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Incidence matrix according to Dynkin symbol

ofxo3xooo3oooo&#xt   → height(1,2) = sqrt[3+sqrt(5)]/4 = 0.572061
                       height(2,3) = sqrt[7+3 sqrt(5)]/4 = 0.925615
                       height(3,4) = height = sqrt(5/8) = 0.790569
(oct || pseudo f-tet || pseudo tet || pt)

o...3o...3o...     | 6 * * * |  4  2 0 0 0 | 2 2 1  4 0 0 | 1 2 2 0
.o..3.o..3.o..     | * 4 * * |  0  3 1 0 0 | 0 0 3  3 0 0 | 0 3 1 0
..o.3..o.3..o.     | * * 4 * |  0  0 1 3 1 | 0 0 3  0 3 3 | 0 3 0 3
...o3...o3...o     | * * * 1 ♦  0  0 0 0 4 | 0 0 0  0 0 6 | 0 0 0 4
-------------------+---------+-------------+--------------+--------
.... x... ....     | 2 0 0 0 | 12  * * * * | 1 1 0  1 0 0 | 1 1 1 0
oo..3oo..3oo..&#x  | 1 1 0 0 |  * 12 * * * | 0 0 1  2 0 0 | 0 2 1 0
.oo.3.oo.3.oo.&#x  | 0 1 1 0 |  *  * 4 * * | 0 0 3  0 0 0 | 0 3 0 0
..x. .... ....     | 0 0 2 0 |  *  * * 6 * | 0 0 1  0 2 1 | 0 2 0 2
..oo3..oo3..oo&#x  | 0 0 1 1 |  *  * * * 4 | 0 0 0  0 0 3 | 0 0 0 3
-------------------+---------+-------------+--------------+--------
o...3x... ....     | 3 0 0 0 |  3  0 0 0 0 | 4 * *  * * * | 1 1 0 0
.... x...3o...     | 3 0 0 0 |  3  0 0 0 0 | * 4 *  * * * | 1 0 1 0
ofx. .... ....&#xt | 1 2 2 0 |  0  2 2 1 0 | * * 6  * * * | 0 2 0 0
.... xo.. ....&#x  | 2 1 0 0 |  1  2 0 0 0 | * * * 12 * * | 0 1 1 0
..x.3..o. ....     | 0 0 3 0 |  0  0 0 3 0 | * * *  * 4 * | 0 1 0 1
..xo .... ....&#x  | 0 0 2 1 |  0  0 0 1 2 | * * *  * * 6 | 0 0 0 2
-------------------+---------+-------------+--------------+--------
o...3x...3o...     ♦ 6 0 0 0 | 12  0 0 0 0 | 4 4 0  0 0 0 | 1 * * *
ofx.3xoo. ....&#xt ♦ 3 3 3 0 |  3  6 3 3 0 | 1 0 3  3 1 0 | * 4 * *
.... xo..3oo..&#x  ♦ 3 1 0 0 |  3  3 0 0 0 | 0 1 0  3 0 0 | * * 4 *
..xo3..oo ....&#x  ♦ 0 0 3 1 |  0  0 0 3 3 | 0 0 0  0 1 3 | * * * 4