Acronym brade
Name birectified dekeract,
birectified icosaxennon,
Gosset polytope 07,1,1
Circumradius 2
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), 0, 0)   & all permutations, all changes of sign
Confer
general polytopal classes:
Coxeter-Elte-Gosset polytopes  
External
links
wikipedia

Incidence matrix according to Dynkin symbol

o3o3o3o3o3o3o3x3o4o

o3o3o3o3o3o3o3o3o4o | 11520 |     32 |    112     32 |    224    112     8 |    280    224    28 |    224    280   56 |    112    224   70 |    32   112  56 |    4    32  28 |    4  8
--------------------+-------+--------+---------------+---------------------+---------------------+--------------------+--------------------+-----------------+----------------+--------
. . . . . . . x . . |     2 | 184320 |      7      2 |     21     14     1 |     35     42     7 |     35     70   21 |     21     70   35 |     7    42  35 |    1    14  21 |    2  7
--------------------+-------+--------+---------------+---------------------+---------------------+--------------------+--------------------+-----------------+----------------+--------
. . . . . . o3x . . |     3 |      3 | 430080      * |      6      2     0 |     15     12     1 |     20     30    6 |     15     40   15 |     6    30  20 |    1    12  15 |    2  6
. . . . . . . x3o . |     3 |      3 |      * 122880 |      0      7     1 |      0     21     7 |      0     35   21 |      0     35   35 |     0    21  35 |    0     7  21 |    1  7
--------------------+-------+--------+---------------+---------------------+---------------------+--------------------+--------------------+-----------------+----------------+--------
. . . . . o3o3x . .      4 |      6 |      4      0 | 645120      *     * |      5      2     0 |     10     10    1 |     10     20    5 |     5    20  10 |    1    10  10 |    2  5
. . . . . . o3x3o .      6 |     12 |      4      4 |      * 215040     * |      0      6     1 |      0     15    6 |      0     20   15 |     0    15  20 |    0     6  15 |    1  6
. . . . . . . x3o4o      6 |     12 |      0      8 |      *      * 15360       0      0     7 |      0      0   21 |      0      0   35 |     0     0  35 |    0     0  21 |    0  7
--------------------+-------+--------+---------------+---------------------+---------------------+--------------------+--------------------+-----------------+----------------+--------
. . . . o3o3o3x . .      5 |     10 |     10      0 |      5      0     0 | 645120      *     * |      4      2    0 |      6      8    1 |     4    12   4 |    1     8   6 |    2  4
. . . . . o3o3x3o .     10 |     30 |     20     10 |      5      5     0 |      * 258048     * |      0      5    1 |      0     10    5 |     0    10  10 |    0     5  10 |    1  5
. . . . . . o3x3o4o     24 |     96 |     32     64 |      0     16     8 |      *      * 13440       0      0    6 |      0      0   15 |     0     0  20 |    0     0  15 |    0  6
--------------------+-------+--------+---------------+---------------------+---------------------+--------------------+--------------------+-----------------+----------------+--------
. . . o3o3o3o3x . .      6 |     15 |     20      0 |     15      0     0 |      6      0     0 | 430080      *    * |      3      2    0 |     3     6   1 |    1     6   3 |    2  3
. . . . o3o3o3x3o .     15 |     60 |     60     20 |     30     15     0 |      6      6     0 |      * 215040    * |      0      4    1 |     0     6   4 |    0     4   6 |    1  4
. . . . . o3o3x3o4o     80 |    480 |    320    320 |     80    160    40 |      0     32    10 |      *      * 8064       0      0    5 |     0     0  10 |    0     0  10 |    0  5
--------------------+-------+--------+---------------+---------------------+---------------------+--------------------+--------------------+-----------------+----------------+--------
. . o3o3o3o3o3x . .      7 |     21 |     35      0 |     35      0     0 |     21      0     0 |      7      0    0 | 184320      *    * |     2     2   0 |    1     4   1 |    2  2
. . . o3o3o3o3x3o .     21 |    105 |    140     35 |    105     35     0 |     42     21     0 |      7      7    0 |      * 122880    * |     0     3   1 |    0     3   3 |    1  3
. . . . o3o3o3x3o4o    240 |   1920 |   1920   1280 |    960    960   160 |    192    384    60 |      0     64   12 |      *      * 3360      0     0   4 |    0     0   6 |    0  4
--------------------+-------+--------+---------------+---------------------+---------------------+--------------------+--------------------+-----------------+----------------+--------
. o3o3o3o3o3o3x . .      8 |     28 |     56      0 |     70      0     0 |     56      0     0 |     28      0    0 |      8      0    0 | 46080     *   * |    1     2   0 |    2  1
. . o3o3o3o3o3x3o .     28 |    168 |    280     56 |    280     70     0 |    168     56     0 |     56     28    0 |      8      8    0 |     * 46080   * |    0     2   1 |    1  2
. . . o3o3o3o3x3o4o    672 |   6720 |   8960   4480 |   6720   4480   560 |   2688   2688   280 |    448    896   84 |      0    128   14 |     *     * 960 |    0     0   3 |    0  3
--------------------+-------+--------+---------------+---------------------+---------------------+--------------------+--------------------+-----------------+----------------+--------
o3o3o3o3o3o3o3x . .      9 |     36 |     84      0 |    126      0     0 |    126      0     0 |     84      0    0 |     36      0    0 |     9     0   0 | 5120     *   * |    2  0
. o3o3o3o3o3o3x3o .     36 |    252 |    504     84 |    630    126     0 |    504    126     0 |    252     84    0 |     72     36    0 |     9     9   0 |    * 10240   * |    1  1
. . o3o3o3o3o3x3o4o   1792 |  21504 |  35840  14336 |  35840  17920  1792 |  21504  14336  1120 |   7168   7168  448 |   1024   2048  112 |     0   256  16 |    *     * 180 |    0  2
--------------------+-------+--------+---------------+---------------------+---------------------+--------------------+--------------------+-----------------+----------------+--------
o3o3o3o3o3o3o3x3o .     45 |    360 |    840    120 |   1260    210     0 |   1260    252     0 |    840    210    0 |    360    120    0 |    90    45   0 |   10    10   0 | 1024  *
. o3o3o3o3o3o3x3o4o   4608 |  64512 | 129024  43008 | 161280  64512  5376 | 129024  64512  4032 |  64512  43008 2016 |  18432  18432  672 |  2304  4608 144 |    0   512  18 |    * 20

o3x3o *b3o3o3o3o3o3o3o

o3o3o *b3o3o3o3o3o3o3o | 11520 |     32 |    16    16    112 |     8     56     56    224 |    28    112    112    280 |   56    140    140    224 |   70   112   112    112 |  56    56    56    32 |  28   16   16    4 |  8   2   2
-----------------------+-------+--------+--------------------+----------------------------+----------------------------+---------------------------+-------------------------+-----------------------+--------------------+-----------
. x .    . . . . . . . |     2 | 184320 |     1     1      7 |     1      7      7     21 |     7     21     21     35 |   21     35     35     35 |   35    35    35     21 |  35    21    21     7 |  21    7    7    1 |  7   1   1
-----------------------+-------+--------+--------------------+----------------------------+----------------------------+---------------------------+-------------------------+-----------------------+--------------------+-----------
o3x .    . . . . . . . |     3 |      3 | 61440     *      * |     1      7      0      0 |     7     21      0      0 |   21     35      0      0 |   35    35     0      0 |  35    21     0     0 |  21    7    0    0 |  7   1   0
. x3o    . . . . . . . |     3 |      3 |     * 61440      * |     1      0      7      0 |     7      0     21      0 |   21      0     35      0 |   35     0    35      0 |  35     0    21     0 |  21    0    7    0 |  7   0   1
. x . *b3o . . . . . . |     3 |      3 |     *     * 430080 |     0      1      1      6 |     1      6      6     15 |    6     15     15     20 |   15    20    20     15 |  20    15    15     6 |  15    6    6    1 |  6   1   1
-----------------------+-------+--------+--------------------+----------------------------+----------------------------+---------------------------+-------------------------+-----------------------+--------------------+-----------
o3x3o    . . . . . . .      6 |     12 |     4     4      0 | 15360      *      *      *      7      0      0      0 |   21      0      0      0 |   35     0     0      0 |  35     0     0     0 |  21    0    0    0 |  7   0   0
o3x . *b3o . . . . . .      6 |     12 |     4     0      4 |     * 107520      *      * |     1      6      0      0 |    6     15      0      0 |   15    20     0      0 |  20    15     0     0 |  15    6    0    0 |  6   1   0
. x3o *b3o . . . . . .      6 |     12 |     0     4      4 |     *      * 107520      * |     1      0      6      0 |    6      0     15      0 |   15     0    20      0 |  20     0    15     0 |  15    0    6    0 |  6   0   1
. x . *b3o3o . . . . .      4 |      6 |     0     0      4 |     *      *      * 645120 |     0      1      1      5 |    1      5      5     10 |    5    10    10     10 |  10    10    10     5 |  10    5    5    1 |  5   1   1
-----------------------+-------+--------+--------------------+----------------------------+----------------------------+---------------------------+-------------------------+-----------------------+--------------------+-----------
o3x3o *b3o . . . . . .     24 |     96 |    32    32     32 |     8      8      8      0 | 13440      *      *      *     6      0      0      0 |   15     0     0      0 |  20     0     0     0 |  15    0    0    0 |  6   0   0
o3x . *b3o3o . . . . .     10 |     30 |    10     0     20 |     0      5      0      5 |     * 129024      *      * |    1      5      0      0 |    5    10     0      0 |  10    10     0     0 |  10    5    0    0 |  5   1   0
. x3o *b3o3o . . . . .     10 |     30 |     0    10     20 |     0      0      5      5 |     *      * 129024      * |    1      0      5      0 |    5     0    10      0 |  10     0    10     0 |  10    0    5    0 |  5   0   1
. x . *b3o3o3o . . . .      5 |     10 |     0     0     10 |     0      0      0      5 |     *      *      * 645120 |    0      1      1      4 |    1     4     4      6 |   4     6     6     4 |   6    4    4    1 |  4   1   1
-----------------------+-------+--------+--------------------+----------------------------+----------------------------+---------------------------+-------------------------+-----------------------+--------------------+-----------
o3x3o *b3o3o . . . . .     80 |    480 |   160   160    320 |    40     80     80     80 |    10     16     16      0 | 8064      *      *      *     5     0     0      0 |  10     0     0     0 |  10    0    0    0 |  5   0   0
o3x . *b3o3o3o . . . .     15 |     60 |    20     0     60 |     0     15      0     30 |     0      6      0      6 |    * 107520      *      * |    1     4     0      0 |   4     6     0     0 |   6    4    0    0 |  4   1   0
. x3o *b3o3o3o . . . .     15 |     60 |     0    20     60 |     0      0     15     30 |     0      0      6      6 |    *      * 107520      * |    1     0     4      0 |   4     0     6     0 |   6    0    4    0 |  4   0   1
. x . *b3o3o3o3o . . .      6 |     15 |     0     0     20 |     0      0      0     15 |     0      0      0      6 |    *      *      * 430080 |    0     1     1      3 |   1     3     3     3 |   3    3    3    1 |  3   1   1
-----------------------+-------+--------+--------------------+----------------------------+----------------------------+---------------------------+-------------------------+-----------------------+--------------------+-----------
o3x3o *b3o3o3o . . . .    240 |   1920 |   640   640   1920 |   160    480    480    960 |    60    192    192    192 |   12     32     32      0 | 3360     *     *      *    4     0     0     0 |   6    0    0    0 |  4   0   0
o3x . *b3o3o3o3o . . .     21 |    105 |    35     0    140 |     0     35      0    105 |     0     21      0     42 |    0      7      0      7 |    * 61440     *      * |   1     3     0     0 |   3    3    0    0 |  3   1   0
. x3o *b3o3o3o3o . . .     21 |    105 |     0    35    140 |     0      0     35    105 |     0      0     21     42 |    0      0      7      7 |    *     * 61440      * |   1     0     3     0 |   3    0    3    0 |  3   0   1
. x . *b3o3o3o3o3o . .      7 |     21 |     0     0     35 |     0      0      0     35 |     0      0      0     21 |    0      0      0      7 |    *     *     * 184320 |   0     1     1     2 |   1    2    2    1 |  2   1   1
-----------------------+-------+--------+--------------------+----------------------------+----------------------------+---------------------------+-------------------------+-----------------------+--------------------+-----------
o3x3o *b3o3o3o3o . . .    672 |   6720 |  2240  2240   8960 |   560   2240   2240   6720 |   280   1344   1344   2688 |   84    448    448    448 |   14    64    64      0 | 960     *     *     * |   3    0    0    0 |  3   0   0
o3x . *b3o3o3o3o3o . .     28 |    168 |    56     0    280 |     0     70      0    280 |     0     56      0    168 |    0     28      0     56 |    0     8     0      8 |   * 23040     *     * |   1    2    0    0 |  2   1   0
. x3o *b3o3o3o3o3o . .     28 |    168 |     0    56    280 |     0      0     70    280 |     0      0     56    168 |    0      0     28     56 |    0     0     8      8 |   *     * 23040     * |   1    0    2    0 |  2   0   1
. x . *b3o3o3o3o3o3o .      8 |     28 |     0     0     56 |     0      0      0     70 |     0      0      0     56 |    0      0      0     28 |    0     0     0      8 |   *     *     * 46080 |   0    1    1    1 |  1   1   1
-----------------------+-------+--------+--------------------+----------------------------+----------------------------+---------------------------+-------------------------+-----------------------+--------------------+-----------
o3x3o *b3o3o3o3o3o . .   1792 |  21504 |  7168  7168  35840 |  1792   8960   8960  35840 |  1120   7168   7168  21504 |  448   3584   3584   7168 |  112  1024  1024   1024 |  16   128   128     0 | 180    *    *    * |  2   0   0
o3x . *b3o3o3o3o3o3o .     36 |    252 |    84     0    504 |     0    126      0    630 |     0    126      0    504 |    0     84      0    252 |    0    36     0     72 |   0     9     0     9 |   * 5120    *    * |  1   1   0
. x3o *b3o3o3o3o3o3o .     36 |    252 |     0    84    504 |     0      0    126    630 |     0      0    126    504 |    0      0     84    252 |    0     0    36     72 |   0     0     9     9 |   *    * 5120    * |  1   0   1
. x . *b3o3o3o3o3o3o3o      9 |     36 |     0     0     84 |     0      0      0    126 |     0      0      0    126 |    0      0      0     84 |    0     0     0     36 |   0     0     0     9 |   *    *    * 5120 |  0   1   1
-----------------------+-------+--------+--------------------+----------------------------+----------------------------+---------------------------+-------------------------+-----------------------+--------------------+-----------
o3x3o *b3o3o3o3o3o3o .   4608 |  64512 | 21504 21504 129024 |  5376  32256  32256 161280 |  4032  32256  32256 129024 | 2016  21504  21504  64512 |  672  9216  9216  18432 | 144  2304  2304  2304 |  18  256  256    0 | 20   *   *
o3x . *b3o3o3o3o3o3o3o     45 |    360 |   120     0    840 |     0    210      0   1260 |     0    252      0   1260 |    0    210      0    840 |    0   120     0    360 |   0    45     0    90 |   0   10    0   10 |  * 512   *
. x3o *b3o3o3o3o3o3o3o     45 |    360 |     0   120    840 |     0      0    210   1260 |     0      0    252   1260 |    0      0    210    840 |    0     0   120    360 |   0     0    45    90 |   0    0   10   10 |  *   * 512

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