Acronym brav Name birectified pentacosidodecayotton Circumradius sqrt(3/2) = 1.224745 Coordinates (1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0, 0, 0, 0, 0)   & all permutations, all changes of sign

Incidence matrix according to Dynkin symbol

```o3o3x3o3o3o3o3o4o

. . . . . . . . . | 672 ♦    36 |   36   180 |   12   180   480 |   60   480   720 |  160   720   576 |  240   576   192 |  192  192   3 |  64  3
------------------+-----+-------+------------+------------------+------------------+------------------+------------------+---------------+-------
. . x . . . . . . |   2 | 12096 |    2    10 |    1    20    40 |   10    80    80 |   40   160    80 |   80   160    32 |   80   64   1 |  32  2
------------------+-----+-------+------------+------------------+------------------+------------------+------------------+---------------+-------
. o3x . . . . . . |   3 |     3 | 8064     * |    1    10     0 |   10    40     0 |   40    80     0 |   80    80     0 |   80   32   0 |  32  1
. . x3o . . . . . |   3 |     3 |    * 40320 |    0     2     8 |    1    16    24 |    8    48    32 |   24    64    16 |   16   16   1 |  16  2
------------------+-----+-------+------------+------------------+------------------+------------------+------------------+---------------+-------
o3o3x . . . . . . ♦   4 |     6 |    4     0 | 2016     *     * ♦   10     0     0 |   40     0     0 |   80     0     0 |   80    0   0 |  32  0
. o3x3o . . . . . ♦   6 |    12 |    4     4 |    * 20160     * |    1     8     0 |    8    24     0 |   24    32     0 |   32   16   0 |  16  1
. . x3o3o . . . . ♦   4 |     6 |    0     4 |    *     * 80640 |    0     2     6 |    1    12    12 |    6    24     8 |   12   16   1 |   8  2
------------------+-----+-------+------------+------------------+------------------+------------------+------------------+---------------+-------
o3o3x3o . . . . . ♦  10 |    30 |   20    10 |    5     5     0 | 4032     *     * ♦    8     0     0 |   24     0     0 |   32    0   0 |  16  0
. o3x3o3o . . . . ♦  10 |    30 |   10    20 |    0     5     5 |    * 32256     * |    1     6     0 |    6    12     0 |   12    8   0 |   8  1
. . x3o3o3o . . . ♦   5 |    10 |    0    10 |    0     0     5 |    *     * 96768 |    0     2     4 |    1     8     4 |    4    8   1 |   4  2
------------------+-----+-------+------------+------------------+------------------+------------------+------------------+---------------+-------
o3o3x3o3o . . . . ♦  20 |    90 |   60    60 |   15    30    15 |    6     6     0 | 5376     *     * ♦    6     0     0 |   12    0   0 |   8  0
. o3x3o3o3o . . . ♦  15 |    60 |   20    60 |    0    15    30 |    0     6     6 |    * 32256     * |    1     4     0 |    4    4   0 |   4  1
. . x3o3o3o3o . . ♦   6 |    15 |    0    20 |    0     0    15 |    0     0     6 |    *     * 64512 |    0     2     2 |    1    4   1 |   2  2
------------------+-----+-------+------------+------------------+------------------+------------------+------------------+---------------+-------
o3o3x3o3o3o . . . ♦  35 |   210 |  140   210 |   35   105   105 |   21    42    21 |    7     7     0 | 4608     *     * |    4    0   0 |   4  0
. o3x3o3o3o3o . . ♦  21 |   105 |   35   140 |    0    35   105 |    0    21    42 |    0     7     7 |    * 18432     * |    1    2   0 |   2  1
. . x3o3o3o3o3o . ♦   7 |    21 |    0    35 |    0     0    35 |    0     0    21 |    0     0     7 |    *     * 18432 |    0    2   1 |   1  2
------------------+-----+-------+------------+------------------+------------------+------------------+------------------+---------------+-------
o3o3x3o3o3o3o . . ♦  56 |   420 |  280   560 |   70   280   420 |   56   168   168 |   28    56    28 |    8     8     0 | 2304    *   * |   2  0
. o3x3o3o3o3o3o . ♦  28 |   168 |   56   280 |    0    70   280 |    0    56   168 |    0    28    56 |    0     8     8 |    * 4608   * |   1  1
. . x3o3o3o3o3o4o ♦  14 |    84 |    0   280 |    0     0   560 |    0     0   672 |    0     0   448 |    0     0   128 |    *    * 144 |   0  2
------------------+-----+-------+------------+------------------+------------------+------------------+------------------+---------------+-------
o3o3x3o3o3o3o3o . ♦  84 |   756 |  504  1260 |  126   630  1260 |  126   505   756 |   84   252   252 |   36    72    36 |    9    9   0 | 512  *
. o3x3o3o3o3o3o4o ♦ 112 |  1344 |  448  4480 |    0  1120  8960 |    0  1792 10752 |    0  1792  7168 |    0  1024  2048 |    0  256  16 |   * 18
```

```o3o3o *b3o3o3o3x3o3o

. . .    . . . . . . | 672 ♦    36 |   180   36 |   480   180   12 |   720   480   60 |   576   720  160 |   96   96   576  240 |   3   96   96  192 |  3  32  32
---------------------+-----+-------+------------+------------------+------------------+------------------+----------------------+--------------------+-----------
. . .    . . . x . . |   2 | 12096 |    10    2 |    40    20    1 |    80    80   10 |    80   160   40 |   16   16   160   80 |   1   32   32   80 |  2  16  16
---------------------+-----+-------+------------+------------------+------------------+------------------+----------------------+--------------------+-----------
. . .    . . o3x . . |   3 |     3 | 40320    * |     8     2    0 |    24    16    1 |    32    48    8 |    8    8    64   24 |   1    8    8   16 |  2   8   8
. . .    . . . x3o . |   3 |     3 |     * 8064 |     0    10    1 |     0    40   10 |     0    80   40 |    0    0    80   80 |   0   16   16   80 |  1  16  16
---------------------+-----+-------+------------+------------------+------------------+------------------+----------------------+--------------------+-----------
. . .    . o3o3x . . ♦   4 |     6 |     4    0 | 80640     *    * |     6     2    0 |    12    12    1 |    4    4    24    6 |   1    8    8   12 |  2   4   4
. . .    . . o3x3o . ♦   6 |    12 |     4    4 |     * 20160    * |     0     8    1 |     0    24    8 |    0    0    32   24 |   0    8    8   32 |  1   8   8
. . .    . . . x3o3o ♦   4 |     6 |     0    4 |     *     * 2016 ♦     0     0   10 |     0     0   40 |    0    0     0   80 |   0    0    0   80 |  0  16  16
---------------------+-----+-------+------------+------------------+------------------+------------------+----------------------+--------------------+-----------
. . .    o3o3o3x . . ♦   5 |    10 |    10    0 |     5     0    0 | 96768     *    * |     4     2    0 |    2    2     8    1 |   4    4    4    1 |  2   2   2
. . .    . o3o3x3o . ♦  10 |    30 |    20   10 |     5     5    0 |     * 32256    * |     0     6    1 |    0    0    12    6 |   0    4    4   12 |  1   4   4
. . .    . . o3x3o3o ♦  10 |    30 |    10   20 |     0     5    5 |     *     * 4032 ♦     0     0    8 |    0    0     0   24 |   0    0    0   32 |  0   8   8
---------------------+-----+-------+------------+------------------+------------------+------------------+----------------------+--------------------+-----------
. o . *b3o3o3o3x . . ♦   6 |    15 |    20    0 |    15     0    0 |     6     0    0 | 64512     *    * |    1    1     2    0 |   1    2    2    1 |  2   1   1
. . .    o3o3o3x3o . ♦  15 |    60 |    60   20 |    30    15    0 |     6     6    0 |     * 32256    * |    0    0     4    1 |   0    2    2    4 |  1   2   2
. . .    . o3o3x3o3o ♦  20 |    90 |    60   60 |    15    30   15 |     0     6    6 |     *     * 5376 ♦    0    0     0    6 |   0    0    0   12 |  0   4   4
---------------------+-----+-------+------------+------------------+------------------+------------------+----------------------+--------------------+-----------
o3o . *b3o3o3o3x . . ♦   7 |    21 |    35    0 |    35     0    0 |    21     0    0 |     7     0    0 | 9216    *     *    * |   1    2    0    0 |  2   1   0
. o3o *b3o3o3o3x . . ♦   7 |    21 |    35    0 |    35     0    0 |    21     0    0 |     7     0    0 |    * 9216     *    * |   1    0    2    0 |  2   0   1
. o . *b3o3o3o3x3o . ♦  21 |   105 |   140   35 |   105    35    0 |    42    21    0 |     7     7    0 |    *    * 18432    * |   0    1    1    1 |  1   1   1
. . .    o3o3o3x3o3o ♦  35 |   210 |   210  140 |   105   105   35 |    21    42   21 |     0     7    7 |    *    *     * 4608 |   0    0    0    4 |  0   2   2
---------------------+-----+-------+------------+------------------+------------------+------------------+----------------------+--------------------+-----------
o3o3o *b3o3o3o3x . . ♦  14 |    84 |   280    0 |   560     0    0 |   672     0    0 |   448     0    0 |   64   64     0    0 | 144    *    *    * |  2   0   0
o3o . *b3o3o3o3x3o . ♦  28 |   168 |   280   56 |   280    70    0 |   168    56    0 |    56    28    0 |    8    0     8    0 |   * 2304    *    * |  1   1   0
. o3o *b3o3o3o3x3o . ♦  28 |   168 |   280   56 |   280    70    0 |   168    56    0 |    56    28    0 |    0    8     8    0 |   *    * 2304    * |  1   0   1
. o . *b3o3o3o3x3o3o ♦  56 |   420 |   560  280 |   420   280   70 |   168   168   56 |    28    56   28 |    0    0     8    8 |   *    *    * 2304 |  0   1   1
---------------------+-----+-------+------------+------------------+------------------+------------------+----------------------+--------------------+-----------
o3o3o *b3o3o3o3x3o . ♦ 112 |  1344 |  4480  448 |  8960  1120    0 | 10752  1792    0 |  7168  1792    0 | 1024 1024  1024    0 |  16  128  128    0 | 18   *   *
o3o . *b3o3o3o3x3o3o ♦  84 |   756 |  1260  504 |  1260   630  126 |   756   505  126 |   252   252   84 |   36    0    72   36 |   0    9    0    9 |  * 256   *
. o3o *b3o3o3o3x3o3o ♦  84 |   756 |  1260  504 |  1260   630  126 |   756   505  126 |   252   252   84 |    0   36    72   36 |   0    0    9    9 |  *   * 256
```