Acronym srek
Name small rhombated diacosipentacontahexazetton,
cantellated octacross
Circumradius sqrt(3) = 1.732051
Coordinates (sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0, 0, 0, 0)   & all permutations, all changes of sign

Incidence matrix according to Dynkin symbol

x3o3x3o3o3o3o4o

. . . . . . . . | 1344 |    2    20 |   1   20   10    80 |   12    80   40   160 |   40   160    80   160 |   80   160   80    64 |   80   64   32   2 |  32   2  1
----------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+-----------
x . . . . . . . |    2 | 1344     * |   1   10    0     0 |   10    40    0     0 |   40    80     0     0 |   80    80    0     0 |   80   32    0   0 |  32   1  0
. . x . . . . . |    2 |    * 13440 |   0    1    1     8 |    1     8    8    24 |    8    24    24    32 |   24    32   32    16 |   32   16   16   1 |  16   1  1
----------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+-----------
x3o . . . . . . |    3 |    3     0 | 448    *    *     *    10     0    0     0 |   40     0     0     0 |   80     0    0     0 |   80    0    0   0 |  32   0  0
x . x . . . . . |    4 |    2     2 |   * 6720    *     * |    1     8    0     0 |    8    24     0     0 |   24    32    0     0 |   32   16    0   0 |  16   1  0
. o3x . . . . . |    3 |    0     3 |   *    * 4480     * |    1     0    8     0 |    8     0    24     0 |   24     0   32     0 |   32    0   16   0 |  16   0  1
. . x3o . . . . |    3 |    0     3 |   *    *    * 35840 |    0     1    1     6 |    1     6     6    12 |    6    12   12     8 |   12    8    8   1 |   8   1  1
----------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+-----------
x3o3x . . . . .    12 |   12    12 |   4    6    4     0 | 1120     *    *     *     8     0     0     0 |   24     0    0     0 |   32    0    0   0 |  16   0  0
x . x3o . . . .     6 |    3     6 |   0    3    0     2 |    * 17920    *     * |    1     6     0     0 |    6    12    0     0 |   12    8    0   0 |   8   1  0
. o3x3o . . . .     6 |    0    12 |   0    0    4     4 |    *     * 8960     * |    1     0     6     0 |    6     0   12     0 |   12    0    8   0 |   8   0  1
. . x3o3o . . .     4 |    0     6 |   0    0    0     4 |    *     *    * 53760 |    0     1     1     4 |    1     4    4     4 |    4    4    4   1 |   4   1  1
----------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+-----------
x3o3x3o . . . .    30 |   30    60 |  10   30   20    20 |    5    10    5     0 | 1792     *     *     *     6     0    0     0 |   12    0    0   0 |   8   0  0
x . x3o3o . . .     8 |    4    12 |   0    6    0     8 |    0     4    0     2 |    * 26880     *     * |    1     4    0     0 |    4    4    0   0 |   4   1  0
. o3x3o3o . . .    10 |    0    30 |   0    0   10    20 |    0     0    5     5 |    *     * 10752     * |    1     0    4     0 |    4    0    4   0 |   4   0  1
. . x3o3o3o . .     5 |    0    10 |   0    0    0    10 |    0     0    0     5 |    *     *     * 43008 |    0     1    1     2 |    1    2    2   1 |   2   1  1
----------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+-----------
x3o3x3o3o . . .    60 |   60   180 |  20   90   60   120 |   15    60   30    30 |    6    15     6     0 | 1792     *    *     * |    4    0    0   0 |   4   0  0
x . x3o3o3o . .    10 |    5    20 |   0   10    0    20 |    0    10    0    10 |    0     5     0     2 |    * 21504    *     * |    1    2    0   0 |   2   1  0
. o3x3o3o3o . .    15 |    0    60 |   0    0   20    60 |    0     0   15    30 |    0     0     6     6 |    *     * 7168     * |    1    0    2   0 |   2   0  1
. . x3o3o3o3o .     6 |    0    15 |   0    0    0    20 |    0     0    0    15 |    0     0     0     6 |    *     *    * 14336 |    0    1    1   1 |   1   1  1
----------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+-----------
x3o3x3o3o3o . .   105 |  105   420 |  35  210  140   420 |   35   210  105   210 |   21   105    42    42 |    7    21    7     0 | 1024    *    *   * |   2   0  0
x . x3o3o3o3o .    12 |    6    30 |   0   15    0    40 |    0    20    0    30 |    0    15     0    12 |    0     6    0     2 |    * 7168    *   * |   1   1  0
. o3x3o3o3o3o .    21 |    0   105 |   0    0   35   140 |    0     0   35   105 |    0     0    21    42 |    0     0    7     7 |    *    * 2048   * |   1   0  1
. . x3o3o3o3o4o    12 |    0    60 |   0    0    0   160 |    0     0    0   240 |    0     0     0   192 |    0     0    0    64 |    *    *    * 224 |   0   1  1
----------------+------+------------+---------------------+-----------------------+------------------------+-----------------------+--------------------+-----------
x3o3x3o3o3o3o .   168 |  168   840 |  56  420  280  1120 |   70   560  280   840 |   56   420   168   336 |   28   168   56    56 |    8   28    8   0 | 256   *  *
x . x3o3o3o3o4o    24 |   12   120 |   0   60    0   320 |    0   160    0   480 |    0   240     0   384 |    0   192    0   128 |    0   64    0   2 |   * 112  *
. o3x3o3o3o3o4o    84 |    0   840 |   0    0  280  2240 |    0     0  560  3360 |    0     0   672  2688 |    0     0  448   896 |    0    0  128  14 |   *   * 16

o3o3o *b3o3o3x3o3x

. . .    . . . . . | 1344 |    20    2 |    80   10   20   1 |   160   40    80   12 |   160    80   160   40 |   32   32   80   160   80 |   2   16   32   16   32   80 |  1   2  16  16
-------------------+------+------------+---------------------+-----------------------+------------------------+---------------------------+------------------------------+---------------
. . .    . . x . . |    2 | 13440    * |     8    1    1   0 |    24    8     8    1 |    32    24    24    8 |    8    8   32    32   24 |   1    8    8    8    8   32 |  1   1   8   8
. . .    . . . . x |    2 |     * 1344 |     0    0   10   1 |     0    0    40   10 |     0     0    80   40 |    0    0    0    80   80 |   0    0   16    0   16   80 |  0   1  16  16
-------------------+------+------------+---------------------+-----------------------+------------------------+---------------------------+------------------------------+---------------
. . .    . o3x . . |    3 |     3    0 | 35840    *    *   * |     6    1     1    0 |    12     6     6    1 |    4    4   12    12    6 |   1    4    4    4    4   12 |  1   1   4   4
. . .    . . x3o . |    3 |     3    0 |     * 4480    *   * |     0    8     0    1 |     0    24     0    8 |    0    0   32     0   24 |   0    8    0    8    0   32 |  1   0   8   8
. . .    . . x . x |    4 |     2    2 |     *    * 6720   * |     0    0     8    1 |     0     0    24    8 |    0    0    0    32   24 |   0    0    8    0    8   32 |  0   1   8   8
. . .    . . . o3x |    3 |     0    3 |     *    *    * 448      0    0     0   10 |     0     0     0   40 |    0    0    0     0   80 |   0    0    0    0    0   80 |  0   0  16  16
-------------------+------+------------+---------------------+-----------------------+------------------------+---------------------------+------------------------------+---------------
. . .    o3o3x . .     4 |     6    0 |     4    0    0   0 | 53760    *     *    * |     4     1     1    0 |    2    2    4     4    1 |   1    2    2    2    2    4 |  1   1   2   2
. . .    . o3x3o .     6 |    12    0 |     4    4    0   0 |     * 8960     *    * |     0     6     0    1 |    0    0   12     0    6 |   0    4    0    4    0   12 |  1   0   4   4
. . .    . o3x . x     6 |     6    3 |     2    0    3   0 |     *    * 17920    * |     0     0     6    1 |    0    0    0    12    6 |   0    0    4    0    4   12 |  0   1   4   4
. . .    . . x3o3x    12 |    12   12 |     0    4    6   4 |     *    *     * 1120      0     0     0    8 |    0    0    0     0   24 |   0    0    0    0    0   32 |  0   0   8   8
-------------------+------+------------+---------------------+-----------------------+------------------------+---------------------------+------------------------------+---------------
. o . *b3o3o3x . .     5 |    10    0 |    10    0    0   0 |     5    0     0    0 | 43008     *     *    * |    1    1    1     1    0 |   1    1    1    1    1    1 |  1   1   1   1
. . .    o3o3x3o .    10 |    30    0 |    20   10    0   0 |     5    5     0    0 |     * 10752     *    * |    0    0    4     0    1 |   0    2    0    2    0    4 |  1   0   2   2
. . .    o3o3x . x     8 |    12    4 |     8    0    6   0 |     2    0     4    0 |     *     * 26880    * |    0    0    0     4    1 |   0    0    2    0    2    4 |  0   1   2   2
. . .    . o3x3o3x    30 |    60   30 |    20   20   30  10 |     0    5    10    5 |     *     *     * 1792     0    0    0     0    6 |   0    0    0    0    0   12 |  0   0   4   4
-------------------+------+------------+---------------------+-----------------------+------------------------+---------------------------+------------------------------+---------------
o3o . *b3o3o3x . .     6 |    15    0 |    20    0    0   0 |    15    0     0    0 |     6     0     0    0 | 7168    *    *     *    * |   1    1    1    0    0    0 |  1   1   1   0
. o3o *b3o3o3x . .     6 |    15    0 |    20    0    0   0 |    15    0     0    0 |     6     0     0    0 |    * 7168    *     *    * |   1    0    0    1    1    0 |  1   1   0   1
. o . *b3o3o3x3o .    15 |    60    0 |    60   20    0   0 |    30   15     0    0 |     6     6     0    0 |    *    * 7168     *    * |   0    1    0    1    0    1 |  1   0   1   1
. o . *b3o3o3x . x    10 |    20    5 |    20    0   10   0 |    10    0    10    0 |     2     0     5    0 |    *    *    * 21504    * |   0    0    1    0    1    1 |  0   1   1   1
. . .    o3o3x3o3x    60 |   180   60 |   120   60   90  20 |    30   30    60   15 |     0     6    15    6 |    *    *    *     * 1792 |   0    0    0    0    0    4 |  0   0   2   2
-------------------+------+------------+---------------------+-----------------------+------------------------+---------------------------+------------------------------+---------------
o3o3o *b3o3o3x . .    12 |    60    0 |   160    0    0   0 |   240    0     0    0 |   192     0     0    0 |   32   32    0     0    0 | 224    *    *    *    *    * |  1   1   0   0
o3o . *b3o3o3x3o .    21 |   105    0 |   140   35    0   0 |   105   35     0    0 |    42    21     0    0 |    7    0    7     0    0 |   * 1024    *    *    *    * |  1   0   1   0
o3o . *b3o3o3x . x    12 |    30    6 |    40    0   15   0 |    30    0    20    0 |    12     0    15    0 |    2    0    0     6    0 |   *    * 3584    *    *    * |  0   1   1   0
. o3o *b3o3o3x3o .    21 |   105    0 |   140   35    0   0 |   105   35     0    0 |    42    21     0    0 |    0    7    7     0    0 |   *    *    * 1024    *    * |  1   0   0   1
. o3o *b3o3o3x . x    12 |    30    6 |    40    0   15   0 |    30    0    20    0 |    12     0    15    0 |    0    2    0     6    0 |   *    *    *    * 3584    * |  0   1   0   1
. o . *b3o3o3x3o3x   105 |   420  105 |   420  140  210  35 |   210  105   210   35 |    42    42   105   21 |    0    0    7    21    7 |   *    *    *    *    * 1024 |  0   0   1   1
-------------------+------+------------+---------------------+-----------------------+------------------------+---------------------------+------------------------------+---------------
o3o3o *b3o3o3x3o .    84 |   840    0 |  2240  280    0   0 |  3360  560     0    0 |  2688   672     0    0 |  448  448  448     0    0 |  14   64    0   64    0    0 | 16   *   *   *
o3o3o *b3o3o3x . x    24 |   120   12 |   320    0   60   0 |   480    0   160    0 |   384     0   240    0 |   64   64    0   192    0 |   2    0   32    0   32    0 |  * 112   *   *
o3o . *b3o3o3x3o3x   168 |   840  168 |  1120  280  420  56 |   840  280   560   70 |   336   168   420   56 |   56    0   56   168   28 |   0    8   28    0    0    8 |  *   * 128   *
. o3o *b3o3o3x3o3x   168 |   840  168 |  1120  280  420  56 |   840  280   560   70 |   336   168   420   56 |    0   56   56   168   28 |   0    0    0    8   28    8 |  *   *   * 128

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