Incidence matrix according to Dynkin symbol

ooo3xoo3ooo3oxo3ooo&#x   → height(1,2) = height(1,3) = height(2,3) = 1/sqrt(3) = 0.577350
                           height(12,3) = 1/2

o..3o..3o..3o..3o..    & | 30 * |   8  6  1 |  4  12  36   8  6 |  6  8  16  16  24  4  12  36 |  4  2  7  20  8  6  8  16  16  24 | 1  6  4  4  2  7  20  8 | 1 1  6  4
..o3..o3..o3..o3..o      |  * 1 ♦   0  0 30 |  0   0   0 120 90 |  0  0   0   0   0 40 120 360 |  0  0  0   0  0 30 60 120 120 180 | 0  0  0 12 12 30 120 30 | 0 2 12 20
-------------------------+------+-----------+-------------------+------------------------------+-----------------------------------+-------------------------+----------
... x.. ... ... ...    & |  2 0 | 120  *  * |  1   3   3   1  0 |  3  3   3   3   3  1   3   3 |  3  1  3   4  3  3  3   3   3   3 | 1  4  1  3  1  3   4  3 | 1 1  4  1
oo.3oo.3oo.3oo.3oo.&#x   |  2 0 |   * 90  * |  0   0   8   0  1 |  0  0   4   4   8  0   0   8 |  0  0  2   8  4  0  0   4   4   8 | 0  4  2  0  0  2   8  4 | 1 0  4  2
o.o3o.o3o.o3o.o3o.o&#x & |  1 1 |   *  * 30 ♦  0   0   0   8  6 |  0  0   0   0   0  4  12  36 |  0  0  0   0  0  6  8  16  16  24 | 0  0  0  4  2  7  20  8 | 0 1  6  4
-------------------------+------+-----------+-------------------+------------------------------+-----------------------------------+-------------------------+----------
o..3x.. ... ... ...    & |  3 0 |   3  0  0 | 40   *   *   *  * |  3  0   3   0   0  1   0   0 |  3  0  3   3  0  3  0   3   0   0 | 1  3  1  3  0  3   3  0 | 1 1  3  1
... x..3o.. ... ...    & |  3 0 |   3  0  0 |  * 120   *   *  * |  1  2   0   1   0  0   1   0 |  2  1  1   0  2  1  2   0   1   0 | 1  3  0  2  1  1   0  2 | 1 1  3  0
... xo. ... ... ...&#x & |  3 0 |   1  2  0 |  *   * 360   *  * |  0  0   1   1   2  0   0   1 |  0  0  1   3  2  0  0   1   1   2 | 0  3  1  0  0  1   3  2 | 1 0  3  1
... x.o ... ... ...&#x & |  2 1 |   1  0  2 |  *   *   * 120  * |  0  0   0   0   0  1   3   3 |  0  0  0   0  0  3  3   3   3   3 | 0  0  0  3  1  3   4  3 | 0 1  4  1
ooo3ooo3ooo3ooo3ooo&#x   |  2 1 |   0  1  2 |  *   *   *   * 90 ♦  0  0   0   0   0  0   0   8 |  0  0  0   0  0  0  0   4   4   8 | 0  0  0  0  0  2   8  4 | 0 0  4  2
-------------------------+------+-----------+-------------------+------------------------------+-----------------------------------+-------------------------+----------
o..3x..3o.. ... ...    & ♦  6 0 |  12  0  0 |  4   4   0   0  0 | 30  *   *   *   *  *   *   * |  2  0  1   0  0  1  0   0   0   0 | 1  2  0  2  0  1   0  0 | 1 1  2  0
... x..3o..3o.. ...    & ♦  4 0 |   6  0  0 |  0   4   0   0  0 |  * 60   *   *   *  *   *   * |  1  1  0   0  1  0  1   0   0   0 | 1  2  0  1  1  0   0  1 | 1 1  2  0
oo.3xo. ... ... ...&#x & ♦  4 0 |   3  3  0 |  1   0   3   0  0 |  *  * 120   *   *  *   *   * |  0  0  1   2  0  0  0   1   0   0 | 0  2  1  0  0  1   2  0 | 1 0  2  1
... xo.3oo. ... ...&#x & ♦  4 0 |   3  3  0 |  0   1   3   0  0 |  *  *   * 120   *  *   *   * |  0  0  1   0  2  0  0   0   1   0 | 0  3  0  0  0  1   0  2 | 1 0  3  0
... xo. ... ox. ...&#x   ♦  4 0 |   2  4  0 |  0   0   4   0  0 |  *  *   *   * 180  *   *   * |  0  0  0   2  1  0  0   0   0   1 | 0  2  1  0  0  0   2  1 | 1 0  2  1
o.o3x.o ... ... ...&#x & ♦  3 1 |   3  0  3 |  1   0   0   3  0 |  *  *   *   *   * 40   *   * |  0  0  0   0  0  3  0   3   0   0 | 0  0  0  3  0  3   3  0 | 0 1  3  1
... x.o3o.o ... ...&#x & ♦  3 1 |   3  0  3 |  0   1   0   3  0 |  *  *   *   *   *  * 120   * |  0  0  0   0  0  1  2   0   1   0 | 0  0  0  2  1  1   0  2 | 0 1  3  0
... xoo ... ... ...&#x & ♦  3 1 |   1  2  3 |  0   0   1   1  2 |  *  *   *   *   *  *   * 360 |  0  0  0   0  0  0  0   1   1   2 | 0  0  0  0  0  1   3  2 | 0 0  3  1
-------------------------+------+-----------+-------------------+------------------------------+-----------------------------------+-------------------------+----------
o..3x..3o..3o.. ...    & ♦ 10 0 |  30  0  0 | 10  20   0   0  0 |  5  5   0   0   0  0   0   0 | 12  *  *   *  *  *  *   *   *   * | 1  1  0  1  0  0   0  0 | 1 1  1  0
... x..3o..3o..3o..    & ♦  5 0 |  10  0  0 |  0  10   0   0  0 |  0  5   0   0   0  0   0   0 |  * 12  *   *  *  *  *   *   *   * | 1  1  0  0  1  0   0  0 | 1 1  1  0
oo.3xo.3oo. ... ...&#x & ♦  7 0 |  12  6  0 |  4   4  12   0  0 |  1  0   4   4   0  0   0   0 |  *  * 30   *  *  *  *   *   *   * | 0  2  0  0  0  1   0  0 | 1 0  2  0
oo.3xo. ... ox. ...&#x & ♦  5 0 |   4  6  0 |  1   0   9   0  0 |  0  0   2   0   3  0   0   0 |  *  *  * 120  *  *  *   *   *   * | 0  1  1  0  0  0   1  0 | 1 0  1  1
... xo.3oo.3ox. ...&#x   ♦  8 0 |  12 12  0 |  0   8  24   0  0 |  0  2   0   8   6  0   0   0 |  *  *  *   * 30  *  *   *   *   * | 0  2  0  0  0  0   0  1 | 1 0  2  0
o.o3x.o3o.o ... ...&#x & ♦  6 1 |  12  0  6 |  4   4   0  12  0 |  1  0   0   0   0  4   4   0 |  *  *  *   *  * 30  *   *   *   * | 0  0  0  2  0  1   0  0 | 0 1  2  0
... x.o3o.o3o.o ...&#x & ♦  4 1 |   6  0  4 |  0   4   0   6  0 |  0  1   0   0   0  0   4   0 |  *  *  *   *  *  * 60   *   *   * | 0  0  0  1  1  0   0  1 | 0 1  2  0
ooo3xoo ... ... ...&#x & ♦  4 1 |   3  3  4 |  1   0   3   3  3 |  0  0   1   0   0  1   0   3 |  *  *  *   *  *  *  * 120   *   * | 0  0  0  0  0  1   2  0 | 0 0  2  1
... xoo3ooo ... ...&#x & ♦  4 1 |   3  3  4 |  0   1   3   3  3 |  0  0   0   1   0  0   1   3 |  *  *  *   *  *  *  *   * 120   * | 0  0  0  0  0  1   0  2 | 0 0  3  0
... xoo ... oxo ...&#x   ♦  4 1 |   2  4  4 |  0   0   4   2  4 |  0  0   0   0   1  0   0   4 |  *  *  *   *  *  *  *   *   * 180 | 0  0  0  0  0  0   2  1 | 0 0  2  1
-------------------------+------+-----------+-------------------+------------------------------+-----------------------------------+-------------------------+----------
o..3x..3o..3o..3o..    & ♦ 15 0 |  60  0  0 | 20  60   0   0  0 | 15 30   0   0   0  0   0   0 |  6  6  0   0  0  0  0   0   0   0 | 2  *  *  *  *  *   *  * | 1 1  0  0
oo.3xo.3oo.3ox. ...&#x & ♦ 15 0 |  40 30  0 | 10  30  90   0  0 |  5 10  20  30  30  0   0   0 |  1  1  5  10  5  0  0   0   0   0 | * 12  *  *  *  *   *  * | 1 0  1  0
oo.3xo. ... ox.3oo.&#x   ♦  6 0 |   6  9  0 |  2   0  18   0  0 |  0  0   6   0   9  0   0   0 |  0  0  0   6  0  0  0   0   0   0 | *  * 20  *  *  *   *  * | 1 0  0  1
o.o3x.o3o.o3o.o ...&#x & ♦ 10 1 |  30  0 10 | 10  20   0  30  0 |  5  5   0   0   0 10  20   0 |  1  0  0   0  0  5  5   0   0   0 | *  *  * 12  *  *   *  * | 0 1  1  0
... x.o3o.o3o.o3o.o&#x & ♦  5 1 |  10  0  5 |  0  10   0  10  0 |  0  5   0   0   0  0  10   0 |  0  1  0   0  0  0  5   0   0   0 | *  *  *  * 12  *   *  * | 0 1  1  0
ooo3xoo3ooo ... ...&#x & ♦  7 1 |  12  6  7 |  4   4  12  12  6 |  1  0   4   4   0  4   4  12 |  0  0  1   0  0  1  0   4   4   0 | *  *  *  *  * 30   *  * | 0 0  2  0
ooo3xoo ... oxo ...&#x & ♦  5 1 |   4  6  5 |  1   0   9   4  6 |  0  0   2   0   3  1   0   9 |  0  0  0   1  0  0  0   2   0   3 | *  *  *  *  *  * 120  * | 0 0  1  1
... xoo3ooo3oxo ...&#x   ♦  8 1 |  12 12  8 |  0   8  24  12 12 |  0  2   0   8   6  0   8  24 |  0  0  0   0  1  0  2   0   8   6 | *  *  *  *  *  *   * 30 | 0 0  2  0
-------------------------+------+-----------+-------------------+------------------------------+-----------------------------------+-------------------------+----------
oo.3xo.3oo.3ox.3oo.&#x   ♦ 30 0 | 120 90  0 | 40 120 360   0  0 | 30 60 120 120 180  0   0   0 | 12 12 30 120 30  0  0   0   0   0 | 2 12 20  0  0  0   0  0 | 1 *  *  *
o.o3x.o3o.o3o.o3o.o&#x   ♦ 15 1 |  60  0 15 | 20  60   0  60  0 | 15 30   0   0   0 20  60   0 |  6  6  0   0  0 15 30   0   0   0 | 1  0  0  6  6  0   0  0 | * 2  *  *
ooo3xoo3ooo3oxo ...&#x & ♦ 15 1 |  40 30 15 | 10  30  90  40 30 |  5 10  20  30  30 10  30  90 |  1  1  5  10  5  5 10  20  30  30 | 0  1  0  1  1  5  10  5 | * * 12  *
ooo3xoo ... oxo3ooo&#x   ♦  6 1 |   6  9  6 |  2   0  18   6  9 |  0  0   6   0   9  2   0  18 |  0  0  0   6  0  0  0   6   0   9 | 0  0  1  0  0  0   6  0 | * *  * 20