Sage offers a natural framework to deal with several objects related to finite and infinite Coxeter groups and polyhedral combinatorics under the same roof. In this talk, I will show how some experimental tools implemented using Sage (hopefully that should be merged into Sage) helped to develop the theory of limit roots in infinite Coxeter groups. It turns out that polyhedral computations and visualizations were key in understanding the algebraic structure of Coxeter groups and led to several discoveries and new conjectures.