The magic square of reflections and rotations

Ragnar-Olaf Buchweitz, Eleonore Faber, Colin Ingalls

Published 2018-06-12Version 1

We show how Coxeter's work implies a bijection between complex reflection groups of rank two and real reflection groups in $O(3)$. We also consider this magic square of reflections and rotations in the framework of Clifford algebras: we give an interpretation using (s)pin groups and explore these groups in small dimensions.