  The notion of $SL_2$-tiling is a generalization of that of classical
Coxeter-Conway frieze pattern. We classify doubly antiperiodic $SL_2$-tilings
that contain a rectangular domain of positive integers. Every such
$SL_2$-tiling corresponds to a pair of frieze patterns and a unimodular
$2\times2$-matrix with positive integer coefficients. We relate this notion to
triangulated $n$-gons in the Farey graph.
