The Fano plane is the projective plane over the finite field$\mathbf{F}_2$ with two elements. It is denoted either $\mathbb{F}_2\mathbb{P}^2$, $\mathbb{P}^2_{\mathbb{F}_2}$ (in algebraic geometry), or $PG(2,2)$ (in finite geometry). It is often pictured as at right, but there are many different representations.