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Incidence matrix according to Dynkin symbol

xxo oxx4ooo&#xt   → height(1,2) = 1/sqrt(2) = 0.707107
                    height(2,3) = sqrt(3)/2 = 0.866025
(line || pseudo cube || perp {4})

o.. o..4o..    | 2 * * | 1 4 0 0 0 0 | 4 4 0 0 0 0 0 | 4 1 0 0
.o. .o.4.o.    | * 8 * | 0 1 1 2 1 0 | 1 2 2 1 1 2 0 | 2 1 2 1
..o ..o4..o    | * * 4 | 0 0 0 0 2 2 | 0 0 0 0 1 4 1 | 0 0 2 2
---------------+-------+-------------+---------------+--------
x.. ... ...    | 2 0 0 | 1 * * * * * | 4 0 0 0 0 0 0 | 4 0 0 0
oo. oo.4oo.&#x | 1 1 0 | * 8 * * * * | 1 2 0 0 0 0 0 | 2 1 0 0
.x. ... ...    | 0 2 0 | * * 4 * * * | 1 0 2 0 1 0 0 | 2 0 2 0
... .x. ...    | 0 2 0 | * * * 8 * * | 0 1 1 1 0 1 0 | 1 1 1 1
.oo .oo4.oo&#x | 0 1 1 | * * * * 8 * | 0 0 0 0 1 2 0 | 0 0 2 1
... ..x ...    | 0 0 2 | * * * * * 4 | 0 0 0 0 0 2 1 | 0 0 1 2
---------------+-------+-------------+---------------+--------
xx. ... ...&#x | 2 2 0 | 1 2 1 0 0 0 | 4 * * * * * * | 2 0 0 0
... ox. ...&#x | 1 2 0 | 0 2 0 1 0 0 | * 8 * * * * * | 1 1 0 0
.x. .x. ...    | 0 4 0 | 0 0 2 2 0 0 | * * 4 * * * * | 1 0 1 0
... .x.4.o.    | 0 4 0 | 0 0 0 4 0 0 | * * * 2 * * * | 0 1 0 1
.xo ... ...&#x | 0 2 1 | 0 0 1 0 2 0 | * * * * 4 * * | 0 0 2 0
... .xx ...&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * 8 * | 0 0 1 1
... ..x4..o    | 0 0 4 | 0 0 0 0 0 4 | * * * * * * 1 | 0 0 0 2
---------------+-------+-------------+---------------+--------
xx. ox. ...&#x ♦ 2 4 0 | 1 4 2 2 0 0 | 2 2 1 0 0 0 0 | 4 * * *
... ox.4oo.&#x ♦ 1 4 0 | 0 4 0 4 0 0 | 0 4 0 1 0 0 0 | * 2 * *
.xo .xx ...&#x ♦ 0 4 2 | 0 0 2 2 4 1 | 0 0 1 0 2 2 0 | * * 4 *
... .xx4.oo&#x ♦ 0 4 4 | 0 0 0 4 4 4 | 0 0 0 1 0 4 1 | * * * 2