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