  A convex set with nonempty interior is maximal lattice-free if it is
inclusion-maximal with respect to the property of not containing integer points
in its interior. Maximal lattice-free convex sets are known to be polyhedra.
The precision of a rational polyhedron $P$ in $\mathbb{R}^d$ is the smallest
integer $s$ such that $sP$ is an integral polyhedron. In this paper we show
that, up to affine mappings preserving $\mathbb{Z}^d$, the number of maximal
lattice-free rational polyhedra of a given precision $s$ is finite.
Furthermore, we present the complete list of all maximal lattice-free integral
polyhedra in dimension three. Our results are motivated by recent research on
cutting plane theory in mixed-integer linear optimization.
