Fano configuration

The Fano plane is the configuration consisting of the two-dimensional finite projective plane over G F(2) ("of order two"), 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.

configuration | design | Fano's geometry | Heawood graph | projective plane | Steiner triple system | Transylvania lottery