Rather than trying to cross every line segment just once, label the vertices of this network with values of 1 through 12 such that the sum of the intersections which lie on the perimeter of the internal quadrilaterals is the same.

With a multitude of solutions abound these following impositions are to be applied separately/individually as well:
1. L4=L5 and 3*L1 = 4*L3
2. L4=L5 and 2*L1 = 3*L3
3. L4=L5 and L3<10
where L1=A+B+C+DAA L2=E+F+G+H+IAA
AAAAL3=J+K+LAAAAAAL4=A+E+JAA
AAAAL5=D+I+L.

Each impost has 2 solutions which are not reflections. How many can you find?