We unify many integrable systems studied in discrete differential geometry into reductions of a common lattice equation system which we call a skew parallelogram net. By means of factorization we argue that skew parallelogram nets encompass all systems with a generic polynomial representation. We provide explicit factorization for discrete constant curvature surfaces. We propose a hierarchy of discrete curves in Euclidean space and in two-dimensional space forms and we identify elastic rods and constrained elastic curves as elements of the hierarchy.     «

We unify many integrable systems studied in discrete differential geometry into reductions of a common lattice equation system which we call a skew parallelogram net. By means of factorization we argue that skew parallelogram nets encompass all systems with a generic polynomial representation. We provide explicit factorization for discrete constant curvature surfaces. We propose a hierarchy of discrete curves in Euclidean space and in two-dimensional space forms and we identify elastic rods and...     »