Acronym spuho
Name small petated hemiocteract
Circumradius sqrt(2) = 1.414214
Coordinates (3/sqrt(8), 1/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 *b3o3o3o3o3x

o3o3o *b3o3o3o3o3o | 1024 |    21    7 |   105   105   21 |   35   140   420   210   35 |   35   140   105   420   630   210   35 |   21  105   210   42   210   420   420   105   21 |   7   42  105  140    7   42  105  140  105   21    7 |  1   7  21   35   35   7   1
-------------------+------+------------+------------------+-----------------------------+-----------------------------------------+---------------------------------------------------+-------------------------------------------------------+-----------------------------
x . .    . . . . . |    2 | 10752    * |    10     5    0 |    5    20    40    10    0 |   10    20    20    60    60    10    0 |   10   30    30   10    40    60    40     5    0 |  30   20   30   20    2   10   20   20   10    1    0 |  1   5  10   10    5   2   0
. . .    . . . . x |    2 |     * 3584 |     0    15    6 |    0     0    60    60   15 |    0    20     0    60   180    90   20 |    0   15    60    0    30   120   180    60   15 |   0    6   30   60    0    6   30   60   60   15    6 |  0   1   6   15   20   6   1
-------------------+------+------------+------------------+-----------------------------+-----------------------------------------+---------------------------------------------------+-------------------------------------------------------+-----------------------------
x3o .    . . . . . |    3 |     3    0 | 35840     *    * |    1     4     4     0    0 |    4     4     6    12     6     0    0 |    6   12     6    4    12    12     4     0    0 |   4   12   12    4    1    4    6    4    1    0    0 |  1   4   6    4    1   1   0
x . .    . . . . x |    4 |     2    2 |     * 26880    * |    0     0     8     4    0 |    0     4     0    12    24     6    0 |    0    6    12    0     8    24    24     4    0 |   0    4   12   12    0    2    8   12    8    1    0 |  0   1   4    6    4   2   0
. . .    . . . o3x |    3 |     0    3 |     *     * 7168 |    0     0     0    10    5 |    0     0     0     0    30    30   10 |    0    0    10    0     0    20    60    30   10 |   0    0    5   20    0    0    5   20   30   10    5 |  0   0   1    5   10   5   1
-------------------+------+------------+------------------+-----------------------------+-----------------------------------------+---------------------------------------------------+-------------------------------------------------------+-----------------------------
x3o3o    . . . . .     4 |     6    0 |     4     0    0 | 8960     *     *     *    * |    4     4     0     0     0     0    0 |    6   12     6    0     0     0     0     0    0 |   4   12   12    4    0    0    0    0    0    0    0 |  1   4   6    4    1   0   0
x3o . *b3o . . . .     4 |     6    0 |     4     0    0 |    * 35840     *     *    * |    1     0     3     3     0     0    0 |    3    3     0    3     6     3     0     0    0 |   3    6    3    0    1    3    3    1    0    0    0 |  1   3   3    1    0   1   0
x3o .    . . . . x     6 |     6    3 |     2     3    0 |    *     * 71680     *    * |    0     1     0     3     3     0    0 |    0    3     3    0     3     6     3     0    0 |   0    3    6    3    0    1    3    3    1    0    0 |  0   1   3    3    1   1   0
x . .    . . . o3x     6 |     3    6 |     0     3    2 |    *     *     * 35840    * |    0     0     0     0     6     3    0 |    0    0     3    0     0     6    12     3    0 |   0    0    3    6    0    0    2    6    6    1    0 |  0   0   1    3    3   2   0
. . .    . . o3o3x     4 |     0    6 |     0     0    4 |    *     *     *     * 8960 |    0     0     0     0     0     6    4 |    0    0     0    0     0     0    12    12    6 |   0    0    0    4    0    0    0    4   12    6    4 |  0   0   0    1    4   4   1
-------------------+------+------------+------------------+-----------------------------+-----------------------------------------+---------------------------------------------------+-------------------------------------------------------+-----------------------------
x3o3o *b3o . . . .     8 |    24    0 |    32     0    0 |    8     8     0     0    0 | 4480     *     *     *     *     *    * |    3    3     0    0     0     0     0     0    0 |   3    6    3    0    0    0    0    0    0    0    0 |  1   3   3    1    0   0   0
x3o3o    . . . . x     8 |    12    4 |     8     6    0 |    2     0     4     0    0 |    * 17920     *     *     *     *    * |    0    3     3    0     0     0     0     0    0 |   0    3    6    3    0    0    0    0    0    0    0 |  0   1   3    3    1   0   0
x3o . *b3o3o . . .     5 |    10    0 |    10     0    0 |    0     5     0     0    0 |    *     * 21504     *     *     *    * |    1    0     0    2     2     0     0     0    0 |   2    2    0    0    1    2    1    0    0    0    0 |  1   2   1    0    0   1   0
x3o . *b3o . . . x     8 |    12    4 |     8     6    0 |    0     2     4     0    0 |    *     *     * 53760     *     *    * |    0    1     0    0     2     2     0     0    0 |   0    2    2    0    0    1    2    1    0    0    0 |  0   1   2    1    0   1   0
x3o .    . . . o3x     9 |     9    9 |     3     9    3 |    0     0     3     3    0 |    *     *     *     * 71680     *    * |    0    0     1    0     0     2     2     0    0 |   0    0    2    2    0    0    1    2    1    0    0 |  0   0   1    2    1   1   0
x . .    . . o3o3x     8 |     4   12 |     0     6    8 |    0     0     0     4    2 |    *     *     *     *     * 26880    * |    0    0     0    0     0     0     4     2    0 |   0    0    0    2    0    0    0    2    4    1    0 |  0   0   0    1    2   2   0
. . .    . o3o3o3x     5 |     0   10 |     0     0   10 |    0     0     0     0    5 |    *     *     *     *     *     * 7168 |    0    0     0    0     0     0     0     3    3 |   0    0    0    0    0    0    0    0    3    3    3 |  0   0   0    0    1   3   1
-------------------+------+------------+------------------+-----------------------------+-----------------------------------------+---------------------------------------------------+-------------------------------------------------------+-----------------------------
x3o3o *b3o3o . . .    16 |    80    0 |   160     0    0 |   40    80     0     0    0 |   10     0    16     0     0     0    0 | 1344    *     *    *     *     *     *     *    * |   2    2    0    0    0    0    0    0    0    0    0 |  1   2   1    0    0   0   0
x3o3o *b3o . . . x    16 |    48    8 |    64    24    0 |   16    16    32     0    0 |    2     8     0     8     0     0    0 |    * 6720     *    *     *     *     *     *    * |   0    2    2    0    0    0    0    0    0    0    0 |  0   1   2    1    0   0   0
x3o3o    . . . o3x    12 |    18   12 |    12    18    4 |    3     0    12     6    0 |    0     3     0     0     4     0    0 |    *    * 17920    *     *     *     *     *    * |   0    0    2    2    0    0    0    0    0    0    0 |  0   0   1    2    1   0   0
x3o . *b3o3o3o . .     6 |    15    0 |    20     0    0 |    0    15     0     0    0 |    0     0     6     0     0     0    0 |    *    *     * 7168     *     *     *     *    * |   1    0    0    0    1    1    0    0    0    0    0 |  1   1   0    0    0   1   0
x3o . *b3o3o . . x    10 |    20    5 |    20    10    0 |    0    10    10     0    0 |    0     0     2     5     0     0    0 |    *    *     *    * 21504     *     *     *    * |   0    1    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     3    12     6    0 |    0     0     0     3     4     0    0 |    *    *     *    *     * 35840     *     *    * |   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     6    12    3 |    0     0     0     0     4     3    0 |    *    *     *    *     *     * 35840     *    * |   0    0    0    1    0    0    0    1    1    0    0 |  0   0   0    1    1   1   0
x . .    . o3o3o3x    10 |     5   20 |     0    10   20 |    0     0     0    10   10 |    0     0     0     0     0     5    2 |    *    *     *    *     *     *     * 10752    * |   0    0    0    0    0    0    0    0    2    1    0 |  0   0   0    0    1   2   0
. . .    o3o3o3o3x     6 |     0   15 |     0     0   20 |    0     0     0     0   15 |    0     0     0     0     0     0    6 |    *    *     *    *     *     *     *     * 3584 |   0    0    0    0    0    0    0    0    0    1    2 |  0   0   0    0    0   2   1
-------------------+------+------------+------------------+-----------------------------+-----------------------------------------+---------------------------------------------------+-------------------------------------------------------+-----------------------------
x3o3o *b3o3o3o . .    32 |   240    0 |   640     0    0 |  160   480     0     0    0 |   60     0   192     0     0     0    0 |   12    0     0   32     0     0     0     0    0 | 224    *    *    *    *    *    *    *    *    *    * |  1   1   0    0    0   0   0
x3o3o *b3o3o . . x    32 |   160   16 |   320    80    0 |   80   160   160     0    0 |   20    40    32    80     0     0    0 |    2   10     0    0    16     0     0     0    0 |   * 1344    *    *    *    *    *    *    *    *    * |  0   1   1    0    0   0   0
x3o3o *b3o . . o3x    24 |    72   24 |    96    72    8 |   24    24    96    24    0 |    3    24     0    24    32     0    0 |    0    3     8    0     0     8     0     0    0 |   *    * 4480    *    *    *    *    *    *    *    * |  0   0   1    1    0   0   0
x3o3o    . . o3o3x    16 |    24   24 |    16    36   16 |    4     0    24    24    4 |    0     6     0     0    16     6    0 |    0    0     4    0     0     0     4     0    0 |   *    *    * 8960    *    *    *    *    *    *    * |  0   0   0    1    1   0   0
x3o . *b3o3o3o3o .     7 |    21    0 |    35     0    0 |    0    35     0     0    0 |    0     0    21     0     0     0    0 |    0    0     0    7     0     0     0     0    0 |   *    *    *    * 1024    *    *    *    *    *    * |  1   0   0    0    0   1   0
x3o . *b3o3o3o . x    12 |    30    6 |    40    15    0 |    0    30    20     0    0 |    0     0    12    15     0     0    0 |    0    0     0    2     6     0     0     0    0 |   *    *    *    *    * 3584    *    *    *    *    * |  0   1   0    0    0   1   0
x3o . *b3o3o . o3x    15 |    30   15 |    30    30    5 |    0    15    30    10    0 |    0     0     3    15    10     0    0 |    0    0     0    0     3     5     0     0    0 |   *    *    *    *    *    * 7168    *    *    *    * |  0   0   1    0    0   1   0
x3o . *b3o . o3o3x    16 |    24   24 |    16    36   16 |    0     4    24    24    4 |    0     0     0     6    16     6    0 |    0    0     0    0     0     4     4     0    0 |   *    *    *    *    *    *    * 8960    *    *    * |  0   0   0    1    0   1   0
x3o .    . o3o3o3x    15 |    15   30 |     5    30   30 |    0     0    10    30   15 |    0     0     0     0    10    15    3 |    0    0     0    0     0     0     5     3    0 |   *    *    *    *    *    *    *    * 7168    *    * |  0   0   0    0    1   1   0
x . .    o3o3o3o3x    12 |     6   30 |     0    15   40 |    0     0     0    20   30 |    0     0     0     0     0    15   12 |    0    0     0    0     0     0     0     6    2 |   *    *    *    *    *    *    *    *    * 1792    * |  0   0   0    0    0   2   0
. o . *b3o3o3o3o3x     7 |     0   21 |     0     0   35 |    0     0     0     0   35 |    0     0     0     0     0     0   21 |    0    0     0    0     0     0     0     0    7 |   *    *    *    *    *    *    *    *    *    * 1024 |  0   0   0    0    0   1   1
-------------------+------+------------+------------------+-----------------------------+-----------------------------------------+---------------------------------------------------+-------------------------------------------------------+-----------------------------
x3o3o *b3o3o3o3o .    64 |   672    0 |  2240     0    0 |  560  2240     0     0    0 |  280     0  1344     0     0     0    0 |   84    0     0  448     0     0     0     0    0 |  14    0    0    0   64    0    0    0    0    0    0 | 16   *   *    *    *   *   *
x3o3o *b3o3o3o . x    64 |   480   32 |  1280   240    0 |  320   960   640     0    0 |  120   160   384   480     0     0    0 |   24   60     0   64   192     0     0     0    0 |   2   12    0    0    0   32    0    0    0    0    0 |  * 112   *    *    *   *   *
x3o3o *b3o3o . o3x    48 |   240   48 |   480   240   16 |  120   240   480    80    0 |   30   120    48   240   160     0    0 |    3   30    40    0    48    80     0     0    0 |   0    3   10    0    0    0   16    0    0    0    0 |  *   * 448    *    *   *   *
x3o3o *b3o . o3o3x    32 |    96   48 |   128   144   32 |   32    32   192    96    8 |    4    48     0    48   128    24    0 |    0    6    32    0     0    32    32     0    0 |   0    0    4    8    0    0    0    8    0    0    0 |  *   *   * 1120    *   *   *
x3o3o    . o3o3o3x    20 |    30   40 |    20    60   40 |    5     0    40    60   20 |    0    10     0     0    40    30    4 |    0    0    10    0     0     0    20     6    0 |   0    0    0    5    0    0    0    0    4    0    0 |  *   *   *    * 1792   *   *
x3o . *b3o3o3o3o3x    56 |   168  168 |   280   420  280 |    0   280   560   560  280 |    0     0   168   420   560   420  168 |    0    0     0   56   168   280   280   168   56 |   0    0    0    0    8   28   56   70   56   28    8 |  *   *   *    *    * 128   *
. o3o *b3o3o3o3o3x     8 |     0   28 |     0     0   56 |    0     0     0     0   70 |    0     0     0     0     0     0   56 |    0    0     0    0     0     0     0     0   28 |   0    0    0    0    0    0    0    0    0    0    8 |  *   *   *    *    *   * 128

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