  We report on the implementation of an algorithm for computing the set of all
regular triangulations of finitely many points in Euclidean space. This
algorithm, which we call down-flip reverse search, can be restricted, e.g., to
computing full triangulations only; this case is particularly relevant for
tropical geometry. Most importantly, down-flip reverse search allows for
massive parallelization, i.e., it scales well even for many cores. Our
implementation allows to compute the triangulations of much larger point sets
than before.
