Abstract: Differential complexes that arise as so-called BGG (Bernstein-Gelfand-Gelfand) sequences play an important role in several applications. The original constructions of such sequences rely on substantial background from algebra and/or differential geometry that is not easily accessible. In simplified constructions in the situation needed in applications therefore quite a bit of ad-hoc input is needed. Usually, this involves sums of de Rham complexes which are related by maps, which are "cleverly chosen" in such a way that the cohomology remains unchanged and at the same time they allow for passage to a subcomplex that computes the same cohomology. My talk is devoted to a simple instance of the BGG construction, in which the complex one considers is just the standard de Rham complex of a domain $U_R^3$ and in which the maps mentioned above arise in a more natural way. This is based on work of M. Rumin in the 1990's and is related to a branch of differential geometry known as contact geometry. The resulting complex has smaller spaces (pairs of functions instead of triples of functions in degree 1 and 2) and one second order operator in addition to two simple first order operators. In addition, it  is still invariant under an infinite dimensional group of diffeomorphisms. I'll outline the constructions in the case of a special contact form on $R^3$ that can be restricted to any domain $U$.