  A geometric method for obtaining an infinite family of Cayley digraphs of
constant density on finite Abelian groups is presented. The method works for
any given degree and it is based on consecutive dilates of a minimum distance
diagram associated with a given initial Cayley digraph. The method is used to
obtain infinite families of dense or asymptotically dense Cayley digraphs. In
particular, for degree $d=3$, an infinite family of maximum known density is
proposed.
