Incidence matrix according to Dynkin symbol

xux3xoo3xo(-x)&#xt   → both heights = 0

o..3o..3o.  .      | 24 *  * |  1  1  1  1  0  0  0 | 1 1 1  1  1  1  0 0 0 0 | 1 1 1 1 0 0
.o.3.o.3.o  .      |  * 4  * |  0  0  0  6  3  0  0 | 0 0 0  6  3  3  3 0 0 0 | 0 3 3 1 1 0
..o3..o3..  o      |  * * 12 |  0  0  0  0  1  2  2 | 0 0 0  2  0  0  2 1 2 1 | 0 1 2 0 1 1  (coincide pairwise)
-------------------+---------+----------------------+-------------------------+------------
x.. ... ..  .      |  2 0  0 | 12  *  *  *  *  *  * | 1 1 0  1  0  0  0 0 0 0 | 1 1 1 0 0 0
... x.. ..  .      |  2 0  0 |  * 12  *  *  *  *  * | 1 0 1  0  1  0  0 0 0 0 | 1 1 0 1 0 0
... ... x.  .      |  2 0  0 |  *  * 12  *  *  *  * | 0 1 1  0  0  1  0 0 0 0 | 1 0 1 1 0 0
oo.3oo.3oo  . &#x  |  1 1  0 |  *  *  * 24  *  *  * | 0 0 0  1  1  1  0 0 0 0 | 0 1 1 1 0 0
.oo3.oo3.o  o &#x  |  0 1  1 |  *  *  *  * 12  *  * | 0 0 0  2  0  0  2 0 0 0 | 0 1 2 0 1 0
..x ... ..  .      |  0 0  2 |  *  *  *  *  * 12  * | 0 0 0  1  0  0  0 1 1 0 | 0 1 1 0 0 1  (coincides with following)
... ... ..(-x)     |  0 0  2 |  *  *  *  *  *  * 12 | 0 0 0  0  0  0  1 0 1 1 | 0 0 1 0 1 1  (coincides with previous)
-------------------+---------+----------------------+-------------------------+------------
x..3x.. ..  .      |  6 0  0 |  3  3  0  0  0  0  0 | 4 * *  *  *  *  * * * * | 1 1 0 0 0 0
x.. ... x.  .      |  4 0  0 |  2  0  2  0  0  0  0 | * 6 *  *  *  *  * * * * | 1 0 1 0 0 0
... x..3x.  .      |  6 0  0 |  0  3  3  0  0  0  0 | * * 4  *  *  *  * * * * | 1 0 0 1 0 0  (*)
xux ... ..  . &#xt |  2 2  2 |  1  0  0  2  2  1  0 | * * * 12  *  *  * * * * | 0 1 1 0 0 0
... xo. ..  . &#x  |  2 1  0 |  0  1  0  2  0  0  0 | * * *  * 12  *  * * * * | 0 1 0 1 0 0  (*)
... ... xo  . &#x  |  2 1  0 |  0  0  1  2  0  0  0 | * * *  *  * 12  * * * * | 0 0 1 1 0 0  (*)
... ... .o(-x)&#x  |  0 1  2 |  0  0  0  0  2  0  1 | * * *  *  *  * 12 * * * | 0 0 1 0 1 0
..x3..o ..  .      |  0 0  3 |  0  0  0  0  0  3  0 | * * *  *  *  *  * 4 * * | 0 1 0 0 0 1  (coincides with one-but-following)
..x ... ..(-x)     |  0 0  4 |  0  0  0  0  0  2  2 | * * *  *  *  *  * * 6 * | 0 0 1 0 0 1  (coincide pairwise)
... ..o3..(-x)     |  0 0  3 |  0  0  0  0  0  0  3 | * * *  *  *  *  * * * 4 | 0 0 0 0 1 1  (coincides with one-but-previous)
-------------------+---------+----------------------+-------------------------+------------
x..3x..3x.  .      | 24 0  0 | 12 12 12  0  0  0  0 | 4 6 4  0  0  0  0 0 0 0 | 1 * * * * *  toe
xux3xoo ..  . &#xt |  6 3  3 |  3  3  0  6  3  3  0 | 1 0 0  3  3  0  0 1 0 0 | * 4 * * * *  tut
xux ... xo(-x)&#xt |  4 2  4 |  2  0  2  4  4  2  2 | 0 1 0  2  0  2  2 0 1 0 | * * 6 * * *  ebot
... xo.3xo  . &#x  |  6 1  0 |  0  3  3  6  0  0  0 | 0 0 1  0  3  3  0 0 0 0 | * * * 4 * *  hippy (degenerate in turn)
... .oo3.o(-x)&#x  |  0 1  3 |  0  0  0  0  3  0  3 | 0 0 0  0  0  0  3 0 0 1 | * * * * 4 *  tet
..x3..o3..(-x)     |  0 0 12 |  0  0  0  0  0 12 12 | 0 0 0  0  0  0  0 4 6 4 | * * * * * 1  2thah

(*) all are coplanar