Acronym	bato
Name	bitruncated octeract
Circumradius	5/sqrt(2) = 3.535534
Inradius wrt. betsa	sqrt(2) = 1.414214
Inradius wrt. toc	13/4 = 3.25
Coordinates	(sqrt(2), sqrt(2), sqrt(2), sqrt(2), sqrt(2), sqrt(2), 1/sqrt(2), 0)   & all permutations, all changes of sign
Dihedral angles (at margins)	at hop between toc and toc:   arccos(-3/4) = 138.590378° at til between betsa and toc:   arccos[-1/sqrt(8)] = 110.704811° at botox between betsa and betsa:   90°
Face vector	7168, 28672, 51968, 55552, 36960, 14784, 3184, 272
Confer	general polytopal classes: Wythoffian polyzetta   lace simplices   analogs: bitruncated hypercube btCn
External links

Incidence matrix according to Dynkin symbol

o3o3o3o3o3x3x4o

. . . . . . . . | 7168 |     6    2 |    15    12    1 |    20    30    6 |    15    40   15 |    6   30  20 |    1   12  15 |   2  6
----------------+------+------------+------------------+------------------+------------------+---------------+---------------+-------
. . . . . x . . |    2 | 21504    * |     5     2    0 |    10    10    1 |    10    20    5 |    5   20  10 |    1   10  10 |   2  5
. . . . . . x . |    2 |     * 7168 |     0     6    1 |     0    15    6 |     0    20   15 |    0   15  20 |    0    6  15 |   1  6
----------------+------+------------+------------------+------------------+------------------+---------------+---------------+-------
. . . . o3x . . |    3 |     3    0 | 35840     *    * |     4     2    0 |     6     8    1 |    4   12   4 |    1    8   6 |   2  4
. . . . . x3x . |    6 |     3    3 |     * 14336    * |     0     5    1 |     0    10    5 |    0   10  10 |    0    5  10 |   1  5
. . . . . . x4o |    4 |     0    4 |     *     * 1792 ♦     0     0    6 |     0     0   15 |    0    0  20 |    0    0  15 |   0  6
----------------+------+------------+------------------+------------------+------------------+---------------+---------------+-------
. . . o3o3x . . ♦    4 |     6    0 |     4     0    0 | 35840     *    * |     3     2    0 |    3    6   1 |    1    6   3 |   2  3
. . . . o3x3x . ♦   12 |    12    6 |     4     4    0 |     * 17920    * |     0     4    1 |    0    6   4 |    0    4   6 |   1  4
. . . . . x3x4o ♦   24 |    12   24 |     0     8    6 |     *     * 1792 ♦     0     0    5 |    0    0  10 |    0    0  10 |   0  5
----------------+------+------------+------------------+------------------+------------------+---------------+---------------+-------
. . o3o3o3x . . ♦    5 |    10    0 |    10     0    0 |     5     0    0 | 21504     *    * |    2    2   0 |    1    4   1 |   2  2
. . . o3o3x3x . ♦   20 |    30   10 |    20    10    0 |     5     5    0 |     * 14336    * |    0    3   1 |    0    3   3 |   1  3
. . . . o3x3x4o ♦   96 |    96   96 |    32    64   24 |     0    16    8 |     *     * 1120 ♦    0    0   4 |    0    0   6 |   0  4
----------------+------+------------+------------------+------------------+------------------+---------------+---------------+-------
. o3o3o3o3x . . ♦    6 |    15    0 |    20     0    0 |    15     0    0 |     6     0    0 | 7168    *   * |    1    2   0 |   2  1
. . o3o3o3x3x . ♦   30 |    60   15 |    60    20    0 |    30    15    0 |     6     6    0 |    * 7168   * |    0    2   1 |   1  2
. . . o3o3x3x4o ♦  320 |   480  320 |   320   320   80 |    80   160   40 |     0    32   10 |    *    * 448 |    0    0   3 |   0  3
----------------+------+------------+------------------+------------------+------------------+---------------+---------------+-------
o3o3o3o3o3x . . ♦    7 |    21    0 |    35     0    0 |    35     0    0 |    21     0    0 |    7    0   0 | 1024    *   * |   2  0
. o3o3o3o3x3x . ♦   42 |   105   21 |   140    35    0 |   105    35    0 |    42    21    0 |    7    7   0 |    * 2048   * |   1  1
. . o3o3o3x3x4o ♦  960 |  1920  960 |  1920  1280  240 |   960   960  480 |   192   384   60 |    0   64  12 |    *    * 112 |   0  2
----------------+------+------------+------------------+------------------+------------------+---------------+---------------+-------
o3o3o3o3o3x3x . ♦   56 |   168   28 |   280    56    0 |   280    70    0 |   168    56    0 |   56   28   0 |    8    8   0 | 256  *
. o3o3o3o3x3x4o ♦ 2688 |  6720 2688 |  8960  4480  672 |  6720  4480  560 |  2688  2688  280 |  448  896  84 |    0  128  14 |   * 16

o3o3o3o3o3x3x4/3o

. . . . . . .   . | 7168 |     6    2 |    15    12    1 |    20    30    6 |    15    40   15 |    6   30  20 |    1   12  15 |   2  6
------------------+------+------------+------------------+------------------+------------------+---------------+---------------+-------
. . . . . x .   . |    2 | 21504    * |     5     2    0 |    10    10    1 |    10    20    5 |    5   20  10 |    1   10  10 |   2  5
. . . . . . x   . |    2 |     * 7168 |     0     6    1 |     0    15    6 |     0    20   15 |    0   15  20 |    0    6  15 |   1  6
------------------+------+------------+------------------+------------------+------------------+---------------+---------------+-------
. . . . o3x .   . |    3 |     3    0 | 35840     *    * |     4     2    0 |     6     8    1 |    4   12   4 |    1    8   6 |   2  4
. . . . . x3x   . |    6 |     3    3 |     * 14336    * |     0     5    1 |     0    10    5 |    0   10  10 |    0    5  10 |   1  5
. . . . . . x4/3o |    4 |     0    4 |     *     * 1792 ♦     0     0    6 |     0     0   15 |    0    0  20 |    0    0  15 |   0  6
------------------+------+------------+------------------+------------------+------------------+---------------+---------------+-------
. . . o3o3x .   . ♦    4 |     6    0 |     4     0    0 | 35840     *    * |     3     2    0 |    3    6   1 |    1    6   3 |   2  3
. . . . o3x3x   . ♦   12 |    12    6 |     4     4    0 |     * 17920    * |     0     4    1 |    0    6   4 |    0    4   6 |   1  4
. . . . . x3x4/3o ♦   24 |    12   24 |     0     8    6 |     *     * 1792 ♦     0     0    5 |    0    0  10 |    0    0  10 |   0  5
------------------+------+------------+------------------+------------------+------------------+---------------+---------------+-------
. . o3o3o3x .   . ♦    5 |    10    0 |    10     0    0 |     5     0    0 | 21504     *    * |    2    2   0 |    1    4   1 |   2  2
. . . o3o3x3x   . ♦   20 |    30   10 |    20    10    0 |     5     5    0 |     * 14336    * |    0    3   1 |    0    3   3 |   1  3
. . . . o3x3x4/3o ♦   96 |    96   96 |    32    64   24 |     0    16    8 |     *     * 1120 ♦    0    0   4 |    0    0   6 |   0  4
------------------+------+------------+------------------+------------------+------------------+---------------+---------------+-------
. o3o3o3o3x .   . ♦    6 |    15    0 |    20     0    0 |    15     0    0 |     6     0    0 | 7168    *   * |    1    2   0 |   2  1
. . o3o3o3x3x   . ♦   30 |    60   15 |    60    20    0 |    30    15    0 |     6     6    0 |    * 7168   * |    0    2   1 |   1  2
. . . o3o3x3x4/3o ♦  320 |   480  320 |   320   320   80 |    80   160   40 |     0    32   10 |    *    * 448 |    0    0   3 |   0  3
------------------+------+------------+------------------+------------------+------------------+---------------+---------------+-------
o3o3o3o3o3x .   . ♦    7 |    21    0 |    35     0    0 |    35     0    0 |    21     0    0 |    7    0   0 | 1024    *   * |   2  0
. o3o3o3o3x3x   . ♦   42 |   105   21 |   140    35    0 |   105    35    0 |    42    21    0 |    7    7   0 |    * 2048   * |   1  1
. . o3o3o3x3x4/3o ♦  960 |  1920  960 |  1920  1280  240 |   960   960  480 |   192   384   60 |    0   64  12 |    *    * 112 |   0  2
------------------+------+------------+------------------+------------------+------------------+---------------+---------------+-------
o3o3o3o3o3x3x   . ♦   56 |   168   28 |   280    56    0 |   280    70    0 |   168    56    0 |   56   28   0 |    8    8   0 | 256  *
. o3o3o3o3x3x4/3o ♦ 2688 |  6720 2688 |  8960  4480  672 |  6720  4480  560 |  2688  2688  280 |  448  896  84 |    0  128  14 |   * 16

x3x3x *b3o3o3o3o3o

. . .    . . . . . | 7168 |    1     6    1 |    6    1    6    15 |    6   15   15    20 |   15   20   20    15 |  20   15   15    6 |  15    6    6    1 |  6   1   1
-------------------+------+-----------------+----------------------+----------------------+----------------------+--------------------+--------------------+-----------
x . .    . . . . . |    2 | 3584     *    * |    6    1    0     0 |    6   15    0     0 |   15   20    0     0 |  20   15    0    0 |  15    6    0    0 |  6   1   0
. x .    . . . . . |    2 |    * 21504    * |    1    0    1     5 |    1    5    5    10 |    5   10   10    10 |  10   10   10    5 |  10    5    5    1 |  5   1   1
. . x    . . . . . |    2 |    *     * 3584 |    0    1    6     0 |    6    0   15     0 |   15    0   20     0 |  20    0   15    0 |  15    0    6    0 |  6   0   1
-------------------+------+-----------------+----------------------+----------------------+----------------------+--------------------+--------------------+-----------
x3x .    . . . . . |    6 |    3     3    0 | 7168    *    *     * |    1    5    0     0 |    5   10    0     0 |  10   10    0    0 |  10    5    0    0 |  5   1   0
x . x    . . . . . |    4 |    2     0    2 |    * 1792    *     * ♦    6    0    0     0 |   15    0    0     0 |  20    0    0    0 |  15    0    0    0 |  6   0   0
. x3x    . . . . . |    6 |    0     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 |    0     3    0 |    *    *    * 35840 |    0    1    1     4 |    1    4    4     6 |   4    6    6    4 |   6    4    4    1 |  4   1   1
-------------------+------+-----------------+----------------------+----------------------+----------------------+--------------------+--------------------+-----------
x3x3x    . . . . . ♦   24 |   12    12   12 |    4    6    4     0 | 1792    *    *     * ♦    5    0    0     0 |  10    0    0    0 |  10    0    0    0 |  5   0   0
x3x . *b3o . . . . ♦   12 |    6    12    0 |    4    0    0     4 |    * 8960    *     * |    1    4    0     0 |   4    6    0    0 |   6    4    0    0 |  4   1   0
. x3x *b3o . . . . ♦   12 |    0    12    6 |    0    0    4     4 |    *    * 8960     * |    1    0    4     0 |   4    0    6    0 |   6    0    4    0 |  4   0   1
. x . *b3o3o . . . ♦    4 |    0     6    0 |    0    0    0     4 |    *    *    * 35840 |    0    1    1     3 |   1    3    3    3 |   3    3    3    1 |  3   1   1
-------------------+------+-----------------+----------------------+----------------------+----------------------+--------------------+--------------------+-----------
x3x3x *b3o . . . . ♦   96 |   48    96   48 |   32   24   32    32 |    8    8    8     0 | 1120    *    *     * ♦   4    0    0    0 |   6    0    0    0 |  4   0   0
x3x . *b3o3o . . . ♦   20 |   10    30    0 |   10    0    0    20 |    0    5    0     5 |    * 7168    *     * |   1    3    0    0 |   3    3    0    0 |  3   1   0
. x3x *b3o3o . . . ♦   20 |    0    30   10 |    0    0   10    20 |    0    0    5     5 |    *    * 7168     * |   1    0    3    0 |   3    0    3    0 |  3   0   1
. x . *b3o3o3o . . ♦    5 |    0    10    0 |    0    0    0    10 |    0    0    0     5 |    *    *    * 21504 |   0    1    1    2 |   1    2    2    1 |  2   1   1
-------------------+------+-----------------+----------------------+----------------------+----------------------+--------------------+--------------------+-----------
x3x3x *b3o3o . . . ♦  320 |  160   480  160 |  160   80  160   320 |   40   80   80    80 |   10   16   16     0 | 448    *    *    * |   3    0    0    0 |  3   0   0
x3x . *b3o3o3o . . ♦   30 |   15    60    0 |   20    0    0    60 |    0   15    0    30 |    0    6    0     6 |   * 3584    *    * |   1    2    0    0 |  2   1   0
. x3x *b3o3o3o . . ♦   30 |    0    60   15 |    0    0   20    60 |    0    0   15    30 |    0    0    6     6 |   *    * 3584    * |   1    0    2    0 |  2   0   1
. x . *b3o3o3o3o . ♦    6 |    0    15    0 |    0    0    0    20 |    0    0    0    15 |    0    0    0     6 |   *    *    * 7168 |   0    1    1    1 |  1   1   1
-------------------+------+-----------------+----------------------+----------------------+----------------------+--------------------+--------------------+-----------
x3x3x *b3o3o3o . . ♦  960 |  480  1920  480 |  640  240  640  1920 |  480  480  480   960 |   60  192  192   192 |  12   32   32    0 | 112    *    *    * |  2   0   0
x3x . *b3o3o3o3o . ♦   42 |   21   105    0 |   35    0    0   140 |    0   35    0   105 |    0   21    0    42 |   0    7    0    7 |   * 1024    *    * |  1   1   0
. x3x *b3o3o3o3o . ♦   42 |    0   105   21 |    0    0   35   140 |    0    0   35   105 |    0    0   21    42 |   0    0    7    7 |   *    * 1024    * |  1   0   1
. x . *b3o3o3o3o3o ♦    7 |    0    21    0 |    0    0    0    35 |    0    0    0    35 |    0    0    0    21 |   0    0    0    7 |   *    *    * 1024 |  0   1   1
-------------------+------+-----------------+----------------------+----------------------+----------------------+--------------------+--------------------+-----------
x3x3x *b3o3o3o3o . ♦ 2688 | 1344  6720 1344 | 2240  672 2240  8960 |  560 2240 2240  6720 |  280 1344 1344  2688 |  84  448  448  448 |  14   64   64    0 | 16   *   *
x3x . *b3o3o3o3o3o ♦   56 |   28   168    0 |   56    0    0   280 |    0   70    0   280 |    0   56    0   168 |   0   28    0   56 |   0    8    0    8 |  * 128   *
. x3x *b3o3o3o3o3o ♦   56 |    0   168   28 |    0    0   56   280 |    0    0   70   280 |    0    0   56   168 |   0    0   28   56 |   0    0    8    8 |  *   * 128