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 small side project of polymake is an educational game, which lets you play with 3-dimensional polytopes and their unfoldings. Co-authored with Georg Loho, Benjamin Lorenz and Rico Raber.