find internal rhombi from a list of lines defined by point tuples

Question

I have a image like this:

I have code to extract the lines in the form [x1,x2,y1,y2] Now i need to extract the internal rhombi, one could bruteforce combinations and check for intersections easily, but I was hoping a named, optimal algorithm existed, as the combinatoric explosion would ruin the server,

Any help appreciated