Fano plane
= Fano plane
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The Fano plane is the <projective plane> over the <finite field> $\mathbb F_2$. It has seven points and seven lines, each line contains three points, and two distinct lines meet in one point. A line-point incidence matrix $N$ therefore satisfies $NN^{\mathsf T}=2I+J$, making it invertible over the real numbers and useful for the <transplantation theorem>.