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Definition 1. An affine plane is a pair $(X,\mathcal L)$ consisting of a set $X$ and a family $\mathcal L$ of subsets of $X$ called lines which satisfy the following axioms: Any distinct points $x,y\...

On this web-site, devoted to the Lenz-Barlotti classification of projective planes, it is written that the class IVa.3 (and its dual IVb.3) is somewhat exceptional, because it contains exactly one ...