One of the COGENT topics concerns symmetric spaces and relations to arithmetic. We obtain an example of this when we let a discrete group of isometries act on hyperbolic 3-space for which we can study a fundamental domain. It turns out that for the building blocks of such a fundamental domain one can often find hidden symmetries, giving rise to aesthetically pleasing by-products like highly symmetric polytopes and variants thereof. In this lecture series we will discuss a little bit of the background story and illustrate it by way of a couple of those new kinds of polyhedra, in 3D-printed form. We briefly outline the underlying process of how they were generated and, most importantly, give you a few pointers and examples of how you can rather quickly design a 3D-printed object yourself--on the spot!--using the free software package "OpenSCAD" (similar to Python). We should find time to print some of your designs during the summer school: There is a Fab Lab onsite which we are planning to pay a visit a day later, hopefully allowing us to see it already in the process of realising some of your creations--ideally the latter should reflect some of the beautiful structures that you have encountered in your own studies.