Acronym trihop Name triangle - heptapenton duoprism,vertex figure of breday Circumradius sqrt(16/21) = 0.872872 Volume sqrt(21)/23040 = 0.00019890 Confer general polytopal classes: segmentozetta

Incidence matrix according to Dynkin symbol

```x3o x3o3o3o3o3o

. . . . . . . . | 21 |  2  6 | 1 12  15 |  6  30  20 | 15  40 15 | 20 30  6 | 15 12 1 | 6 2
----------------+----+-------+----------+------------+-----------+----------+---------+----
x . . . . . . . |  2 | 21  * | 1  6   0 |  6  15   0 | 15  20  0 | 20 15  0 | 15  6 0 | 6 1
. . x . . . . . |  2 |  * 63 | 0  2   5 |  1  10  10 |  5  20 10 | 10 20  5 | 10 10 1 | 5 2
----------------+----+-------+----------+------------+-----------+----------+---------+----
x3o . . . . . . |  3 |  3  0 | 7  *   * ♦  6   0   0 | 15   0  0 | 20  0  0 | 15  0 0 | 6 0
x . x . . . . . |  4 |  2  2 | * 63   * |  1   5   0 |  5  10  0 | 10 10  0 | 10  5 0 | 5 1
. . x3o . . . . |  3 |  0  3 | *  * 105 |  0   2   4 |  1   8  6 |  4 12  4 |  6  8 1 | 4 2
----------------+----+-------+----------+------------+-----------+----------+---------+----
x3o x . . . . . ♦  6 |  6  3 | 2  3   0 | 21   *   * ♦  5   0  0 | 10  0  0 | 10  0 0 | 5 0
x . x3o . . . . ♦  6 |  3  6 | 0  3   2 |  * 105   * |  1   4  0 |  4  6  0 |  6  4 0 | 4 1
. . x3o3o . . . ♦  4 |  0  6 | 0  0   4 |  *   * 105 |  0   2  3 |  1  6  3 |  3  6 1 | 3 2
----------------+----+-------+----------+------------+-----------+----------+---------+----
x3o x3o . . . . ♦  9 |  9  9 | 3  9   3 |  3   3   0 | 35   *  * ♦  4  0  0 |  6  0 0 | 4 0
x . x3o3o . . . ♦  8 |  4 12 | 0  6   8 |  0   4   2 |  * 105  * |  1  3  0 |  3  3 0 | 3 1
. . x3o3o3o . . ♦  5 |  0 10 | 0  0  10 |  0   0   5 |  *   * 63 |  0  2  2 |  1  4 1 | 2 2
----------------+----+-------+----------+------------+-----------+----------+---------+----
x3o x3o3o . . . ♦ 12 | 12 18 | 4 18  12 |  6  12   3 |  4   3  0 | 35  *  * |  3  0 0 | 3 0
x . x3o3o3o . . ♦ 10 |  5 20 | 0 10  20 |  0  10  10 |  0   5  2 |  * 63  * |  1  2 0 | 2 1
. . x3o3o3o3o . ♦  6 |  0 15 | 0  0  20 |  0   0  15 |  0   0  6 |  *  * 21 |  0  2 1 | 1 2
----------------+----+-------+----------+------------+-----------+----------+---------+----
x3o x3o3o3o . . ♦ 15 | 15 30 | 5 30  30 | 10  30  15 | 10  15  3 |  5  3  0 | 21  * * | 2 0
x . x3o3o3o3o . ♦ 12 |  6 30 | 0 15  40 |  0  20  30 |  0  15 12 |  0  6  2 |  * 21 * | 1 1
. . x3o3o3o3o3o ♦  7 |  0 21 | 0  0  35 |  0   0  35 |  0   0 21 |  0  0  7 |  *  * 3 | 0 2
----------------+----+-------+----------+------------+-----------+----------+---------+----
x3o x3o3o3o3o . ♦ 18 | 18 45 | 6 45  60 | 15  60  45 | 20  45 18 | 15 18  3 |  6  3 0 | 7 *
x . x3o3o3o3o3o ♦ 14 |  7 42 | 0 21  70 |  0  35  70 |  0  35 42 |  0 21 14 |  0  7 2 | * 3
```

```ox xx3oo3oo3oo3oo3oo&#x   → height = sqrt(3)/2 = 0.866025
(hop || hopip)

o. o.3o.3o.3o.3o.3o.    | 7  * |  6  2 0  0 | 15 1 12  0  0 | 20  6 30  0  0 | 15 15 40  0  0 | 6 20 30  0  0 | 1 15 12 0 0 | 6 2 0
.o .o3.o3.o3.o3.o3.o    | * 14 |  0  1 1  6 |  0 1  6  6 15 |  0  6 15 15 20 |  0 15 20 20 15 | 0 20 15 15  6 | 0 15  6 6 1 | 6 1 1
------------------------+------+------------+---------------+----------------+----------------+---------------+-------------+------
.. x. .. .. .. .. ..    | 2  0 | 21  * *  * |  5 0  2  0  0 | 10  1 10  0  0 | 10  5 20  0  0 | 5 10 20  0  0 | 1 10 10 0 0 | 5 2 0
oo oo3oo3oo3oo3oo3oo&#x | 1  1 |  * 14 *  * |  0 1  6  0  0 |  0  6 15  0  0 |  0 15 20  0  0 | 0 20 15  0  0 | 0 15  6 0 0 | 6 1 0
.x .. .. .. .. .. ..    | 0  2 |  *  * 7  * |  0 1  0  6  0 |  0  6  0 15  0 |  0 15  0 20  0 | 0 20  0 15  0 | 0 15  0 6 0 | 6 0 1
.. .x .. .. .. .. ..    | 0  2 |  *  * * 42 |  0 0  1  1  5 |  0  1  5  5 10 |  0  5 10 10 10 | 0 10 10 10  5 | 0 10  5 5 1 | 5 1 1
------------------------+------+------------+---------------+----------------+----------------+---------------+-------------+------
.. x.3o. .. .. .. ..    | 3  0 |  3  0 0  0 | 35 *  *  *  * |  4  0  2  0  0 |  6  1  8  0  0 | 4  4 12  0  0 | 1  6  8 0 0 | 4 2 0
ox .. .. .. .. .. ..&#x | 1  2 |  0  2 1  0 |  * 7  *  *  * ♦  0  6  0  0  0 |  0 15  0  0  0 | 0 20  0  0  0 | 0 15  0 0 0 | 6 0 0
.. xx .. .. .. .. ..&#x | 2  2 |  1  2 0  1 |  * * 42  *  * |  0  1  5  0  0 |  0  5 10  0  0 | 0 10 10  0  0 | 0 10  5 0 0 | 5 1 0
.x .x .. .. .. .. ..    | 0  4 |  0  0 2  2 |  * *  * 21  * |  0  1  0  5  0 |  0  5  0 10  0 | 0 10  0 10  0 | 0 10  0 5 0 | 5 0 1
.. .x3.o .. .. .. ..    | 0  3 |  0  0 0  3 |  * *  *  * 70 |  0  0  1  1  4 |  0  1  4  4  6 | 0  4  6  6  4 | 0  6  4 4 1 | 4 1 1
------------------------+------+------------+---------------+----------------+----------------+---------------+-------------+------
.. x.3o.3o. .. .. ..    ♦ 4  0 |  6  0 0  0 |  4 0  0  0  0 | 35  *  *  *  * |  3  0  2  0  0 | 3  1  6  0  0 | 1  3  6 0 0 | 3 2 0
ox xx .. .. .. .. ..&#x ♦ 2  4 |  1  4 2  2 |  0 2  2  1  0 |  * 21  *  *  * ♦  0  5  0  0  0 | 0 10  0  0  0 | 0 10  0 0 0 | 5 0 0
.. xx3oo .. .. .. ..&#x ♦ 3  3 |  3  3 0  3 |  1 0  3  0  1 |  *  * 70  *  * |  0  1  4  0  0 | 0  4  6  0  0 | 0  6  4 0 0 | 4 1 0
.x .x3.o .. .. .. ..    ♦ 0  6 |  0  0 3  6 |  0 0  0  3  2 |  *  *  * 35  * |  0  1  0  4  0 | 0  4  0  6  0 | 0  6  0 4 0 | 4 0 1
.. .x3.o3.o .. .. ..    ♦ 0  4 |  0  0 0  6 |  0 0  0  0  4 |  *  *  *  * 70 |  0  0  1  1  3 | 0  1  3  3  3 | 0  3  3 3 1 | 3 1 1
------------------------+------+------------+---------------+----------------+----------------+---------------+-------------+------
.. x.3o.3o.3o. .. ..    ♦ 5  0 | 10  0 0  0 | 10 0  0  0  0 |  5  0  0  0  0 | 21  *  *  *  * | 2  0  2  0  0 | 1  1  4 0 0 | 2 2 0
ox xx3oo .. .. .. ..&#x ♦ 3  6 |  3  6 3  6 |  1 3  6  3  2 |  0  3  2  1  0 |  * 35  *  *  * ♦ 0  4  0  0  0 | 0  6  0 0 0 | 4 0 0
.. xx3oo3oo .. .. ..&#x ♦ 4  4 |  6  4 0  6 |  4 0  6  0  4 |  1  0  4  0  1 |  *  * 70  *  * | 0  1  3  0  0 | 0  3  3 0 0 | 3 1 0
.x .x3.o3.o .. .. ..    ♦ 0  8 |  0  0 4 12 |  0 0  0  6  8 |  0  0  0  4  2 |  *  *  * 35  * | 0  1  0  3  0 | 0  3  0 3 0 | 3 0 1
.. .x3.o3.o3.o .. ..    ♦ 0  5 |  0  0 0 10 |  0 0  0  0 10 |  0  0  0  0  5 |  *  *  *  * 42 | 0  0  1  1  2 | 0  1  2 2 1 | 2 1 1
------------------------+------+------------+---------------+----------------+----------------+---------------+-------------+------
.. x.3o.3o.3o.3o. ..    ♦ 6  0 | 15  0 0  0 | 20 0  0  0  0 | 15  0  0  0  0 |  6  0  0  0  0 | 7  *  *  *  * | 1  0  2 0 0 | 1 2 0
ox xx3oo3oo .. .. ..&#x ♦ 4  8 |  6  8 4 12 |  4 4 12  6  8 |  1  6  8  4  2 |  0  4  2  1  0 | * 35  *  *  * | 0  3  0 0 0 | 3 0 0
.. xx3oo3oo3oo .. ..&#x ♦ 5  5 | 10  5 0 10 | 10 0 10  0 10 |  5  0 10  0  5 |  1  0  5  0  1 | *  * 42  *  * | 0  1  2 0 0 | 2 1 0
.x .x3.o3.o3.o .. ..    ♦ 0 10 |  0  0 5 20 |  0 0  0 10 20 |  0  0  0 10 10 |  0  0  0  5  2 | *  *  * 21  * | 0  1  0 2 0 | 2 0 1
.. .x3.o3.o3.o3.o ..    ♦ 0  6 |  0  0 0 15 |  0 0  0  0 20 |  0  0  0  0 15 |  0  0  0  0  6 | *  *  *  * 14 | 0  0  1 1 1 | 1 1 1
------------------------+------+------------+---------------+----------------+----------------+---------------+-------------+------
.. .x3.o3.o3.o3.o3.o    ♦ 7  0 | 21  0 0  0 | 35 0  0  0  0 | 35  0  0  0  0 | 21  0  0  0  0 | 7  0  0  0  0 | 1  *  * * * | 0 2 0
ox xx3oo3oo3oo .. ..&#x ♦ 5 10 | 10 10 5 20 | 10 5 20 10 20 |  5 10 20 10 10 |  1 10 10  5  2 | 0  5  2  1  0 | * 21  * * * | 2 0 0
.. xx3oo3oo3oo3oo ..&#x ♦ 6  6 | 15  6 0 15 | 20 0 15  0 20 | 15  0 20  0 15 |  6  0 15  0  6 | 1  0  6  0  1 | *  * 14 * * | 1 1 0
.x .x3.o3.o3.o3.o ..    ♦ 0 12 |  0  0 6 30 |  0 0  0 15 40 |  0  0  0 20 30 |  0  0  0 15 12 | 0  0  0  6  2 | *  *  * 7 * | 1 0 1
.. .x3.o3.o3.o3.o3.o    ♦ 0  7 |  0  0 0 21 |  0 0  0  0 35 |  0  0  0  0 35 |  0  0  0  0 21 | 0  0  0  0  7 | *  *  * * 2 | 0 1 1
------------------------+------+------------+---------------+----------------+----------------+---------------+-------------+------
ox xx3oo3oo3oo3oo ..&#x ♦ 6 12 | 15 12 6 30 | 20 6 30 15 40 | 15 15 40 20 30 |  6 20 30 15 12 | 1 15 12  6  2 | 0  6  2 1 0 | 7 * *
.. xx3oo3oo3oo3oo3oo&#x ♦ 7  7 | 21  7 0 21 | 35 0 21  0 35 | 35  0 35  0 35 | 21  0 35  0 21 | 7  0 21  0  7 | 1  0  7 0 1 | * 2 *
.x .x3.o3.o3.o3.o3.o    ♦ 0 14 |  0  0 7 42 |  0 0  0 21 70 |  0  0  0 35 70 |  0  0  0 35 42 | 0  0  0 21 14 | 0  0  0 7 2 | * * 1
```