Acronym	til
Name	truncated heptapeton
Circumradius	sqrt(13/7) = 1.362771
Inradius wrt. hix	11/sqrt(84) = 1.200198
Inradius wrt. tix	sqrt(3/28) = 0.327327
Lace city in approx. ASCII-art	o3o3o3o x3o3o3o -- x3o3o3o3o (hix) o3o3o3o u3o3o3o -- u3o3o3o3o (u-hix) x3o3o3o u3o3o3o x3x3o3o -- x3x3o3o3o (tix)
Volume	361 sqrt(7)/2880 = 0.331638
Surface	833 sqrt(3)/240 = 6.011660
Dihedral angles (at margins)	at pen between hix and tix:   arccos(-1/6) = 99.594068° at tip between tix and tix:   arccos(1/6) = 80.405932°
Face vector	42, 126, 175, 140, 63, 14
Confer	general polytopal classes: Wythoffian polypeta   lace simplices   analogs: truncated simplex tSn
External links

Incidence matrix according to Dynkin symbol

x3x3o3o3o3o

. . . . . . | 42 |  1   5 |  5  10 | 10  10 | 10  5 | 5 1
------------+----+--------+--------+--------+-------+----
x . . . . . |  2 | 21   * ♦  5   0 | 10   0 | 10  0 | 5 0
. x . . . . |  2 |  * 105 |  1   4 |  4   6 |  6  4 | 4 1
------------+----+--------+--------+--------+-------+----
x3x . . . . |  6 |  3   3 | 35   * ♦  4   0 |  6  0 | 4 0
. x3o . . . |  3 |  0   3 |  * 140 |  1   3 |  3  3 | 3 1
------------+----+--------+--------+--------+-------+----
x3x3o . . . ♦ 12 |  6  12 |  4   4 | 35   * |  3  0 | 3 0
. x3o3o . . ♦  4 |  0   6 |  0   4 |  * 105 |  1  2 | 2 1
------------+----+--------+--------+--------+-------+----
x3x3o3o . . ♦ 20 | 10  30 | 10  20 |  5   5 | 21  * | 2 0
. x3o3o3o . ♦  5 |  0  10 |  0  10 |  0   5 |  * 42 | 1 1
------------+----+--------+--------+--------+-------+----
x3x3o3o3o . ♦ 30 | 15  60 | 20  60 | 15  30 |  6  6 | 7 *
. x3o3o3o3o ♦  6 |  0  15 |  0  20 |  0  15 |  0  6 | * 7

xux3oox3ooo3ooo3ooo&#xt   → both heights = sqrt(7/12) = 0.763763
(hix || pseudo u-hix || tix)

o..3o..3o..3o..3o..     | 6 *  * |  5 1  0  0  0 | 10  5  0  0  0 | 10 10  0  0  0 | 5 10  0 0 0 | 1 5 0 0
.o.3.o.3.o.3.o.3.o.     | * 6  * |  0 1  5  0  0 |  0  5 10  0  0 |  0 10 10  0  0 | 0 10  5 0 0 | 0 5 1 0
..o3..o3..o3..o3..o     | * * 30 |  0 0  1  1  4 |  0  1  4  4  6 |  0  4  6  6  4 | 0  6  4 4 1 | 0 4 1 1
------------------------+--------+---------------+----------------+----------------+-------------+--------
x.. ... ... ... ...     | 2 0  0 | 15 *  *  *  * |  4  1  0  0  0 |  6  4  0  0  0 | 4  6  0 0 0 | 1 4 0 0
oo.3oo.3oo.3oo.3oo.&#x  | 1 1  0 |  * 6  *  *  * ♦  0  5  0  0  0 |  0 10  0  0  0 | 0 10  0 0 0 | 0 5 0 0
.oo3.oo3.oo3.oo3.oo&#x  | 0 1  1 |  * * 30  *  * |  0  1  4  0  0 |  0  4  6  0  0 | 0  6  4 0 0 | 0 4 1 0
..x ... ... ... ...     | 0 0  2 |  * *  * 15  * ♦  0  1  0  4  0 |  0  4  0  6  0 | 0  6  0 4 0 | 0 4 0 1
... ..x ... ... ...     | 0 0  2 |  * *  *  * 60 |  0  0  1  1  3 |  0  1  3  3  3 | 0  3  3 3 1 | 0 3 1 1
------------------------+--------+---------------+----------------+----------------+-------------+--------
x..3o.. ... ... ...     | 3 0  0 |  3 0  0  0  0 | 20  *  *  *  * |  3  1  0  0  0 | 3  3  0 0 0 | 1 3 0 0
xux ... ... ... ...&#xt | 2 2  2 |  1 2  2  1  0 |  * 15  *  *  * ♦  0  4  0  0  0 | 0  6  0 0 0 | 0 4 0 0
... .ox ... ... ...&#x  | 0 1  2 |  0 0  2  0  1 |  *  * 60  *  * |  0  1  3  0  0 | 0  3  3 0 0 | 0 3 1 0
..x3..x ... ... ...     | 0 0  6 |  0 0  0  3  3 |  *  *  * 20  * ♦  0  1  0  3  0 | 0  3  0 3 0 | 0 3 0 1
... ..x3..o ... ...     | 0 0  3 |  0 0  0  0  3 |  *  *  *  * 60 |  0  0  1  1  2 | 0  1  2 2 1 | 0 2 1 1
------------------------+--------+---------------+----------------+----------------+-------------+--------
x..3o..3o.. ... ...     ♦ 4 0  0 |  6 0  0  0  0 |  4  0  0  0  0 | 15  *  *  *  * | 2  1  0 0 0 | 1 2 0 0
xux3oox ... ... ...&#xt ♦ 3 3  6 |  3 3  6  3  3 |  1  3  3  1  0 |  * 20  *  *  * | 0  3  0 0 0 | 0 3 0 0
... .ox3.oo ... ...&#x  ♦ 0 1  3 |  0 0  3  0  3 |  0  0  3  0  1 |  *  * 60  *  * | 0  1  2 0 0 | 0 2 1 0
..x3..x3..o ... ...     ♦ 0 0 12 |  0 0  0  6 12 |  0  0  0  4  4 |  *  *  * 15  * | 0  1  0 2 0 | 0 2 0 1
... ..x3..o3..o ...     ♦ 0 0  4 |  0 0  0  0  6 |  0  0  0  0  4 |  *  *  *  * 30 | 0  0  1 1 1 | 0 1 1 1
------------------------+--------+---------------+----------------+----------------+-------------+--------
x..3o..3o..3o.. ...     ♦ 5 0  0 | 10 0  0  0  0 | 10  0  0  0  0 |  5  0  0  0  0 | 6  *  * * * | 1 1 0 0
xux3oox3ooo ... ...&#xt ♦ 4 4 12 |  6 4 12  6 12 |  4  6 12  4  4 |  1  4  4  1  0 | * 15  * * * | 0 2 0 0
... .ox3.oo3.oo ...&#x  ♦ 0 1  4 |  0 0  4  0  6 |  0  0  6  0  4 |  0  0  4  0  1 | *  * 30 * * | 0 1 1 0
..x3..x3..o3..o ...     ♦ 0 0 20 |  0 0  0 10 30 |  0  0  0 10 20 |  0  0  0  5  5 | *  *  * 6 * | 0 1 0 1
... ..x3..o3..o3..o     ♦ 0 0  5 |  0 0  0  0 10 |  0  0  0  0 10 |  0  0  0  0  5 | *  *  * * 6 | 0 0 1 1
------------------------+--------+---------------+----------------+----------------+-------------+--------
x..3o..3o..3o..3o..     ♦ 6 0  0 | 15 0  0  0  0 | 20  0  0  0  0 | 15  0  0  0  0 | 6  0  0 0 0 | 1 * * *
xux3oox3ooo3ooo ...&#xt ♦ 5 5 20 | 10 5 20 10 30 | 10 10 30 10 20 |  5 10 20  5  5 | 1  5  5 1 0 | * 6 * *
... .ox3.oo3.oo3.oo&#x  ♦ 0 1  5 |  0 0  5  0 10 |  0  0 10  0 10 |  0  0 10  0  5 | 0  0  5 0 1 | * * 6 *
..x3..x3..o3..o3..o     ♦ 0 0 30 |  0 0  0 15 60 |  0  0  0 20 60 |  0  0  0 15 30 | 0  0  0 6 6 | * * * 1