Acronym rade
Name rectified dekeract,
rectified icosaxennon
Circumradius 3/sqrt(2) = 2.121320
Coordinates (1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0)   & all permutations, all changes of sign
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Incidence matrix according to Dynkin symbol

o3o3o3o3o3o3o3o3x4o

. . . . . . . . . . | 5120 |    18 |     72     9 |    168    36 |    252    84 |    252  126 |    168  126 |    72  84 |    18  36 |    2  9
--------------------+------+-------+--------------+--------------+--------------+-------------+-------------+-----------+-----------+--------
. . . . . . . . x . |    2 | 46080 |      8     1 |     28     8 |     56    28 |     70   56 |     56   70 |    28  56 |     8  28 |    1  8
--------------------+------+-------+--------------+--------------+--------------+-------------+-------------+-----------+-----------+--------
. . . . . . . o3x . |    3 |     3 | 122880     * |      7     1 |     21     7 |     35   21 |     35   35 |    21  35 |     7  21 |    1  7
. . . . . . . . x4o |    4 |     4 |      * 11520       0     8 |      0    28 |      0   56 |      0   70 |     0  56 |     0  28 |    0  8
--------------------+------+-------+--------------+--------------+--------------+-------------+-------------+-----------+-----------+--------
. . . . . . o3o3x .     4 |     6 |      4     0 | 215040     * |      6     1 |     15    6 |     20   15 |    15  20 |     6  15 |    1  6
. . . . . . . o3x4o    12 |    24 |      8     6 |      * 15360       0     7 |      0   21 |      0   35 |     0  35 |     0  21 |    0  7
--------------------+------+-------+--------------+--------------+--------------+-------------+-------------+-----------+-----------+--------
. . . . . o3o3o3x .     5 |    10 |     10     0 |      5     0 | 258048     * |      5    1 |     10    5 |    10  10 |     5  10 |    1  5
. . . . . . o3o3x4o    32 |    96 |     64    24 |     16     8 |      * 13440       0    6 |      0   15 |     0  20 |     0  15 |    0  6
--------------------+------+-------+--------------+--------------+--------------+-------------+-------------+-----------+-----------+--------
. . . . o3o3o3o3x .     6 |    15 |     20     0 |     15     0 |      6     0 | 215040    * |      4    1 |     6   4 |     4   6 |    1  4
. . . . . o3o3o3x4o    80 |   320 |    320    80 |    160    40 |     32    10 |      * 8064       0    5 |     0  10 |     0  10 |    0  5
--------------------+------+-------+--------------+--------------+--------------+-------------+-------------+-----------+-----------+--------
. . . o3o3o3o3o3x .     7 |    21 |     35     0 |     35     0 |     21     0 |      7    0 | 122880    * |     3   1 |     3   3 |    1  3
. . . . o3o3o3o3x4o   192 |   960 |   1280   240 |    960   160 |    384    60 |     64   12 |      * 3360      0   4 |     0   6 |    0  4
--------------------+------+-------+--------------+--------------+--------------+-------------+-------------+-----------+-----------+--------
. . o3o3o3o3o3o3x .     8 |    28 |     56     0 |     70     0 |     56     0 |     28    0 |      8    0 | 46080   * |     2   1 |    1  2
. . . o3o3o3o3o3x4o   448 |  2688 |   4480   672 |   4480   560 |   2688   280 |    896   84 |    128   14 |     * 960 |     0   3 |    0  3
--------------------+------+-------+--------------+--------------+--------------+-------------+-------------+-----------+-----------+--------
. o3o3o3o3o3o3o3x .     9 |    36 |     84     0 |    126     0 |    126     0 |     84    0 |     36    0 |     9   0 | 10240   * |    1  1
. . o3o3o3o3o3o3x4o  1024 |  7168 |  14336  1792 |  17920  1792 |  14336  1120 |   7168  448 |   2048  112 |   256  16 |     * 180 |    0  2
--------------------+------+-------+--------------+--------------+--------------+-------------+-------------+-----------+-----------+--------
o3o3o3o3o3o3o3o3x .    10 |    45 |    120     0 |    210     0 |    252     0 |    210    0 |    120    0 |    45   0 |    10   0 | 1024  *
. o3o3o3o3o3o3o3x4o  2304 | 18432 |  43008  4608 |  64512  5376 |  64512  4032 |  43008 2016 |  18432  672 |  4608 144 |   512  18 |    * 20

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