Incidence matrix according to Dynkin symbol

xoox oxox&#x   → height(1,2) = height(3,4) = 1/sqrt(2) = 0.707107
                 height(1,3) = height(1,4) = height(2,3) = height(2,4) = sqrt(3)/2 = 0.866025

o... o...    & | 4 * * | 1 2 1 2 0 0 | 3 1 2 1 2 2 2 0 0 | 1 1 3 3 2 1 2 0 | 1 1 1 3
..o. ..o.      | * 1 * ♦ 0 0 4 0 4 0 | 0 2 0 0 4 0 8 4 0 | 0 0 4 0 4 4 4 1 | 1 0 2 4
...o ...o      | * * 4 | 0 0 0 2 1 2 | 0 0 2 2 0 1 2 2 1 | 0 2 0 2 2 2 1 1 | 0 1 2 2
---------------+-------+-------------+-------------------+-----------------+--------
x... ....    & | 2 0 0 | 2 * * * * * | 2 1 2 0 0 0 0 0 0 | 1 1 2 2 2 0 0 0 | 1 1 1 2
oo.. oo..&#x   | 2 0 0 | * 4 * * * * | 2 0 0 0 1 1 0 0 0 | 1 0 2 2 0 0 1 0 | 1 1 0 2
o.o. o.o.&#x & | 1 1 0 | * * 4 * * * | 0 1 0 0 2 0 2 0 0 | 0 0 3 0 2 1 2 0 | 1 0 1 3
o..o o..o&#x & | 1 0 1 | * * * 8 * * | 0 0 1 1 0 1 1 0 0 | 0 1 0 2 1 1 1 0 | 0 1 1 2
..oo ..oo&#x   | 0 1 1 | * * * * 4 * | 0 0 0 0 0 0 2 2 0 | 0 0 0 0 2 2 1 1 | 0 0 2 2
...x ....    & | 0 0 2 | * * * * * 4 | 0 0 1 1 0 0 0 1 1 | 0 2 0 1 1 1 0 1 | 0 1 2 1
---------------+-------+-------------+-------------------+-----------------+--------
xo.. ....&#x & | 3 0 0 | 1 2 0 0 0 0 | 4 * * * * * * * * | 1 0 1 1 0 0 0 0 | 1 1 0 1
x.o. ....&#x & | 2 1 0 | 1 0 2 0 0 0 | * 2 * * * * * * * | 0 0 2 0 2 0 0 0 | 1 0 1 2
x..x ....&#x & | 2 0 2 | 1 0 0 2 0 1 | * * 4 * * * * * * | 0 1 0 1 1 0 0 0 | 0 1 1 1
.... o..x&#x & | 1 0 2 | 0 0 0 2 0 1 | * * * 4 * * * * * | 0 1 0 1 0 1 0 0 | 0 1 1 1
ooo. ooo.&#x   | 2 1 0 | 0 1 2 0 0 0 | * * * * 4 * * * * | 0 0 2 0 0 0 1 0 | 1 0 0 2
oo.o oo.o&#x   | 2 0 1 | 0 1 0 2 0 0 | * * * * * 4 * * * | 0 0 0 2 0 0 1 0 | 0 1 0 2
o.oo o.oo&#x & | 1 1 1 | 0 0 1 1 1 0 | * * * * * * 8 * * | 0 0 0 0 1 1 1 0 | 0 0 1 2
..ox ....&#x & | 0 1 2 | 0 0 0 0 2 1 | * * * * * * * 4 * | 0 0 0 0 1 1 0 1 | 0 0 2 1
...x ...x      | 0 0 4 | 0 0 0 0 0 4 | * * * * * * * * 1 | 0 2 0 0 0 0 0 1 | 0 1 2 0
---------------+-------+-------------+-------------------+-----------------+--------
xo.. ox..&#x   ♦ 4 0 0 | 2 4 0 0 0 0 | 4 0 0 0 0 0 0 0 0 | 1 * * * * * * * | 1 1 0 0
x..x o..x&#x   ♦ 2 0 4 | 1 0 0 4 0 4 | 0 0 2 2 0 0 0 0 1 | * 2 * * * * * * | 0 1 1 0
xoo. ....&#x & ♦ 3 1 0 | 1 2 3 0 0 0 | 1 1 0 0 2 0 0 0 0 | * * 4 * * * * * | 1 0 0 1
xo.x ....&#x & ♦ 3 0 2 | 1 2 0 4 0 1 | 1 0 1 1 0 2 0 0 0 | * * * 4 * * * * | 0 1 0 1
x.ox ....&#x & ♦ 2 1 2 | 1 0 2 2 2 1 | 0 1 1 0 0 0 2 1 0 | * * * * 4 * * * | 0 0 1 1
.... o.ox&#x & ♦ 1 1 2 | 0 0 1 2 2 1 | 0 0 0 1 0 0 2 1 0 | * * * * * 4 * * | 0 0 1 1
oooo oooo&#x   ♦ 2 1 1 | 0 1 2 2 1 0 | 0 0 0 0 1 1 2 0 0 | * * * * * * 4 * | 0 0 0 2
..ox ..ox&#x   ♦ 0 1 4 | 0 0 0 0 4 4 | 0 0 0 0 0 0 0 4 1 | * * * * * * * 1 | 0 0 2 0
---------------+-------+-------------+-------------------+-----------------+--------
xoo. oxo.&#x   ♦ 4 1 0 | 2 4 4 0 0 0 | 4 2 0 0 4 0 0 0 0 | 1 0 4 0 0 0 0 0 | 1 * * *
xo.x ox.x&#x   ♦ 4 0 4 | 2 4 0 8 0 4 | 4 0 4 4 0 4 0 0 1 | 1 2 0 4 0 0 0 0 | * 1 * *
x.ox o.ox&#x & ♦ 2 1 4 | 1 0 2 4 4 4 | 0 1 2 2 0 0 4 4 1 | 0 1 0 0 2 2 0 1 | * * 2 *
xoox ....&#x & ♦ 3 1 2 | 1 2 3 4 2 1 | 1 1 1 1 2 2 4 1 0 | 0 0 1 1 1 1 2 0 | * * * 4