Acronym bro
Name birectified octeract,
birectified hexadecazetton,
Gosset polytopes 05,1,1
Circumradius sqrt(3) = 1.732051
Coordinates (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

o3o3o3o3o3x3o4o

. . . . . . . . | 1792     24 |    60    24 |    80    60    6 |    60    80   15 |   24   60  20 |    4   24  15 |   4  6
----------------+------+-------+-------------+------------------+------------------+---------------+---------------+-------
. . . . . x . . |    2 | 21504 |     5     2 |    10    10    1 |    10    20    5 |    5   20  10 |    1   10  10 |   2  5
----------------+------+-------+-------------+------------------+------------------+---------------+---------------+-------
. . . . o3x . . |    3 |     3 | 35840     * |     4     2    0 |     6     8    1 |    4   12   4 |    1    8   6 |   2  4
. . . . . x3o . |    3 |     3 |     * 14336 |     0     5    1 |     0    10    5 |    0   10  10 |    0    5  10 |   1  5
----------------+------+-------+-------------+------------------+------------------+---------------+---------------+-------
. . . o3o3x . .     4 |     6 |     4     0 | 35840     *    * |     3     2    0 |    3    6   1 |    1    6   3 |   2  3
. . . . o3x3o .     6 |    12 |     4     4 |     * 17920    * |     0     4    1 |    0    6   4 |    0    4   6 |   1  4
. . . . . x3o4o     6 |    12 |     0     8 |     *     * 1792      0     0    5 |    0    0  10 |    0    0  10 |   0  5
----------------+------+-------+-------------+------------------+------------------+---------------+---------------+-------
. . o3o3o3x . .     5 |    10 |    10     0 |     5     0    0 | 21504     *    * |    2    2   0 |    1    4   1 |   2  2
. . . o3o3x3o .    10 |    30 |    20    10 |     5     5    0 |     * 14336    * |    0    3   1 |    0    3   3 |   1  3
. . . . o3x3o4o    24 |    96 |    32    64 |     0    16    8 |     *     * 1120     0    0   4 |    0    0   6 |   0  4
----------------+------+-------+-------------+------------------+------------------+---------------+---------------+-------
. o3o3o3o3x . .     6 |    15 |    20     0 |    15     0    0 |     6     0    0 | 7168    *   * |    1    2   0 |   2  1
. . o3o3o3x3o .    15 |    60 |    60    20 |    30    15    0 |     6     6    0 |    * 7168   * |    0    2   1 |   1  2
. . . o3o3x3o4o    80 |   480 |   320   320 |    80   160   40 |     0    32   10 |    *    * 448 |    0    0   3 |   0  3
----------------+------+-------+-------------+------------------+------------------+---------------+---------------+-------
o3o3o3o3o3x . .     7 |    21 |    35     0 |    35     0    0 |    21     0    0 |    7    0   0 | 1024    *   * |   2  0
. o3o3o3o3x3o .    21 |   105 |   140    35 |   105    35    0 |    42    21    0 |    7    7   0 |    * 2048   * |   1  1
. . o3o3o3x3o4o   240 |  1920 |  1920  1280 |   960   960  160 |   192   384   60 |    0   64  12 |    *    * 112 |   0  2
----------------+------+-------+-------------+------------------+------------------+---------------+---------------+-------
o3o3o3o3o3x3o .    28 |   168 |   280    56 |   280    70    0 |   168    56    0 |   56   28   0 |    8    8   0 | 256  *
. o3o3o3o3x3o4o   672 |  6720 |  8960  4480 |  6720  4480  560 |  2688  2688  280 |  448  896  84 |    0  128  14 |   * 16

o3x3o *b3o3o3o3o3o

. . .    . . . . . | 1792     24 |   12   12    60 |    6   30   30    80 |   15   40   40    60 |  20   30   30   24 |  15   12   12    4 |  6   2   2
-------------------+------+-------+-----------------+----------------------+----------------------+--------------------+--------------------+-----------
. x .    . . . . . |    2 | 21504 |    1    1     5 |    1    5    5    10 |    5   10   10    10 |  10   10   10    5 |  10    5    5    1 |  5   1   1
-------------------+------+-------+-----------------+----------------------+----------------------+--------------------+--------------------+-----------
o3x .    . . . . . |    3 |     3 | 7168    *     * |    1    5    0     0 |    5   10    0     0 |  10   10    0    0 |  10    5    0    0 |  5   1   0
. x3o    . . . . . |    3 |     3 |    * 7168     * |    1    0    5     0 |    5    0   10     0 |  10    0   10    0 |  10    0    5    0 |  5   0   1
. x . *b3o . . . . |    3 |     3 |    *    * 35840 |    0    1    1     4 |    1    4    4     6 |   4    6    6    4 |   6    4    4    1 |  4   1   1
-------------------+------+-------+-----------------+----------------------+----------------------+--------------------+--------------------+-----------
o3x3o    . . . . .     6 |    12 |    4    4     0 | 1792    *    *     *     5    0    0     0 |  10    0    0    0 |  10    0    0    0 |  5   0   0
o3x . *b3o . . . .     6 |    12 |    4    0     4 |    * 8960    *     * |    1    4    0     0 |   4    6    0    0 |   6    4    0    0 |  4   1   0
. x3o *b3o . . . .     6 |    12 |    0    4     4 |    *    * 8960     * |    1    0    4     0 |   4    0    6    0 |   6    0    4    0 |  4   0   1
. x . *b3o3o . . .     4 |     6 |    0    0     4 |    *    *    * 35840 |    0    1    1     3 |   1    3    3    3 |   3    3    3    1 |  3   1   1
-------------------+------+-------+-----------------+----------------------+----------------------+--------------------+--------------------+-----------
o3x3o *b3o . . . .    24 |    96 |   32   32    32 |    8    8    8     0 | 1120    *    *     *    4    0    0    0 |   6    0    0    0 |  4   0   0
o3x . *b3o3o . . .    10 |    30 |   10    0    20 |    0    5    0     5 |    * 7168    *     * |   1    3    0    0 |   3    3    0    0 |  3   1   0
. x3o *b3o3o . . .    10 |    30 |    0   10    20 |    0    0    5     5 |    *    * 7168     * |   1    0    3    0 |   3    0    3    0 |  3   0   1
. x . *b3o3o3o . .     5 |    10 |    0    0    10 |    0    0    0     5 |    *    *    * 21504 |   0    1    1    2 |   1    2    2    1 |  2   1   1
-------------------+------+-------+-----------------+----------------------+----------------------+--------------------+--------------------+-----------
o3x3o *b3o3o . . .    80 |   480 |  160  160   320 |   40   80   80    80 |   10   16   16     0 | 448    *    *    * |   3    0    0    0 |  3   0   0
o3x . *b3o3o3o . .    15 |    60 |   20    0    60 |    0   15    0    30 |    0    6    0     6 |   * 3584    *    * |   1    2    0    0 |  2   1   0
. x3o *b3o3o3o . .    15 |    60 |    0   20    60 |    0    0   15    30 |    0    0    6     6 |   *    * 3584    * |   1    0    2    0 |  2   0   1
. x . *b3o3o3o3o .     6 |    15 |    0    0    20 |    0    0    0    15 |    0    0    0     6 |   *    *    * 7168 |   0    1    1    1 |  1   1   1
-------------------+------+-------+-----------------+----------------------+----------------------+--------------------+--------------------+-----------
o3x3o *b3o3o3o . .   240 |  1920 |  640  640  1920 |  160  480  480   960 |   60  192  192   192 |  12   32   32    0 | 112    *    *    * |  2   0   0
o3x . *b3o3o3o3o .    21 |   105 |   35    0   140 |    0   35    0   105 |    0   21    0    42 |   0    7    0    7 |   * 1024    *    * |  1   1   0
. x3o *b3o3o3o3o .    21 |   105 |    0   35   140 |    0    0   35   105 |    0    0   21    42 |   0    0    7    7 |   *    * 1024    * |  1   0   1
. x . *b3o3o3o3o3o     7 |    21 |    0    0    35 |    0    0    0    35 |    0    0    0    21 |   0    0    0    7 |   *    *    * 1024 |  0   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 | 16   *   *
o3x . *b3o3o3o3o3o    28 |   168 |   56    0   280 |    0   70    0   280 |    0   56    0   168 |   0   28    0   56 |   0    8    0    8 |  * 128   *
. x3o *b3o3o3o3o3o    28 |   168 |    0   56   280 |    0    0   70   280 |    0    0   56   168 |   0    0   28   56 |   0    0    8    8 |  *   * 128

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