A semiplane is a collection of lines such that every pair of lines intersects in a unique point. Semiplanes provide a natural starting point for computer searches to find projective planes with certain properties, e.g., planes of non-prime-power order.
A non-desarguean configuration can generate 845 distinct semiplanes, which fall into 105 isomorphism classes. Of these, 15 are minimal in the sense that every non-desarguean plane must contain one of these semiplanes.
This is joint work with Jiajia Seffrood.