0     0     0     0    0    0 |   0    3    0   10    0    0    0   16    0    0    0    0    0 |  * 448    *    *   *   *
x3o3o *b3o . o3x3o    48 |   144    96 |   192    288    32   32 |    48    48    384     96    96     0    8 |    6    96     0     96    128   128     0    24     0    0 |    0    12    32    32    0     0    32    32     0    32     0     0    0    0 |   0    0    4    4    0    8    0    0    8    0    0    0    0 |  *   * 1120    *   *   *
x3o3o    . o3o3x3o    40 |    60   120 |    40    180    80   40 |    10     0    120    120    60    20   20 |    0    30     0      0     80    40    30    30     0    4 |    0     0    20    10    0     0     0     0    20    20     0     6    0    0 |   0    0    0    0    5    5    0    0    0    4    0    0    0 |  *   *    * 1792   *   *
x3o . *b3o3o3o3x3o   168 |   420   840 |   560   1680  1120  280 |     0   420   1680   1680   560   840  280 |    0     0   168    840   1120   560   840   420   336  168 |    0     0     0     0   28   168   280   280   280   280   168   168   56   56 |   0    0    0    0    0    0    8   56   70   56   28    0    8 |  *   *    *    * 128   *
. o3o *b3o3o3o3x3o    28 |     0   168 |     0      0   280   56 |     0     0      0      0     0   280   70 |    0     0     0      0      0     0     0     0   168   56 |    0     0     0     0    0     0     0     0     0     0     0     0   56   28 |   0    0    0    0    0    0    0    0    0    0    0    8    8 |  *   *    *    *   * 128

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