Acronym	bittoc
Name	bitruncated octaexon
Circumradius	sqrt(47)/4 = 1.713914
Inradius wrt. til	11/sqrt(112) = 1.039402
Inradius wrt. batal	5/sqrt(112) = 0.472456
Lace city in approx. ASCII-art	o3o3o3o3x o3o3o3o3u o3o3o3x3x -- o3o3o3o3x3x (til) o3o3o3o3u o3o3o3u3o -- o3o3o3o3u3o (u-ril) o3o3o3x3x o3o3o3u3o o3o3x3x3o -- o3o3o3x3x3o (batal)
Dihedral angles (at margins)	at tix between batal and til:   arccos(-1/7) = 98.213211° at bittix between batal and batal:   arccos(1/7) = 81.786789° at hix between til and til:   arccos(1/7) = 81.786789°
Face vector	168, 588, 896, 770, 392, 112, 16
Confer	general polytopal classes: Wythoffian polyexa   analogs: bitruncated simplex btSn
External links

Incidence matrix according to Dynkin symbol

o3x3x3o3o3o3o

. . . . . . . | 168 |   2   5 |  1  10  10 |  5  20  10 | 10  20   5 | 10 10  1 | 5 2
--------------+-----+---------+------------+------------+------------+----------+----
. x . . . . . |   2 | 168   * |  1   5   0 |  5  10   0 | 10  10   0 | 10  5  0 | 5 1
. . x . . . . |   2 |   * 420 |  0   2   4 |  1   8   6 |  4  12   4 |  6  8  1 | 4 2
--------------+-----+---------+------------+------------+------------+----------+----
o3x . . . . . |   3 |   3   0 | 56   *   * ♦  5   0   0 | 10   0   0 | 10  0  0 | 5 0
. x3x . . . . |   6 |   3   3 |  * 280   * |  1   4   0 |  4   6   0 |  6  4  0 | 4 1
. . x3o . . . |   3 |   0   3 |  *   * 560 |  0   2   3 |  1   6   3 |  3  6  1 | 3 2
--------------+-----+---------+------------+------------+------------+----------+----
o3x3x . . . . ♦  12 |  12   6 |  4   4   0 | 70   *   * ♦  4   0   0 |  6  0  0 | 4 0
. x3x3o . . . ♦  12 |   6  12 |  0   4   4 |  * 280   * |  1   3   0 |  3  3  0 | 3 1
. . x3o3o . . ♦   4 |   0   6 |  0   0   4 |  *   * 420 |  0   2   2 |  1  4  1 | 2 2
--------------+-----+---------+------------+------------+------------+----------+----
o3x3x3o . . . ♦  30 |  30  30 | 10  20  10 |  5   5   0 | 56   *   * |  3  0  0 | 3 0
. x3x3o3o . . ♦  20 |  10  30 |  0  10  20 |  0   5   5 |  * 168   * |  1  2  0 | 2 1
. . x3o3o3o . ♦   5 |   0  10 |  0   0  10 |  0   0   5 |  *   * 168 |  0  2  1 | 1 2
--------------+-----+---------+------------+------------+------------+----------+----
o3x3x3o3o . . ♦  60 |  60  90 | 20  60  60 | 15  30  15 |  6   6   0 | 28  *  * | 2 0
. x3x3o3o3o . ♦  30 |  15  60 |  0  20  60 |  0  15  30 |  0   6   6 |  * 56  * | 1 1
. . x3o3o3o3o ♦   6 |   0  15 |  0   0  20 |  0   0  15 |  0   0   6 |  *  * 28 | 0 2
--------------+-----+---------+------------+------------+------------+----------+----
o3x3x3o3o3o . ♦ 105 | 105 210 | 35 140 210 | 35 105 105 | 21  42  21 |  7  7  0 | 8 *
. x3x3o3o3o3o ♦  42 |  21 105 |  0  35 140 |  0  35 105 |  0  21  42 |  0  7  7 | * 8

xoo3xux3oox3ooo3ooo3ooo&#xt   → both heights = 2/sqrt(7) = 0.755929
(til || u-ril || batal)

o..3o..3o..3o..3o..3o..     | 42  *   * |  1   5  1   0   0   0 |  5  10  1   5   0  0   0   0 | 10  10  5  10   0  0   0   0 | 10  5 10  10   0  0  0  0 | 5 1 10  5  0 0 0 | 1 5 1 0
.o.3.o.3.o.3.o.3.o.3.o.     |  * 21   * |  0   0  2   5   0   0 |  0   0  1  10  10  0   0   0 |  0   0  5  20  10  0   0   0 |  0  0 10  20   5  0  0  0 | 0 0 10 10  1 0 0 | 0 5 2 0
..o3..o3..o3..o3..o3..o     |  *  * 105 |  0   0  0   1   2   4 |  0   0  0   2   4  1   8   6 |  0   0  1   8   6  4  12   4 |  0  0  4  12   4  6  8  1 | 0 0  6  8  1 4 2 | 0 4 2 1
----------------------------+-----------+-----------------------+------------------------------+------------------------------+---------------------------+------------------+--------
x.. ... ... ... ... ...     |  2  0   0 | 21   *  *   *   *   * |  5   0  1   0   0  0   0   0 | 10   0  5   0   0  0   0   0 | 10  0 10   0   0  0  0  0 | 5 0 10  0  0 0 0 | 1 5 0 0
... x.. ... ... ... ...     |  2  0   0 |  * 105  *   *   *   * |  1   4  0   1   0  0   0   0 |  4   6  1   4   0  0   0   0 |  6  4  4   6   0  0  0  0 | 4 1  6  4  0 0 0 | 1 4 1 0
oo.3oo.3oo.3oo.3oo.3oo.&#x  |  1  1   0 |  *   * 42   *   *   * |  0   0  1   5   0  0   0   0 |  0   0  5  10   0  0   0   0 |  0  0 10  10   0  0  0  0 | 0 0 10  5  0 0 0 | 0 5 1 0
.oo3.oo3.oo3.oo3.oo3.oo&#x  |  0  1   1 |  *   *  * 105   *   * |  0   0  0   2   4  0   0   0 |  0   0  1   8   6  0   0   0 |  0  0  4  12   4  0  0  0 | 0 0  6  8  1 0 0 | 0 4 2 0
... ..x ... ... ... ...     |  0  0   2 |  *   *  *   * 105   * |  0   0  0   1   0  1   4   0 |  0   0  1   4   0  4   6   0 |  0  0  4   6   0  6  4  0 | 0 0  6  4  0 4 1 | 0 4 1 1
... ... ..x ... ... ...     |  0  0   2 |  *   *  *   *   * 210 |  0   0  0   0   1  0   2   3 |  0   0  0   2   3  1   6   3 |  0  0  1   6   3  3  6  1 | 0 0  3  6  1 3 2 | 0 3 2 1
----------------------------+-----------+-----------------------+------------------------------+------------------------------+---------------------------+------------------+--------
x..3x.. ... ... ... ...     |  6  0   0 |  3   3  0   0   0   0 | 35   *  *   *   *  *   *   * |  4   0  1   0   0  0   0   0 |  6  0  4   0   0  0  0  0 | 4 0  6  0  0 0 0 | 1 4 0 0
... x..3o.. ... ... ...     |  3  0   0 |  0   3  0   0   0   0 |  * 140  *   *   *  *   *   * |  1   3  0   1   0  0   0   0 |  3  3  1   3   0  0  0  0 | 3 1  3  3  0 0 0 | 1 3 1 0
xo. ... ... ... ... ...&#x  |  2  1   0 |  1   0  2   0   0   0 |  *   * 21   *   *  *   *   * ♦  0   0  5   0   0  0   0   0 |  0  0 10   0   0  0  0  0 | 0 0 10  0  0 0 0 | 0 5 0 0
... xux ... ... ... ...&#xt |  2  2   2 |  0   1  2   2   1   0 |  *   *  * 105   *  *   *   * |  0   0  1   4   0  0   0   0 |  0  0  4   6   0  0  0  0 | 0 0  6  4  0 0 0 | 0 4 1 0
... ... .ox ... ... ...&#x  |  0  1   2 |  0   0  0   2   0   1 |  *   *  *   * 210  *   *   * |  0   0  0   2   3  0   0   0 |  0  0  1   6   3  0  0  0 | 0 0  3  6  1 0 0 | 0 3 2 0
..o3..x ... ... ... ...     |  0  0   3 |  0   0  0   0   3   0 |  *   *  *   *   * 35   *   * ♦  0   0  1   0   0  4   0   0 |  0  0  4   0   0  6  0  0 | 0 0  6  0  0 4 0 | 0 4 0 1
... ..x3..x ... ... ...     |  0  0   6 |  0   0  0   0   3   3 |  *   *  *   *   *  * 140   * |  0   0  0   1   0  1   3   0 |  0  0  1   3   0  3  3  0 | 0 0  3  3  0 3 1 | 0 3 1 1
... ... ..x3..o ... ...     |  0  0   3 |  0   0  0   0   0   3 |  *   *  *   *   *  *   * 210 |  0   0  0   0   1  0   2   2 |  0  0  0   2   2  1  4  1 | 0 0  1  4  1 2 2 | 0 2 2 1
----------------------------+-----------+-----------------------+------------------------------+------------------------------+---------------------------+------------------+--------
x..3x..3o.. ... ... ...     ♦ 12  0   0 |  6  12  0   0   0   0 |  4   4  0   0   0  0   0   0 | 35   *  *   *   *  *   *   * |  3  0  1   0   0  0  0  0 | 3 0  3  0  0 0 0 | 1 3 0 0
... x..3o..3o.. ... ...     ♦  4  0   0 |  0   6  0   0   0   0 |  0   4  0   0   0  0   0   0 |  * 105  *   *   *  *   *   * |  1  2  0   1   0  0  0  0 | 2 1  1  2  0 0 0 | 1 2 1 0
xoo3xux ... ... ... ...&#xt ♦  6  3   3 |  3   3  6   3   3   0 |  1   0  3   3   0  1   0   0 |  *   * 35   *   *  *   *   * ♦  0  0  4   0   0  0  0  0 | 0 0  6  0  0 0 0 | 0 4 0 0
... xux3oox ... ... ...&#xt ♦  3  3   6 |  0   3  3   6   3   3 |  0   1  0   3   3  0   1   0 |  *   *  * 140   *  *   *   * |  0  0  1   3   0  0  0  0 | 0 0  3  3  0 0 0 | 0 3 1 0
... ... .ox3.oo ... ...&#x  ♦  0  1   3 |  0   0  0   3   0   3 |  0   0  0   0   3  0   0   1 |  *   *  *   * 210  *   *   * |  0  0  0   2   2  0  0  0 | 0 0  1  4  1 0 0 | 0 2 2 0
..o3..x3..x ... ... ...     ♦  0  0  12 |  0   0  0   0  12   6 |  0   0  0   0   0  4   4   0 |  *   *  *   *   * 35   *   * ♦  0  0  1   0   0  3  0  0 | 0 0  3  0  0 3 0 | 0 3 0 1
... ..x3..x3..o ... ...     ♦  0  0  12 |  0   0  0   0   6  12 |  0   0  0   0   0  0   4   4 |  *   *  *   *   *  * 105   * |  0  0  0   1   0  1  2  0 | 0 0  1  2  0 2 1 | 0 2 1 1
... ... ..x3..o3..o ...     ♦  0  0   4 |  0   0  0   0   0   6 |  0   0  0   0   0  0   0   4 |  *   *  *   *   *  *   * 105 |  0  0  0   0   1  0  2  1 | 0 0  0  2  1 1 2 | 0 1 2 1
----------------------------+-----------+-----------------------+------------------------------+------------------------------+---------------------------+------------------+--------
x..3x..3o..3o.. ... ...     ♦ 20  0   0 | 10  30  0   0   0   0 | 10  20  0   0   0  0   0   0 |  5   5  0   0   0  0   0   0 | 21  *  *   *   *  *  *  * | 2 0  1  0  0 0 0 | 1 2 0 0
... x..3o..3o..3o.. ...     ♦  5  0   0 |  0  10  0   0   0   0 |  0  10  0   0   0  0   0   0 |  0   5  0   0   0  0   0   0 |  * 42  *   *   *  *  *  * | 1 1  0  1  0 0 0 | 1 1 1 0
xoo3xux3oox ... ... ...&#xt ♦ 12  6  12 |  6  12 12  12  12   6 |  4   4  6  12   6  4   4   0 |  1   0  4   4   0  1   0   0 |  *  * 35   *   *  *  *  * | 0 0  3  0  0 0 0 | 0 3 0 0
... xux3oox3ooo ... ...&#xt ♦  4  4  12 |  0   6  4  12   6  12 |  0   4  0   6  12  0   4   4 |  0   1  0   4   4  0   1   0 |  *  *  * 105   *  *  *  * | 0 0  1  2  0 0 0 | 0 2 1 0
... ... .ox3.oo3.oo ...&#x  ♦  0  1   4 |  0   0  0   4   0   6 |  0   0  0   0   6  0   0   4 |  0   0  0   0   4  0   0   1 |  *  *  *   * 105  *  *  * | 0 0  0  2  1 0 0 | 0 1 2 0
..o3..x3..x3..o ... ...     ♦  0  0  30 |  0   0  0   0  30  30 |  0   0  0   0   0 10  20  10 |  0   0  0   0   0  5   5   0 |  *  *  *   *   * 21  *  * | 0 0  1  0  0 2 0 | 0 2 0 1
... ..x3..x3..o3..o ...     ♦  0  0  20 |  0   0  0   0  10  30 |  0   0  0   0   0  0  10  20 |  0   0  0   0   0  0   5   5 |  *  *  *   *   *  * 42  * | 0 0  0  1  0 1 1 | 0 1 1 1
... ... ..x3..o3..o3..o     ♦  0  0   5 |  0   0  0   0   0  10 |  0   0  0   0   0  0   0  10 |  0   0  0   0   0  0   0   5 |  *  *  *   *   *  *  * 21 | 0 0  0  0  1 0 2 | 0 0 2 1
----------------------------+-----------+-----------------------+------------------------------+------------------------------+---------------------------+------------------+--------
x..3x..3o..3o..3o.. ...     ♦ 30  0   0 | 15  60  0   0   0   0 | 20  60  0   0   0  0   0   0 | 15  30  0   0   0  0   0   0 |  6  6  0   0   0  0  0  0 | 7 *  *  *  * * * | 1 1 0 0
... x..3o..3o..3o..3o..     ♦  6  0   0 |  0  15  0   0   0   0 |  0  20  0   0   0  0   0   0 |  0  15  0   0   0  0   0   0 |  0  6  0   0   0  0  0  0 | * 7  *  *  * * * | 1 0 1 0
xoo3xux3oox3ooo ... ...&#xt ♦ 20 10  30 | 10  30 20  30  30  30 | 10  20 10  30  30 10  20  10 |  5   5 10  20  10  5   5   0 |  1  0  5   5   0  1  0  0 | * * 21  *  * * * | 0 2 0 0
... xux3oox3ooo3ooo ...&#xt ♦  5  5  20 |  0  10  5  20  10  30 |  0  10  0  10  30  0  10  20 |  0   5  0  10  20  0   5   5 |  0  1  0   5   5  0  1  0 | * *  * 42  * * * | 0 1 1 0
... ... .ox3.oo3.oo3.oo&#x  ♦  0  1   5 |  0   0  0   5   0  10 |  0   0  0   0  10  0   0  10 |  0   0  0   0  10  0   0   5 |  0  0  0   0   5  0  0  1 | * *  *  * 21 * * | 0 0 2 0
..o3..x3..x3..o3..o ...     ♦  0  0  60 |  0   0  0   0  60  90 |  0   0  0   0   0 20  60  60 |  0   0  0   0   0 15  30  15 |  0  0  0   0   0  6  6  0 | * *  *  *  * 7 * | 0 1 0 1
... ..x3..x3..o3..o3..o     ♦  0  0  30 |  0   0  0   0  15  60 |  0   0  0   0   0  0  20  60 |  0   0  0   0   0  0  15  30 |  0  0  0   0   0  0  6  6 | * *  *  *  * * 7 | 0 0 1 1
----------------------------+-----------+-----------------------+------------------------------+------------------------------+---------------------------+------------------+--------
x..3x..3o..3o..3o..3o..     ♦ 42  0   0 | 21 105  0   0   0   0 | 35 140  0   0   0  0   0   0 | 35 105  0   0   0  0   0   0 | 21 42  0   0   0  0  0  0 | 7 7  0  0  0 0 0 | 1 * * *
xoo3xux3oox3ooo3ooo ...&#xt ♦ 30 15  60 | 15  60 30  60  60  90 | 20  60 15  60  90 20  60  60 | 15  30 20  60  60 15  30  15 |  6  6 15  30  15  6  6  0 | 1 0  6  6  0 1 0 | * 7 * *
... xux3oox3ooo3ooo3ooo&#xt ♦  6  6  30 |  0  15  6  30  15  60 |  0  20  0  15  60  0  20  60 |  0  15  0  20  60  0  15  30 |  0  6  0  15  30  0  6  6 | 0 1  0  6  6 0 1 | * * 7 *
..o3..x3..x3..o3..o3..o     ♦  0  0 105 |  0   0  0   0 105 210 |  0   0  0   0   0 35 140 210 |  0   0  0   0   0 35 105 105 |  0  0  0   0   0 21 42 21 | 0 0  0  0  0 7 7 | * * * 1