Fano plane

A diagram of the finite projective plane ${\displaystyle \mathbb {P} ^{2}(\mathbb {F} _{2})}$, a.k.a. Fano plane. (In this presentation of it, the labels are vectors over the finite field ${\displaystyle \mathbb {F} _{2}}$; vectors on the same line are linearly dependent. Vectors whose third component is zero are “at infinity”, whereas the ones whose third component is one form a 2x2 array, suggestive of ${\displaystyle \mathbb {F} _{2}^{2}}$.)