Acronym hopalril
Name hop atop inverted ril,
hop-first cap of naq
Circumradius sqrt(3)/2 = 0.866025
Confer
uniform relative:
naq  
general polytopal classes:
segmentoexa   fundamental lace prisms  

Incidence matrix according to Dynkin symbol

xo3oo3oo3oo3ox3oo&#x   → height = 1/sqrt(7) = 0.377964
(hop || inv ril)

o.3o.3o.3o.3o.3o.    | 7  *   6  15   0 | 15  60  60   0  0 | 20  90 180  60  20   0  0 | 15  60 180 120  60  30   0  0  0 | 6 15  60  60  60  30  30  6  6 0 0 | 1 6 20 15  6 1 0
.o3.o3.o3.o3.o3.o    | * 21 |  0   5  10 |  0  10  40  20  5 |  0  10  60  60  20  20 10 |  0   5  40  60  30  40  30 10 10 | 0  1  10  20  20  20  30 10 20 2 5 | 0 2  5 10 10 5 1
---------------------+------+------------+-------------------+---------------------------+----------------------------------+------------------------------------+-----------------
x. .. .. .. .. ..    | 2  0 | 21   *   *   5  10   0   0  0 | 10  30  30   0   0   0  0 | 10  30  60  20  10   0   0  0  0 | 5 10  30  20  20   5   5  0  0 0 0 | 1 5 10  5  1 0 0
oo3oo3oo3oo3oo3oo&#x | 1  1 |  * 105   * |  0   4   8   0  0 |  0   6  24  12   4   0  0 |  0   4  24  24  12   8   6  0  0 | 0  1   8  12  12   8  12  2  4 0 0 | 0 2  4  6  4 1 0
.. .. .. .. .x ..    | 0  2 |  *   * 105 |  0   0   4   4  1 |  0   0   6  12   4   6  4 |  0   0   4  12   6  12  12  4  6 | 0  0   1   4   4   6  12  4 12 1 4 | 0 1  1  4  6 4 1
---------------------+------+------------+-------------------+---------------------------+----------------------------------+------------------------------------+-----------------
x.3o. .. .. .. ..    | 3  0 |  3   0   0 | 35   *   *   *  *   4   6   0   0   0   0  0 |  6  12  12   0   0   0   0  0  0 | 4  6  12   4   4   0   0  0  0 0 0 | 1 4  4  1  0 0 0
xo .. .. .. .. ..&#x | 2  1 |  1   2   0 |  * 210   *   *  * |  0   3   6   0   0   0  0 |  0   3  12   6   3   0   0  0  0 | 0  1   6   6   6   2   3  0  0 0 0 | 0 2  3  3  1 0 0
.. .. .. .. ox ..&#x | 1  2 |  0   2   1 |  *   * 420   *  * |  0   0   3   3   1   0  0 |  0   0   3   6   3   3   3  0  0 | 0  0   1   3   3   3   6  1  3 0 0 | 0 1  1  3  3 1 0
.. .. .. .o3.x ..    | 0  3 |  0   0   3 |  *   *   * 140  * |  0   0   0   3   0   3  1 |  0   0   0   3   0   6   3  3  3 | 0  0   0   1   0   3   3  3  6 1 3 | 0 1  0  1  3 3 1
.. .. .. .. .x3.o    | 0  3 |  0   0   3 |  *   *   *   * 35 |  0   0   0   0   4   0  4 |  0   0   0   0   6   0  12  0  6 | 0  0   0   0   4   0  12  0 12 0 4 | 0 0  1  4  6 4 1
---------------------+------+------------+-------------------+---------------------------+----------------------------------+------------------------------------+-----------------
x.3o.3o. .. .. ..     4  0 |  6   0   0 |  4   0   0   0  0 | 35   *   *   *   *   *  *   3   3   0   0   0   0   0  0  0 | 3  3   3   0   0   0   0  0  0 0 0 | 1 3  1  0  0 0 0
xo3oo .. .. .. ..&#x  3  1 |  3   3   0 |  1   3   0   0  0 |  * 210   *   *   *   *  * |  0   2   4   0   0   0   0  0  0 | 0  1   4   2   2   0   0  0  0 0 0 | 0 2  2  1  0 0 0
xo .. .. .. ox ..&#x  2  2 |  1   4   1 |  0   2   2   0  0 |  *   * 630   *   *   *  * |  0   0   2   2   1   0   0  0  0 | 0  0   1   2   2   1   2  0  0 0 0 | 0 1  1  2  1 0 0
.. .. .. oo3ox ..&#x  1  3 |  0   3   3 |  0   0   3   1  0 |  *   *   * 420   *   *  * |  0   0   0   2   0   2   1  0  0 | 0  0   0   1   0   2   2  1  2 0 0 | 0 1  0  1  2 1 0
.. .. .. .. ox3oo&#x  1  3 |  0   3   3 |  0   0   3   0  1 |  *   *   *   * 140   *  * |  0   0   0   0   3   0   3  0  0 | 0  0   0   0   3   0   6  0  3 0 0 | 0 0  1  3  3 1 0
.. .. .o3.o3.x ..     0  4 |  0   0   6 |  0   0   0   4  0 |  *   *   *   *   * 105  * |  0   0   0   0   0   2   0  2  1 | 0  0   0   0   0   1   0  2  2 1 2 | 0 1  0  0  1 2 1
.. .. .. .o3.x3.o     0  6 |  0   0  12 |  0   0   0   4  4 |  *   *   *   *   *   * 35 |  0   0   0   0   0   0   3  0  3 | 0  0   0   0   0   0   3  0  6 0 3 | 0 0  0  1  3 3 1
---------------------+------+------------+-------------------+---------------------------+----------------------------------+------------------------------------+-----------------
x.3o.3o.3o. .. ..     5  0 | 10   0   0 | 10   0   0   0  0 |  5   0   0   0   0   0  0 | 21   *   *   *   *   *   *  *  * | 2  1   0   0   0   0   0  0  0 0 0 | 1 2  0  0  0 0 0
xo3oo3oo .. .. ..&#x  4  1 |  6   4   0 |  4   6   0   0  0 |  1   4   0   0   0   0  0 |  * 105   *   *   *   *   *  *  * | 0  1   2   0   0   0   0  0  0 0 0 | 0 2  1  0  0 0 0
xo3oo .. .. ox ..&#x  3  2 |  3   6   1 |  1   6   3   0  0 |  0   2   3   0   0   0  0 |  *   * 420   *   *   *   *  *  * | 0  0   1   1   1   0   0  0  0 0 0 | 0 1  1  1  0 0 0
xo .. .. oo3ox ..&#x  2  3 |  1   6   3 |  0   3   6   1  0 |  0   0   3   2   0   0  0 |  *   *   * 420   *   *   *  *  * | 0  0   0   1   0   1   1  0  0 0 0 | 0 1  0  1  1 0 0
xo .. .. .. ox3oo&#x  2  3 |  1   6   3 |  0   3   6   0  1 |  0   0   3   0   2   0  0 |  *   *   *   * 210   *   *  *  * | 0  0   0   0   2   0   2  0  0 0 0 | 0 0  1  2  1 0 0
.. .. oo3oo3ox ..&#x  1  4 |  0   4   6 |  0   0   6   4  0 |  0   0   0   4   0   1  0 |  *   *   *   *   * 210   *  *  * | 0  0   0   0   0   1   0  1  1 0 0 | 0 1  0  0  1 1 0
.. .. .. oo3ox3oo&#x  1  6 |  0   6  12 |  0   0  12   4  4 |  0   0   0   4   4   0  1 |  *   *   *   *   *   * 105  *  * | 0  0   0   0   0   0   2  0  2 0 0 | 0 0  0  1  2 1 0
.. .o3.o3.o3.x ..     0  5 |  0   0  10 |  0   0   0  10  0 |  0   0   0   0   0   5  0 |  *   *   *   *   *   *   * 42  * | 0  0   0   0   0   0   0  1  0 1 1 | 0 1  0  0  0 1 1
.. .. .o3.o3.x3.o     0 10 |  0   0  30 |  0   0   0  20 10 |  0   0   0   0   0   5  5 |  *   *   *   *   *   *   *  * 21 | 0  0   0   0   0   0   0  0  2 0 2 | 0 0  0  0  1 2 1
---------------------+------+------------+-------------------+---------------------------+----------------------------------+------------------------------------+-----------------
x.3o.3o.3o.3o. ..     6  0 | 15   0   0 | 20   0   0   0  0 | 15   0   0   0   0   0  0 |  6   0   0   0   0   0   0  0  0 | 7  *   *   *   *   *   *  *  * * * | 1 1  0  0  0 0 0
xo3oo3oo3oo .. ..&#x  5  1 | 10   5   0 | 10  10   0   0  0 |  5  10   0   0   0   0  0 |  1   5   0   0   0   0   0  0  0 | * 21   *   *   *   *   *  *  * * * | 0 2  0  0  0 0 0
xo3oo3oo .. ox ..&#x  4  2 |  6   8   1 |  4  12   4   0  0 |  1   8   6   0   0   0  0 |  0   2   4   0   0   0   0  0  0 | *  * 105   *   *   *   *  *  * * * | 0 1  1  0  0 0 0
xo3oo .. oo3ox ..&#x  3  3 |  3   9   3 |  1   9   9   1  0 |  0   3   9   3   0   0  0 |  0   0   3   3   0   0   0  0  0 | *  *   * 140   *   *   *  *  * * * | 0 1  0  1  0 0 0
xo3oo .. .. ox3oo&#x  3  3 |  3   9   3 |  1   9   9   0  1 |  0   3   9   0   3   0  0 |  0   0   3   0   3   0   0  0  0 | *  *   *   * 140   *   *  *  * * * | 0 0  1  1  0 0 0
xo .. oo3oo3ox ..&#x  2  4 |  1   8   6 |  0   4  12   4  0 |  0   0   6   8   0   1  0 |  0   0   0   4   0   2   0  0  0 | *  *   *   *   * 105   *  *  * * * | 0 1  0  0  1 0 0
xo .. .. oo3ox3oo&#x  2  6 |  1  12  12 |  0   6  24   4  4 |  0   0  12   8   8   0  1 |  0   0   0   4   4   0   2  0  0 | *  *   *   *   *   * 105  *  * * * | 0 0  0  1  1 0 0
.. oo3oo3oo3ox ..&#x  1  5 |  0   5  10 |  0   0  10  10  0 |  0   0   0  10   0   5  0 |  0   0   0   0   0   5   0  1  0 | *  *   *   *   *   *   * 42  * * * | 0 1  0  0  0 1 0
.. .. oo3oo3ox3oo&#x  1 10 |  0  10  30 |  0   0  30  20 10 |  0   0   0  20  10   5  5 |  0   0   0   0   0   5   5  0  1 | *  *   *   *   *   *   *  * 42 * * | 0 0  0  0  1 1 0
.o3.o3.o3.o3.x ..     0  6 |  0   0  15 |  0   0   0  20  0 |  0   0   0   0   0  15  0 |  0   0   0   0   0   0   0  6  0 | *  *   *   *   *   *   *  *  * 7 * | 0 1  0  0  0 0 1
.. .o3.o3.o3.x3.o     0 15 |  0   0  60 |  0   0   0  60 20 |  0   0   0   0   0  30 15 |  0   0   0   0   0   0   0  6  6 | *  *   *   *   *   *   *  *  * * 7 | 0 0  0  0  0 1 1
---------------------+------+------------+-------------------+---------------------------+----------------------------------+------------------------------------+-----------------
x.3o.3o.3o.3o.3o.     7  0 | 21   0   0 | 35   0   0   0  0 | 35   0   0   0   0   0  0 | 21   0   0   0   0   0   0  0  0 | 7  0   0   0   0   0   0  0  0 0 0 | 1 *  *  *  * * *
xo3oo3oo3oo3ox ..&#x  6  6 | 15  30  15 | 20  60  60  20  0 | 15  60  90  60   0  15  0 |  6  30  60  60   0  30   0  6  0 | 1  6  15  20   0  15   0  6  0 1 0 | * 7  *  *  * * *
xo3oo3oo .. ox3oo&#x  4  3 |  6  12   3 |  4  18  12   0  1 |  1  12  18   0   4   0  0 |  0   3  12   0   6   0   0  0  0 | 0  0   3   0   4   0   0  0  0 0 0 | * * 35  *  * * *
xo3oo .. oo3ox3oo&#x  3  6 |  3  18  12 |  1  18  36   4  4 |  0   6  36  12  12   0  1 |  0   0  12  12  12   0   3  0  0 | 0  0   0   4   4   0   3  0  0 0 0 | * *  * 35  * * *
xo .. oo3oo3ox3oo&#x  2 10 |  1  20  30 |  0  10  60  20 10 |  0   0  30  40  20   5  5 |  0   0   0  20  10  10  10  0  1 | 0  0   0   0   0   5   5  0  2 0 0 | * *  *  * 21 * *
.. oo3oo3oo3ox3oo&#x  1 15 |  0  15  60 |  0   0  60  60 20 |  0   0   0  60  20  30 15 |  0   0   0   0   0  30  15  6  6 | 0  0   0   0   0   0   0  6  6 0 1 | * *  *  *  * 7 *
.o3.o3.o3.o3.x3.o     0 21 |  0   0 105 |  0   0   0 140 35 |  0   0   0   0   0 105 35 |  0   0   0   0   0   0   0 42 21 | 0  0   0   0   0   0   0  0  0 7 7 | * *  *  *  * * 1

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