Incidence matrix according to Dynkin symbol

xo ox3oo ox3oo&#x   → height = 1/sqrt(12) = 0.288675
(pyramid product of line with triddip)

o. o.3o. o.3o.      | 2 * | 1  9  0 | 9 18 0 0 | 18  6  9 0 | 6 9  6 0 | 6 1
.o .o3.o .o3.o      | * 9 | 0  2  4 | 1  8 2 4 |  4  4  8 4 | 2 4  8 1 | 4 2
--------------------+-----+---------+----------+------------+----------+----
x. .. .. .. ..      | 2 0 | 1  *  * ♦ 9  0 0 0 | 18  0  0 0 | 6 9  0 0 | 6 0
oo oo3oo oo3oo&#x   | 1 1 | * 18  * | 1  4 0 0 |  4  2  4 0 | 2 4  4 0 | 4 1
.. .x .. .. ..    & | 0 2 | *  * 18 | 0  2 1 2 |  1  2  4 2 | 1 2  6 1 | 3 2
--------------------+-----+---------+----------+------------+----------+----
xo .. .. .. ..&#x   | 2 1 | 1  2  0 | 9  * * * |  4  0  0 0 | 2 4  0 0 | 4 0
.. ox .. .. ..&#x & | 1 2 | 0  2  1 | * 36 * * |  1  1  2 0 | 1 2  3 0 | 3 1
.. .x3.o .. ..    & | 0 3 | 0  0  3 | *  * 6 * |  0  2  0 2 | 1 0  4 1 | 2 2
.. .x .. .x ..      | 0 4 | 0  0  4 | *  * * 9 |  0  0  2 2 | 0 1  4 1 | 2 2
--------------------+-----+---------+----------+------------+----------+----
xo ox .. .. ..&#x & ♦ 2 2 | 1  4  1 | 2  2 0 0 | 18  *  * * | 1 2  0 0 | 3 0
.. ox3oo .. ..&#x & ♦ 1 3 | 0  3  3 | 0  3 1 0 |  * 12  * * | 1 0  2 0 | 2 1
.. ox .. ox ..&#x   ♦ 1 4 | 0  4  4 | 0  4 0 1 |  *  * 18 * | 0 1  2 0 | 2 1
.. .x3.o .x ..    & ♦ 0 6 | 0  0  9 | 0  0 2 3 |  *  *  * 6 | 0 0  2 1 | 1 2
--------------------+-----+---------+----------+------------+----------+----
xo ox3oo .. ..&#x & ♦ 2 3 | 1  6  3 | 3  6 1 0 |  3  2  0 0 | 6 *  * * | 2 0
xo ox .. ox ..&#x   ♦ 2 4 | 1  8  4 | 4  8 0 1 |  4  0  2 0 | * 9  * * | 2 0
.. ox3oo ox ..&#x & ♦ 1 6 | 0  6  9 | 0  9 2 3 |  0  2  3 1 | * * 12 * | 1 1
.. .x3.o .x3.o      ♦ 0 9 | 0  0 18 | 0  0 6 9 |  0  0  0 6 | * *  * 1 | 0 2
--------------------+-----+---------+----------+------------+----------+----
xo ox3oo ox ..&#x & ♦ 2 6 | 1 12  9 | 6 18 2 3 |  9  4  6 1 | 2 3  2 0 | 6 *
.. ox3oo ox3oo&#x   ♦ 1 9 | 0  9 18 | 0 18 6 9 |  0  6  9 6 | 0 0  6 1 | * 2

xoo oxo ooo3xox&#x   → height(1,2) = 1/sqrt(6) = 0.408248
                       height(1,3) = sqrt(3)/2 = 0.866025
                       height(2,3) = sqrt(5/12) = 0.645497

o.. o.. o..3o..    | 6 * * | 1 2  2 1 0 0 0 | 2 1 2 1  4 1 2  2 0 0 0 | 1 1 4 2 2 2 1 2 1  4 0 0 | 2 2 1 1 1 4 2 2 0 | 1 2 2 1
.o. .o. .o.3.o.    | * 2 * | 0 0  6 0 1 3 0 | 0 0 3 6  6 0 0  6 3 3 0 | 0 3 3 6 2 0 0 3 6  6 3 1 | 3 1 2 0 3 3 6 2 1 | 1 3 1 2
..o ..o ..o3..o    | * * 3 | 0 0  0 2 0 2 2 | 0 0 0 0  0 1 4  4 1 4 1 | 0 0 0 0 0 2 2 2 2  8 2 2 | 0 0 0 1 1 4 4 4 1 | 0 2 2 2
-------------------+-------+----------------+-------------------------+--------------------------+-------------------+--------
x.. ... ... ...    | 2 0 0 | 3 *  * * * * * | 2 0 2 0  0 1 0  0 0 0 0 | 1 1 4 0 0 2 0 2 0  0 0 0 | 2 2 0 1 1 4 0 0 0 | 1 2 2 0
... ... ... x..    | 2 0 0 | * 6  * * * * * | 1 1 0 0  2 0 1  0 0 0 0 | 1 0 2 1 2 1 1 0 0  2 0 0 | 1 2 1 1 0 2 1 2 0 | 1 1 2 1
oo. oo. oo.3oo.&#x | 1 1 0 | * * 12 * * * * | 0 0 1 1  2 0 0  1 0 0 0 | 0 1 2 2 1 0 0 1 1  2 0 0 | 2 1 1 0 1 2 2 1 0 | 1 2 1 1
o.o o.o o.o3o.o&#x | 1 0 1 | * *  * 6 * * * | 0 0 0 0  0 1 2  2 0 0 0 | 0 0 0 0 0 2 1 2 1  4 0 0 | 0 0 0 1 1 4 2 2 0 | 0 2 2 1
... .x. ... ...    | 0 2 0 | * *  * * 1 * * ♦ 0 0 0 6  0 0 0  0 3 0 0 | 0 3 0 6 0 0 0 0 6  0 3 0 | 3 0 2 0 3 0 6 0 1 | 1 3 0 2
.oo .oo .oo3.oo&#x | 0 1 1 | * *  * * * 6 * | 0 0 0 0  0 0 0  2 1 2 0 | 0 0 0 0 0 0 0 1 2  4 2 1 | 0 0 0 0 1 2 4 2 1 | 0 2 1 2
... ... ... ..x    | 0 0 2 | * *  * * * * 3 | 0 0 0 0  0 0 2  0 0 2 1 | 0 0 0 0 0 1 2 0 0  4 1 2 | 0 0 0 1 0 2 2 4 1 | 0 1 2 2
-------------------+-------+----------------+-------------------------+--------------------------+-------------------+--------
x.. ... ... x..    | 4 0 0 | 2 2  0 0 0 0 0 | 3 * * *  * * *  * * * * | 1 0 2 0 0 1 0 0 0  0 0 0 | 1 2 0 1 0 2 0 0 0 | 1 1 2 0
... ... o..3x..    | 3 0 0 | 0 3  0 0 0 0 0 | * 2 * *  * * *  * * * * | 1 0 0 0 2 0 1 0 0  0 0 0 | 0 2 1 1 0 0 0 2 0 | 1 0 2 1
xo. ... ... ...&#x | 2 1 0 | 1 0  2 0 0 0 0 | * * 6 *  * * *  * * * * | 0 1 2 0 0 0 0 1 0  0 0 0 | 2 1 0 0 1 2 0 0 0 | 1 2 1 0
... ox. ... ...&#x | 1 2 0 | 0 0  2 0 1 0 0 | * * * 6  * * *  * * * * | 0 1 0 2 0 0 0 0 1  0 0 0 | 2 0 1 0 1 0 2 0 0 | 1 2 0 1
... ... ... xo.&#x | 2 1 0 | 0 1  2 0 0 0 0 | * * * * 12 * *  * * * * | 0 0 1 1 1 0 0 0 0  1 0 0 | 1 1 1 0 0 1 1 1 0 | 1 1 1 1
x.o ... ... ...&#x | 2 0 1 | 1 0  0 2 0 0 0 | * * * *  * 3 *  * * * * | 0 0 0 0 0 2 0 2 0  0 0 0 | 0 0 0 1 1 4 0 0 0 | 0 2 2 0
... ... ... x.x&#x | 2 0 2 | 0 1  0 2 0 0 1 | * * * *  * * 6  * * * * | 0 0 0 0 0 1 1 0 0  2 0 0 | 0 0 0 1 0 2 1 2 0 | 0 1 2 1
ooo ooo ooo3ooo&#x | 1 1 1 | 0 0  1 1 0 1 0 | * * * *  * * * 12 * * * | 0 0 0 0 0 0 0 1 1  2 0 0 | 0 0 0 0 1 2 2 1 0 | 0 2 1 1
... .xo ... ...&#x | 0 2 1 | 0 0  0 0 1 2 0 | * * * *  * * *  * 3 * * | 0 0 0 0 0 0 0 0 2  0 2 0 | 0 0 0 0 1 0 4 0 1 | 0 2 0 2
... ... ... .ox&#x | 0 1 2 | 0 0  0 0 0 2 1 | * * * *  * * *  * * 6 * | 0 0 0 0 0 0 0 0 0  2 1 1 | 0 0 0 0 0 1 2 2 1 | 0 1 1 2
... ... ..o3..x    | 0 0 3 | 0 0  0 0 0 0 3 | * * * *  * * *  * * * 1 | 0 0 0 0 0 0 2 0 0  0 0 2 | 0 0 0 1 0 0 0 4 1 | 0 0 2 2
-------------------+-------+----------------+-------------------------+--------------------------+-------------------+--------
x.. ... o..3x..    ♦ 6 0 0 | 3 6  0 0 0 0 0 | 3 2 0 0  0 0 0  0 0 0 0 | 1 * * * * * * * *  * * * | 0 2 0 1 0 0 0 0 0 | 1 0 2 0
xo. ox. ... ...&#x ♦ 2 2 0 | 1 0  4 0 1 0 0 | 0 0 2 2  0 0 0  0 0 0 0 | * 3 * * * * * * *  * * * | 2 0 0 0 1 0 0 0 0 | 1 2 0 0
xo. ... ... xo.&#x ♦ 4 1 0 | 2 2  4 0 0 0 0 | 1 0 2 0  2 0 0  0 0 0 0 | * * 6 * * * * * *  * * * | 1 1 0 0 0 1 0 0 0 | 1 1 1 0
... ox. ... xo.&#x ♦ 2 2 0 | 0 1  4 0 1 0 0 | 0 0 0 2  2 0 0  0 0 0 0 | * * * 6 * * * * *  * * * | 1 0 1 0 0 0 1 0 0 | 1 1 0 1
... ... oo.3xo.&#x ♦ 3 1 0 | 0 3  3 0 0 0 0 | 0 1 0 0  3 0 0  0 0 0 0 | * * * * 4 * * * *  * * * | 0 1 1 0 0 0 0 1 0 | 1 0 1 1
x.o ... ... x.x&#x ♦ 4 0 2 | 2 2  0 4 0 0 1 | 1 0 0 0  0 2 2  0 0 0 0 | * * * * * 3 * * *  * * * | 0 0 0 1 0 2 0 0 0 | 0 1 2 0
... ... o.o3x.x&#x ♦ 3 0 3 | 0 3  0 3 0 0 3 | 0 1 0 0  0 0 3  0 0 0 1 | * * * * * * 2 * *  * * * | 0 0 0 1 0 0 0 2 0 | 0 0 2 1
xoo ... ... ...&#x ♦ 2 1 1 | 1 0  2 2 0 1 0 | 0 0 1 0  0 1 0  2 0 0 0 | * * * * * * * 6 *  * * * | 0 0 0 0 1 2 0 0 0 | 0 2 1 0
... oxo ... ...&#x ♦ 1 2 1 | 0 0  2 1 1 2 0 | 0 0 0 1  0 0 0  2 1 0 0 | * * * * * * * * 6  * * * | 0 0 0 0 1 0 2 0 0 | 0 2 0 1
... ... ... xox&#x ♦ 2 1 2 | 0 1  2 2 0 2 1 | 0 0 0 0  1 0 1  2 0 1 0 | * * * * * * * * * 12 * * | 0 0 0 0 0 1 1 1 0 | 0 1 1 1
... .xo ... .ox&#x ♦ 0 2 2 | 0 0  0 0 1 4 1 | 0 0 0 0  0 0 0  0 2 2 0 | * * * * * * * * *  * 3 * | 0 0 0 0 0 0 2 0 1 | 0 1 0 2
... ... .oo3.ox&#x ♦ 0 1 3 | 0 0  0 0 0 3 3 | 0 0 0 0  0 0 0  0 0 3 1 | * * * * * * * * *  * * 2 | 0 0 0 0 0 0 0 2 1 | 0 0 1 2
-------------------+-------+----------------+-------------------------+--------------------------+-------------------+--------
xo. ox. ... xo.&#x ♦ 4 2 0 | 2 2  8 0 1 0 0 | 1 0 4 4  4 0 0  0 0 0 0 | 0 2 2 2 0 0 0 0 0  0 0 0 | 3 * * * * * * * * | 1 1 0 0
xo. ... oo.3xo.&#x ♦ 6 1 0 | 3 6  6 0 0 0 0 | 3 2 3 0  6 0 0  0 0 0 0 | 1 0 3 0 2 0 0 0 0  0 0 0 | * 2 * * * * * * * | 1 0 1 0
... ox. oo.3xo.&#x ♦ 3 2 0 | 0 3  6 0 1 0 0 | 0 1 0 3  6 0 0  0 0 0 0 | 0 0 0 3 2 0 0 0 0  0 0 0 | * * 2 * * * * * * | 1 0 0 1
x.o ... o.o3x.x&#x ♦ 6 0 3 | 3 6  0 6 0 0 3 | 3 2 0 0  0 3 6  0 0 0 1 | 1 0 0 0 0 3 2 0 0  0 0 0 | * * * 1 * * * * * | 0 0 2 0
xoo oxo ... ...&#x ♦ 2 2 1 | 1 0  4 2 1 2 0 | 0 0 2 2  0 1 0  4 1 0 0 | 0 1 0 0 0 0 0 2 2  0 0 0 | * * * * 3 * * * * | 0 2 0 0
xoo ... ... xox&#x ♦ 4 1 2 | 2 2  4 4 0 2 1 | 1 0 2 0  2 2 2  4 0 1 0 | 0 0 1 0 0 1 0 2 0  2 0 0 | * * * * * 6 * * * | 0 1 1 0
... oxo ... xox&#x ♦ 2 2 2 | 0 1  4 2 1 4 1 | 0 0 0 2  2 0 1  4 2 2 0 | 0 0 0 1 0 0 0 0 2  2 1 0 | * * * * * * 6 * * | 0 1 0 1
... ... ooo3xox&#x ♦ 3 1 3 | 0 3  3 3 0 3 3 | 0 1 0 0  3 0 3  3 0 3 1 | 0 0 0 0 1 0 1 0 0  3 0 1 | * * * * * * * 4 * | 0 0 1 1
... .xo .oo3.ox&#x ♦ 0 2 3 | 0 0  0 0 1 6 3 | 0 0 0 0  0 0 0  0 3 6 1 | 0 0 0 0 0 0 0 0 0  0 3 2 | * * * * * * * * 1 | 0 0 0 2
-------------------+-------+----------------+-------------------------+--------------------------+-------------------+--------
xo. ox. oo.3xo.&#x ♦ 6 2 0 | 3 6 12 0 1 0 0 | 3 2 6 6 12 0 0  0 0 0 0 | 1 3 6 6 4 0 0 0 0  0 0 0 | 3 2 2 0 0 0 0 0 0 | 1 * * *
xoo oxo ... xox&#x ♦ 4 2 2 | 2 2  8 4 1 4 1 | 1 0 4 4  4 2 2  8 2 2 0 | 0 2 2 2 0 1 0 4 4  4 1 0 | 1 0 0 0 2 2 2 0 0 | * 3 * *
xoo ... ooo3xox&#x ♦ 6 1 3 | 3 6  6 6 0 3 3 | 3 2 3 0  6 3 6  6 0 3 1 | 1 0 3 0 2 3 2 3 0  6 0 1 | 0 1 0 1 0 3 0 2 0 | * * 2 *
... oxo ooo3xox&#x ♦ 3 2 3 | 0 3  6 3 1 6 3 | 0 1 0 3  6 0 3  6 3 6 1 | 0 0 0 3 2 0 1 0 3  6 3 2 | 0 0 1 0 0 0 3 2 1 | * * * 2