Incidence matrix
point || pseudo ike || cube → height(1,2) = (sqrt(5)-1)/4 = 0.309017
height(2,3) = (1+sqrt(5))/4 = 0.809017
1 * * | 12 0 0 0 0 | 6 24 0 0 0 0 0 0 | 12 8 0 0 0 0 verf: ike
* 12 * | 1 1 4 2 0 | 1 4 3 2 2 4 1 0 | 3 2 3 2 1 0
* * 8 | 0 0 0 3 3 | 0 0 0 0 3 3 3 3 | 0 0 3 1 3 1
-------+---------------+----------------------+--------------
1 1 0 | 12 * * * * | 1 4 0 0 0 0 0 0 | 3 2 0 0 0 0
0 2 0 | * 6 * * * | 1 0 2 0 2 0 0 0 | 2 0 2 0 1 0
0 2 0 | * * 24 * * | 0 1 1 1 0 1 0 0 | 1 1 1 1 0 0
0 1 1 | * * * 24 * | 0 0 0 0 1 2 1 0 | 0 0 2 1 1 0
0 0 2 | * * * * 12 | 0 0 0 0 1 0 1 2 | 0 0 1 0 2 1
-------+---------------+----------------------+--------------
1 2 0 | 2 1 0 0 0 | 6 * * * * * * * | 2 0 0 0 0 0
1 2 0 | 2 0 1 0 0 | * 24 * * * * * * | 1 1 0 0 0 0
0 3 0 | 0 1 2 0 0 | * * 12 * * * * * | 1 0 1 0 0 0
0 3 0 | 0 0 3 0 0 | * * * 8 * * * * | 0 1 0 1 0 0
0 2 2 | 0 1 0 2 1 | * * * * 12 * * * | 0 0 1 0 1 0
0 2 1 | 0 0 1 2 0 | * * * * * 24 * * | 0 0 1 1 0 0
0 1 2 | 0 0 0 2 1 | * * * * * * 12 * | 0 0 1 0 1 0
0 0 4 | 0 0 0 0 4 | * * * * * * * 6 | 0 0 0 0 1 1
-------+---------------+----------------------+--------------
1 3 0 | 3 1 2 0 0 | 1 2 1 0 0 0 0 0 | 12 * * * * * tet
1 3 0 | 3 0 3 0 0 | 0 3 0 1 0 0 0 0 | * 8 * * * * tet
0 3 2 | 0 1 2 4 1 | 0 0 1 0 1 2 1 0 | * * 12 * * * squippy
0 3 1 | 0 0 3 3 0 | 0 0 0 1 0 3 0 0 | * * * 8 * * tet
0 2 4 | 0 1 0 4 4 | 0 0 0 0 2 0 2 1 | * * * * 6 * trip
0 0 8 | 0 0 0 0 12 | 0 0 0 0 0 0 0 6 | * * * * * 1 cube