We classify all possible moduli space geometries of 4-dimensional field theories with at least \( \mathcal{N}=3 \) extended supersymmetry, modulo some "technical" assumptions. (Most of the talk will end up being about those technical assumptions.) There are many infinite series and 22 sporadic cases associated to complex crystallographic reflection groups. These represent a kind of generalization of the familiar association of 4d \(\mathcal{N}=4\) field theories with the simple Lie algebras.