For more than twenty years I have studied instantons and monopoles and tools like the Nahm transform transforming the problem of their study to a seemingly easier problem. With a few of my students and collaborators, we have studied over the past few years how symmetry can alter the problem. From Platonic solids, to the classification of all discrete groups generated by reflections by Coxeter 90 years ago, to kaleidoscopes, to the unreasonable effectiveness of physics in mathematics, and the frontiers of our ignorance.