Given a crystallographic root system with a fixed simple system, it is associated to a Weyl group $W$ and a polytope $P$ that is the convex hull of the $W$-orbit of a well-chosen dominant weight. The quotient $P/W$ can be identified with a polytope. Polytopes $P$ and $P/W$ are associated to toric varieties $X_P$ and $X_{P/W}$ respectively. It turns out the underlying topological spaces $X_P/W$ and $X_{P/W}$ are homotopy equivalent.

As the use of software becomes more common amongst mathematicians, there is an increasing need for supporting infrastructure. We will discuss the ongoing efforts of the MaRDI project and how it aligns with the FAIR principles. Then we will highlight some key features of the Julia programming language, give an overview of the computer algebra system OSCAR, and discuss the tools they provide to help mathematicians share software and data.