The Fano plane is the configuration consisting of the two-dimensional finite projective plane the Galois field of order 2 G F(2). It is not realizable over the real or rational numbers. The incidence structure of the Fano is plane illustrated above. It is a block design with ν = 7, k = 3, λ = 1, r = 3, and b = 7, the Steiner triple system S(7), and the unique 7_3 configuration. The Levi graph of the Fano plane is the Heawood graph. The connectivity of the Fano plane corresponds to the order-2 two-dimensional Apollonian network.
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