Acronym barn
Name birectified enneract,
birectified octadecayotton,
Gosset polytope 06,1,1
Circumradius sqrt(7/2) = 1.870829
Coordinates (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  

Incidence matrix according to Dynkin symbol

o3o3o3o3o3o3x3o4o

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

o3x3o *b3o3o3o3o3o3o

. . .    . . . . . . | 4608     28 |    14    14     84 |    7    42    42    140 |   21    70    70    140 |   35    70    70    84 |  35   42   42    28 |  21   14   14    4 |  7   2   2
---------------------+------+-------+--------------------+-------------------------+-------------------------+------------------------+---------------------+--------------------+-----------
. x .    . . . . . . |    2 | 64512 |     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
---------------------+------+-------+--------------------+-------------------------+-------------------------+------------------------+---------------------+--------------------+-----------
o3x .    . . . . . . |    3 |     3 | 21504     *      * |    1     6     0      0 |    6    15     0      0 |   15    20     0     0 |  20   15    0     0 |  15    6    0    0 |  6   1   0
. x3o    . . . . . . |    3 |     3 |     * 21504      * |    1     0     6      0 |    6     0    15      0 |   15     0    20     0 |  20    0   15     0 |  15    0    6    0 |  6   0   1
. x . *b3o . . . . . |    3 |     3 |     *     * 129024 |    0     1     1      5 |    1     5     5     10 |    5    10    10    10 |  10   10   10     5 |  10    5    5    1 |  5   1   1
---------------------+------+-------+--------------------+-------------------------+-------------------------+------------------------+---------------------+--------------------+-----------
o3x3o    . . . . . .     6 |    12 |     4     4      0 | 5376     *     *      *     6     0     0      0 |   15     0     0     0 |  20    0    0     0 |  15    0    0    0 |  6   0   0
o3x . *b3o . . . . .     6 |    12 |     4     0      4 |    * 32256     *      * |    1     5     0      0 |    5    10     0     0 |  10   10    0     0 |  10    5    0    0 |  5   1   0
. x3o *b3o . . . . .     6 |    12 |     0     4      4 |    *     * 32256      * |    1     0     5      0 |    5     0    10     0 |  10    0   10     0 |  10    0    5    0 |  5   0   1
. x . *b3o3o . . . .     4 |     6 |     0     0      4 |    *     *     * 161280 |    0     1     1      4 |    1     4     4     6 |   4    6    6     4 |   6    4    4    1 |  4   1   1
---------------------+------+-------+--------------------+-------------------------+-------------------------+------------------------+---------------------+--------------------+-----------
o3x3o *b3o . . . . .    24 |    96 |    32    32     32 |    8     8     8      0 | 4032     *     *      *     5     0     0     0 |  10    0    0     0 |  10    0    0    0 |  5   0   0
o3x . *b3o3o . . . .    10 |    30 |    10     0     20 |    0     5     0      5 |    * 32256     *      * |    1     4     0     0 |   4    6    0     0 |   6    4    0    0 |  4   1   0
. x3o *b3o3o . . . .    10 |    30 |     0    10     20 |    0     0     5      5 |    *     * 32256      * |    1     0     4     0 |   4    0    6     0 |   6    0    4    0 |  4   0   1
. x . *b3o3o3o . . .     5 |    10 |     0     0     10 |    0     0     0      5 |    *     *     * 129024 |    0     1     1     3 |   1    3    3     3 |   3    3    3    1 |  3   1   1
---------------------+------+-------+--------------------+-------------------------+-------------------------+------------------------+---------------------+--------------------+-----------
o3x3o *b3o3o . . . .    80 |   480 |   160   160    320 |   40    80    80     80 |   10    16    16      0 | 2016     *     *     *    4    0    0     0 |   6    0    0    0 |  4   0   0
o3x . *b3o3o3o . . .    15 |    60 |    20     0     60 |    0    15     0     30 |    0     6     0      6 |    * 21504     *     * |   1    3    0     0 |   3    3    0    0 |  3   1   0
. x3o *b3o3o3o . . .    15 |    60 |     0    20     60 |    0     0    15     30 |    0     0     6      6 |    *     * 21504     * |   1    0    3     0 |   3    0    3    0 |  3   0   1
. x . *b3o3o3o3o . .     6 |    15 |     0     0     20 |    0     0     0     15 |    0     0     0      6 |    *     *     * 64512 |   0    1    1     2 |   1    2    2    1 |  2   1   1
---------------------+------+-------+--------------------+-------------------------+-------------------------+------------------------+---------------------+--------------------+-----------
o3x3o *b3o3o3o . . .   240 |  1920 |   640   640   1920 |  160   480   480    960 |   60   192   192    192 |   12    32    32     0 | 672    *    *     * |   3    0    0    0 |  3   0   0
o3x . *b3o3o3o3o . .    21 |   105 |    35     0    140 |    0    35     0    105 |    0    21     0     42 |    0     7     0     7 |   * 9216    *     * |   1    2    0    0 |  2   1   0
. x3o *b3o3o3o3o . .    21 |   105 |     0    35    140 |    0     0    35    105 |    0     0    21     42 |    0     0     7     7 |   *    * 9216     * |   1    0    2    0 |  2   0   1
. x . *b3o3o3o3o3o .     7 |    21 |     0     0     35 |    0     0     0     35 |    0     0     0     21 |    0     0     0     7 |   *    *    * 18432 |   0    1    1    1 |  1   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 | 144    *    *    * |  2   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 |   * 2304    *    * |  1   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 |   *    * 2304    * |  1   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 |   *    *    * 2304 |  0   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 | 18   *   *
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 |  * 256   *
. 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 |  *   * 256

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