Specialized software is the key tool to help the mind doing research in mathematics. At the same time mathematical software bridges the gap between the diverse fields of mathematics and their application areas.
polymake is a software system for convex polytopes, simplicial complexes, and more. Co-authored with Ewgenij Gawrilow (now TomTom) and actively supported by many people [BibTeX-Entry]. If you are interested to see how polymake can be used, see the documentation or this extra page with references. This is a long term project first released in 1997.
This is a brandnew parallel implementation of the down-flip reverse search algorithm for enumerating the (regular) triangulations of a point set. Co-authored with Skip Jordan and Lars Kastner. Our arXiv preprint explains the method and reports on experimental results. Release of version 1.0 on March 28, 2018.
Thanks to Benjamin Lorenz and Sebastian Gutsche we already have a first tech preview (from March/April 2018):