Acronym sril
Name small rhombated heptapeton,
cantellated heptapeton
Circumradius sqrt(13/7) = 1.362770
Lace city
in approx. ASCII-art
        x3o3o3o  o3x3o3o  		-- o3x3o3o3o (rix)
                          
                          
                          
                          
x3o3o3o  u3o3o3o  x3x3o3o 		-- x3x3o3o3o (tix)
                          
                          
                          
                          
 o3x3o3o  x3x3o3o  x3o3x3o		-- x3o3x3o3o (sarx)
External
links
wikipedia   polytopewiki  

Incidence matrix according to Dynkin symbol

x3o3x3o3o3o

. . . . . . | 105 |   2   8 |  1   8   4  12 |  4  12   6   8 |  6   8  4  2 | 4  2 1
------------+-----+---------+----------------+----------------+--------------+-------
x . . . . . |   2 | 105   * |  1   4   0   0 |  4   6   0   0 |  6   4  0  0 | 4  1 0
. . x . . . |   2 |   * 420 |  0   1   1   3 |  1   3   3   3 |  3   3  3  1 | 3  1 1
------------+-----+---------+----------------+----------------+--------------+-------
x3o . . . . |   3 |   3   0 | 35   *   *   *   4   0   0   0 |  6   0  0  0 | 4  0 0
x . x . . . |   4 |   2   2 |  * 210   *   * |  1   3   0   0 |  3   3  0  0 | 3  1 0
. o3x . . . |   3 |   0   3 |  *   * 140   * |  1   0   3   0 |  3   0  3  0 | 3  0 1
. . x3o . . |   3 |   0   3 |  *   *   * 420 |  0   1   1   2 |  1   2  2  1 | 2  1 1
------------+-----+---------+----------------+----------------+--------------+-------
x3o3x . . .   12 |  12  12 |  4   6   4   0 | 35   *   *   * |  3   0  0  0 | 3  0 0
x . x3o . .    6 |   3   6 |  0   3   0   2 |  * 210   *   * |  1   2  0  0 | 2  1 0
. o3x3o . .    6 |   0  12 |  0   0   4   4 |  *   * 105   * |  1   0  2  0 | 2  0 1
. . x3o3o .    4 |   0   6 |  0   0   0   4 |  *   *   * 210 |  0   1  1  1 | 1  1 1
------------+-----+---------+----------------+----------------+--------------+-------
x3o3x3o . .   30 |  30  60 | 10  30  20  20 |  5  10   5   0 | 21   *  *  * | 2  0 0
x . x3o3o .    8 |   4  12 |  0   6   0   8 |  0   4   0   2 |  * 105  *  * | 1  1 0
. o3x3o3o .   10 |   0  30 |  0   0  10  20 |  0   0   5   5 |  *   * 42  * | 1  0 1
. . x3o3o3o    5 |   0  10 |  0   0   0  10 |  0   0   0   5 |  *   *  * 42 | 0  1 1
------------+-----+---------+----------------+----------------+--------------+-------
x3o3x3o3o .   60 |  60 180 | 20  90  60 120 | 15  60  30  30 |  6  15  6  0 | 7  * *
x . x3o3o3o   10 |   5  20 |  0  10   0  20 |  0  10   0  10 |  0   5  0  2 | * 21 *
. o3x3o3o3o   15 |   0  60 |  0   0  20  60 |  0   0  15  30 |  0   0  6  6 | *  * 7

oxx3xxo3oox3ooo3ooo&#xt   → all heights = sqrt(7/12) = 0.763763
(rix || pseudo tix || sarx)

o..3o..3o..3o..3o..     | 15  *  * |  8  2  0  0   0  0   0 |  4 12  1  8  0  0  0   0  0  0  0   0 |  6  8  4 12  0  0  0   0  0  0  0  0 | 4 2  6  8 0  0  0  0 0  0 0 | 1 4 2  0 0 0
.o.3.o.3.o.3.o.3.o.     |  * 30  * |  0  1  1  4   4  0   0 |  0  0  1  4  6  4  4   6  0  0  0   0 |  0  0  4  6  4  6  6   4  0  0  0  0 | 0 0  6  4 1  4  4  1 0  0 0 | 0 4 1  1 1 0
..o3..o3..o3..o3..o     |  *  * 60 |  0  0  0  0   2  2   6 |  0  0  0  0  0  2  1   6  1  6  3   6 |  0  0  1  0  0  6  3   6  3  6  3  2 | 0 0  3  0 0  6  3  2 3  2 1 | 0 3 0  2 1 1
------------------------+----------+------------------------+---------------------------------------+--------------------------------------+-----------------------------+-------------
... x.. ... ... ...     |  2  0  0 | 60  *  *  *   *  *   * |  1  3  0  1  0  0  0   0  0  0  0   0 |  3  3  1  3  0  0  0   0  0  0  0  0 | 3 1  3  3 0  0  0  0 0  0 0 | 1 3 1  0 0 0
oo.3oo.3oo.3oo.3oo.&#x  |  1  1  0 |  * 30  *  *   *  *   * |  0  0  1  4  0  0  0   0  0  0  0   0 |  0  0  4  6  0  0  0   0  0  0  0  0 | 0 0  6  4 0  0  0  0 0  0 0 | 0 4 1  0 0 0
.x. ... ... ... ...     |  0  2  0 |  *  * 15  *   *  *   * |  0  0  1  0  0  4  0   0  0  0  0   0 |  0  0  4  0  0  6  0   0  0  0  0  0 | 0 0  6  0 0  4  0  0 0  0 0 | 0 4 0  1 0 0
... .x. ... ... ...     |  0  2  0 |  *  *  * 60   *  *   * |  0  0  0  1  3  0  1   0  0  0  0   0 |  0  0  1  3  3  0  3   0  0  0  0  0 | 0 0  3  3 1  0  3  0 0  0 0 | 0 3 1  0 1 0
.oo3.oo3.oo3.oo3.oo&#x  |  0  1  1 |  *  *  *  * 120  *   * |  0  0  0  0  0  1  1   3  0  0  0   0 |  0  0  1  0  0  3  3   3  0  0  0  0 | 0 0  3  0 0  3  3  1 0  0 0 | 0 3 0  1 1 0
..x ... ... ... ...     |  0  0  2 |  *  *  *  *   * 60   * |  0  0  0  0  0  1  0   0  1  3  0   0 |  0  0  1  0  0  3  0   0  3  3  0  0 | 0 0  3  0 0  3  0  0 3  1 0 | 0 3 0  1 0 1
... ... ..x ... ...     |  0  0  2 |  *  *  *  *   *  * 180 |  0  0  0  0  0  0  0   1  0  1  1   2 |  0  0  0  0  0  1  1   2  1  2  2  1 | 0 0  1  0 0  2  2  1 2  1 1 | 0 2 0  1 1 1
------------------------+----------+------------------------+---------------------------------------+--------------------------------------+-----------------------------+-------------
o..3x.. ... ... ...     |  3  0  0 |  3  0  0  0   0  0   0 | 20  *  *  *  *  *  *   *  *  *  *   * |  3  0  1  0  0  0  0   0  0  0  0  0 | 3 0  3  0 0  0  0  0 0  0 0 | 1 3 0  0 0 0
... x..3o.. ... ...     |  3  0  0 |  3  0  0  0   0  0   0 |  * 60  *  *  *  *  *   *  *  *  *   * |  1  2  0  1  0  0  0   0  0  0  0  0 | 2 1  1  2 0  0  0  0 0  0 0 | 1 2 1  0 0 0
ox. ... ... ... ...&#x  |  1  2  0 |  0  2  1  0   0  0   0 |  *  * 15  *  *  *  *   *  *  *  *   *   0  0  4  0  0  0  0   0  0  0  0  0 | 0 0  6  0 0  0  0  0 0  0 0 | 0 4 0  0 0 0
... xx. ... ... ...&#x  |  2  2  0 |  1  2  0  1   0  0   0 |  *  *  * 60  *  *  *   *  *  *  *   * |  0  0  1  3  0  0  0   0  0  0  0  0 | 0 0  3  3 0  0  0  0 0  0 0 | 0 3 1  0 0 0
... .x.3.o. ... ...     |  0  3  0 |  0  0  0  3   0  0   0 |  *  *  *  * 60  *  *   *  *  *  *   * |  0  0  0  1  2  0  1   0  0  0  0  0 | 0 0  1  2 1  0  2  0 0  0 0 | 0 2 1  0 1 0
.xx ... ... ... ...&#x  |  0  2  2 |  0  0  1  0   2  1   0 |  *  *  *  *  * 60  *   *  *  *  *   * |  0  0  1  0  0  3  0   0  0  0  0  0 | 0 0  3  0 0  3  0  0 0  0 0 | 0 3 0  1 0 0
... .xo ... ... ...&#x  |  0  2  1 |  0  0  0  1   2  0   0 |  *  *  *  *  *  * 60   *  *  *  *   * |  0  0  1  0  0  0  3   0  0  0  0  0 | 0 0  3  0 0  0  3  0 0  0 0 | 0 3 0  0 1 0
... ... .ox ... ...&#x  |  0  1  2 |  0  0  0  0   2  0   1 |  *  *  *  *  *  *  * 180  *  *  *   * |  0  0  0  0  0  1  1   2  0  0  0  0 | 0 0  1  0 0  2  2  1 0  0 0 | 0 2 0  1 1 0
..x3..o ... ... ...     |  0  0  3 |  0  0  0  0   0  3   0 |  *  *  *  *  *  *  *   * 20  *  *   *   0  0  1  0  0  0  0   0  3  0  0  0 | 0 0  3  0 0  0  0  0 3  0 0 | 0 3 0  0 0 1
..x ... ..x ... ...     |  0  0  4 |  0  0  0  0   0  2   2 |  *  *  *  *  *  *  *   *  * 90  *   * |  0  0  0  0  0  1  0   0  1  2  0  0 | 0 0  1  0 0  2  0  0 2  1 0 | 0 2 0  1 0 1
... ..o3..x ... ...     |  0  0  3 |  0  0  0  0   0  0   3 |  *  *  *  *  *  *  *   *  *  * 60   * |  0  0  0  0  0  0  1   0  1  0  2  0 | 0 0  1  0 0  0  2  0 2  0 1 | 0 2 0  0 1 1
... ... ..x3..o ...     |  0  0  3 |  0  0  0  0   0  0   3 |  *  *  *  *  *  *  *   *  *  *  * 120 |  0  0  0  0  0  0  0   1  0  1  1  1 | 0 0  0  0 0  1  1  1 1  1 1 | 0 1 0  1 1 1
------------------------+----------+------------------------+---------------------------------------+--------------------------------------+-----------------------------+-------------
o..3x..3o.. ... ...       6  0  0 | 12  0  0  0   0  0   0 |  4  4  0  0  0  0  0   0  0  0  0   0 | 15  *  *  *  *  *  *   *  *  *  *  * | 2 0  1  0 0  0  0  0 0  0 0 | 1 2 0  0 0 0
... x..3o..3o.. ...       4  0  0 |  6  0  0  0   0  0   0 |  0  4  0  0  0  0  0   0  0  0  0   0 |  * 30  *  *  *  *  *   *  *  *  *  * | 1 1  0  1 0  0  0  0 0  0 0 | 1 1 1  0 0 0
oxx3xxo ... ... ...&#xt   3  6  3 |  3  6  3  3   6  3   0 |  1  0  3  3  0  3  3   0  1  0  0   0 |  *  * 20  *  *  *  *   *  *  *  *  * | 0 0  3  0 0  0  0  0 0  0 0 | 0 3 0  0 0 0
... xx.3oo. ... ...&#x    3  3  0 |  3  3  0  3   0  0   0 |  0  1  0  3  1  0  0   0  0  0  0   0 |  *  *  * 60  *  *  *   *  *  *  *  * | 0 0  1  2 0  0  0  0 0  0 0 | 0 2 1  0 0 0
... .x.3.o.3.o. ...       0  4  0 |  0  0  0  6   0  0   0 |  0  0  0  0  4  0  0   0  0  0  0   0 |  *  *  *  * 30  *  *   *  *  *  *  * | 0 0  0  1 1  0  1  0 0  0 0 | 0 1 1  0 1 0
.xx ... .ox ... ...&#x    0  2  4 |  0  0  1  0   4  2   2 |  0  0  0  0  0  2  0   2  0  1  0   0 |  *  *  *  *  * 90  *   *  *  *  *  * | 0 0  1  0 0  2  0  0 0  0 0 | 0 2 0  1 0 0
... .xo3.ox ... ...&#x    0  3  3 |  0  0  0  3   6  0   3 |  0  0  0  0  1  0  3   3  0  0  1   0 |  *  *  *  *  *  * 60   *  *  *  *  * | 0 0  1  0 0  0  2  0 0  0 0 | 0 2 0  0 1 0
... ... .ox3.oo ...&#x    0  1  3 |  0  0  0  0   3  0   3 |  0  0  0  0  0  0  0   3  0  0  0   1 |  *  *  *  *  *  *  * 120  *  *  *  * | 0 0  0  0 0  1  1  1 0  0 0 | 0 1 0  1 1 0
..x3..o3..x ... ...       0  0 12 |  0  0  0  0   0 12  12 |  0  0  0  0  0  0  0   0  4  6  4   0 |  *  *  *  *  *  *  *   * 15  *  *  * | 0 0  1  0 0  0  0  0 2  0 0 | 0 2 0  0 0 1
..x ... ..x3..o ...       0  0  6 |  0  0  0  0   0  3   6 |  0  0  0  0  0  0  0   0  0  3  0   2 |  *  *  *  *  *  *  *   *  * 60  *  * | 0 0  0  0 0  1  0  0 1  1 0 | 0 1 0  1 0 1
... ..o3..x3..o ...       0  0  6 |  0  0  0  0   0  0  12 |  0  0  0  0  0  0  0   0  0  0  4   4 |  *  *  *  *  *  *  *   *  *  * 30  * | 0 0  0  0 0  0  1  0 1  0 1 | 0 1 0  0 1 1
... ... ..x3..o3..o       0  0  4 |  0  0  0  0   0  0   6 |  0  0  0  0  0  0  0   0  0  0  0   4 |  *  *  *  *  *  *  *   *  *  *  * 30 | 0 0  0  0 0  0  0  1 0  1 1 | 0 0 0  1 1 1
------------------------+----------+------------------------+---------------------------------------+--------------------------------------+-----------------------------+-------------
o..3x..3o..3o.. ...      10  0  0 | 30  0  0  0   0  0   0 | 10 20  0  0  0  0  0   0  0  0  0   0 |  5  5  0  0  0  0  0   0  0  0  0  0 | 6 *  *  * *  *  *  * *  * * | 1 1 0  0 0 0
...3x..3o..3o..3o..       5  0  0 | 10  0  0  0   0  0   0 |  0 10  0  0  0  0  0   0  0  0  0   0 |  0  5  0  0  0  0  0   0  0  0  0  0 | * 6  *  * *  *  *  * *  * * | 1 0 1  0 0 0
oxx3xxo3oox ... ...&#xt   6 12 12 | 12 12  6 12  24 12  12 |  4  4  6 12  4 12 12  12  4  6  4   0 |  1  0  4  4  0  6  4   0  1  0  0  0 | * * 15  * *  *  *  * *  * * | 0 2 0  0 0 0
... xx.3oo.3oo. ...&#x    4  4  0 |  6  4  0  6   0  0   0 |  0  4  0  6  4  0  0   0  0  0  0   0 |  0  1  0  4  1  0  0   0  0  0  0  0 | * *  * 30 *  *  *  * *  * * | 0 1 1  0 0 0
... .x.3.o.3.o.3.o.       0  5  0 |  0  0  0 10   0  0   0 |  0  0  0  0 10  0  0   0  0  0  0   0 |  0  0  0  0  5  0  0   0  0  0  0  0 | * *  *  * 6  *  *  * *  * * | 0 0 1  0 1 0
.xx ... .ox3.oo ...&#x    0  2  6 |  0  0  1  0   6  3   6 |  0  0  0  0  0  3  0   6  0  3  0   2 |  0  0  0  0  0  3  0   2  0  1  0  0 | * *  *  * * 60  *  * *  * * | 0 1 0  1 0 0
... .xo3.ox3.oo ...&#x    0  4  6 |  0  0  0  6  12  0  12 |  0  0  0  0  4  0  6  12  0  0  4   4 |  0  0  0  0  1  0  4   4  0  0  1  0 | * *  *  * *  * 30  * *  * * | 0 1 0  0 1 0
... ... .ox3.oo3.oo&#x    0  1  4 |  0  0  0  0   4  0   6 |  0  0  0  0  0  0  0   6  0  0  0   4 |  0  0  0  0  0  0  0   4  0  0  0  1 | * *  *  * *  *  * 30 *  * * | 0 0 0  1 1 0
..x3..o3..x3..o ...       0  0 30 |  0  0  0  0   0 30  60 |  0  0  0  0  0  0  0   0 10 30 20  20 |  0  0  0  0  0  0  0   0  5 10  5  0 | * *  *  * *  *  *  * 6  * * | 0 1 0  0 0 1
..x ... ..x3..o3..o       0  0  8 |  0  0  0  0   0  4  12 |  0  0  0  0  0  0  0   0  0  6  0   8 |  0  0  0  0  0  0  0   0  0  4  0  2 | * *  *  * *  *  *  * * 15 * | 0 0 0  1 0 1
... ..o3..x3..o3..o       0  0 10 |  0  0  0  0   0  0  30 |  0  0  0  0  0  0  0   0  0  0 10  20 |  0  0  0  0  0  0  0   0  0  0  5  5 | * *  *  * *  *  *  * *  * 6 | 0 0 0  0 1 1
------------------------+----------+------------------------+---------------------------------------+--------------------------------------+-----------------------------+-------------
o..3x..3o..3o..3o..      15  0  0 | 60  0  0  0   0  0   0 | 20 60  0  0  0  0  0   0  0  0  0   0 | 15 30  0  0  0  0  0   0  0  0  0  0 | 6 6  0  0 0  0  0  0 0  0 0 | 1 * *  * * *
oxx3xxo3oox3ooo ...&#xt  10 20 30 | 30 20 10 30  60 30  60 | 10 20 10 30 20 30 30  60 10 30 20  20 |  5  5 10 20  5 30 20  20  5 10  5  0 | 1 0  5  5 0 10  5  0 1  0 0 | * 6 *  * * *
... xx.3oo.3oo.3oo.&#x    5  5  0 | 10  5  0 10   0  0   0 |  0 10  0 10 10  0  0   0  0  0  0   0 |  0  5  0 10  5  0  0   0  0  0  0  0 | 0 1  0  5 1  0  0  0 0  0 0 | * * 6  * * *
.xx ... .ox3.oo3oo.&#x    0  2  8 |  0  0  1  0   8  4  12 |  0  0  0  0  0  4  0  12  0  6  0   8 |  0  0  0  0  0  6  0   8  0  4  0  2 | 0 0  0  0 0  4  0  2 0  1 0 | * * * 15 * *
... .xo3.ox3.oo3.oo&#x    0  5 10 |  0  0  0 10  20  0  30 |  0  0  0  0 10  0 10  30  0  0 10  20 |  0  0  0  0  5  0 10  20  0  0  5  5 | 0 0  0  0 1  0  5  5 0  0 1 | * * *  * 6 *
..x3..o3..x3..o3..o       0  0 60 |  0  0  0  0   0 60 180 |  0  0  0  0  0  0  0   0 20 90 60 120 |  0  0  0  0  0  0  0   0 15 60 30 30 | 0 0  0  0 0  0  0  0 6 15 6 | * * *  * * 1

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