Acronym	betsa
Name	bitruncated hepteract
Circumradius	sqrt(21/2) = 3.240370
Inradius wrt. botox	sqrt(2) = 1.414214
Inradius wrt. til	11/sqrt(14) = 2.939874
Coordinates	(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 hix between til and til:   arccos(-5/7) = 135.584691° at tix between botox and til:   arccos[-1/sqrt(7)] = 112.207654° at bittin between botox and botox:   90°
Face vector	2688, 9408, 14112, 11760, 5656, 1428, 142
Confer	general polytopal classes: Wythoffian polyexa   lace simplices   analogs: bitruncated hypercube btCn
External links

Incidence matrix according to Dynkin symbol

o3o3o3o3x3x4o

. . . . . . . | 2688 |    5    2 |   10   10   1 |   10   20   5 |    5   20  10 |   1  10 10 |   2  5
--------------+------+-----------+---------------+---------------+---------------+------------+-------
. . . . x . . |    2 | 6720    * |    4    2   0 |    6    8   1 |    4   12   4 |   1   8  6 |   2  4
. . . . . x . |    2 |    * 2688 |    0    5   1 |    0   10   5 |    0   10  10 |   0   5 10 |   1  5
--------------+------+-----------+---------------+---------------+---------------+------------+-------
. . . o3x . . |    3 |    3    0 | 8960    *   * |    3    2   0 |    3    6   1 |   1   6  3 |   2  3
. . . . x3x . |    6 |    3    3 |    * 4480   * |    0    4   1 |    0    6   4 |   0   4  6 |   1  4
. . . . . x4o |    4 |    0    4 |    *    * 672 ♦    0    0   5 |    0    0  10 |   0   0 10 |   0  5
--------------+------+-----------+---------------+---------------+---------------+------------+-------
. . o3o3x . . ♦    4 |    6    0 |    4    0   0 | 6720    *   * |    2    2   0 |   1   4  1 |   2  2
. . . o3x3x . ♦   12 |   12    6 |    4    4   0 |    * 4480   * |    0    3   1 |   0   3  3 |   1  3
. . . . x3x4o ♦   24 |   12   24 |    0    8   6 |    *    * 560 ♦    0    0   4 |   0   0  6 |   0  4
--------------+------+-----------+---------------+---------------+---------------+------------+-------
. o3o3o3x . . ♦    5 |   10    0 |   10    0   0 |    5    0   0 | 2688    *   * |   1   2  0 |   2  1
. . o3o3x3x . ♦   20 |   30   10 |   20   10   0 |    5    5   0 |    * 2688   * |   0   2  1 |   1  2
. . . o3x3x4o ♦   96 |   96   96 |   32   64  24 |    0   16   8 |    *    * 280 |   0   0  3 |   0  3
--------------+------+-----------+---------------+---------------+---------------+------------+-------
o3o3o3o3x . . ♦    6 |   15    0 |   20    0   0 |   15    0   0 |    6    0   0 | 448   *  * |   2  0
. o3o3o3x3x . ♦   30 |   60   15 |   60   20   0 |   30   15   0 |    6    6   0 |   * 896  * |   1  1
. . o3o3x3x4o ♦  320 |  480  320 |  320  320  80 |   80  160  40 |    0   32  10 |   *   * 84 |   0  2
--------------+------+-----------+---------------+---------------+---------------+------------+-------
o3o3o3o3x3x . ♦   42 |  105   21 |  140   35   0 |  105   35   0 |   42   21   0 |   7   7  0 | 128  *
. o3o3o3x3x4o ♦  960 | 1920  960 | 1920 1280 240 |  960  960 160 |  192  384  60 |   0  64 12 |   * 14

o3o3o3o3x3x4/3o

. . . . . .   . | 2688 |    5    2 |   10   10   1 |   10   20   5 |    5   20  10 |   1  10 10 |   2  5
----------------+------+-----------+---------------+---------------+---------------+------------+-------
. . . . x .   . |    2 | 6720    * |    4    2   0 |    6    8   1 |    4   12   4 |   1   8  6 |   2  4
. . . . . x   . |    2 |    * 2688 |    0    5   1 |    0   10   5 |    0   10  10 |   0   5 10 |   1  5
----------------+------+-----------+---------------+---------------+---------------+------------+-------
. . . o3x .   . |    3 |    3    0 | 8960    *   * |    3    2   0 |    3    6   1 |   1   6  3 |   2  3
. . . . x3x   . |    6 |    3    3 |    * 4480   * |    0    4   1 |    0    6   4 |   0   4  6 |   1  4
. . . . . x4/3o |    4 |    0    4 |    *    * 672 ♦    0    0   5 |    0    0  10 |   0   0 10 |   0  5
----------------+------+-----------+---------------+---------------+---------------+------------+-------
. . o3o3x .   . ♦    4 |    6    0 |    4    0   0 | 6720    *   * |    2    2   0 |   1   4  1 |   2  2
. . . o3x3x   . ♦   12 |   12    6 |    4    4   0 |    * 4480   * |    0    3   1 |   0   3  3 |   1  3
. . . . x3x4/3o ♦   24 |   12   24 |    0    8   6 |    *    * 560 ♦    0    0   4 |   0   0  6 |   0  4
----------------+------+-----------+---------------+---------------+---------------+------------+-------
. o3o3o3x .   . ♦    5 |   10    0 |   10    0   0 |    5    0   0 | 2688    *   * |   1   2  0 |   2  1
. . o3o3x3x   . ♦   20 |   30   10 |   20   10   0 |    5    5   0 |    * 2688   * |   0   2  1 |   1  2
. . . o3x3x4/3o ♦   96 |   96   96 |   32   64  24 |    0   16   8 |    *    * 280 |   0   0  3 |   0  3
----------------+------+-----------+---------------+---------------+---------------+------------+-------
o3o3o3o3x .   . ♦    6 |   15    0 |   20    0   0 |   15    0   0 |    6    0   0 | 448   *  * |   2  0
. o3o3o3x3x   . ♦   30 |   60   15 |   60   20   0 |   30   15   0 |    6    6   0 |   * 896  * |   1  1
. . o3o3x3x4/3o ♦  320 |  480  320 |  320  320  80 |   80  160  40 |    0   32  10 |   *   * 84 |   0  2
----------------+------+-----------+---------------+---------------+---------------+------------+-------
o3o3o3o3x3x   . ♦   42 |  105   21 |  140   35   0 |  105   35   0 |   42   21   0 |   7   7  0 | 128  *
. o3o3o3x3x4/3o ♦  960 | 1920  960 | 1920 1280 240 |  960  960 160 |  192  384  60 |   0  64 12 |   * 14

x3x3x *b3o3o3o3o

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