The Koebe-Andreev-Thurston construction associated to every combinatorial 3d polyhedron is a canonical 3d hyperbolic polyhedron, which happens to be right-angled and ideal. In particular, it is the fundamental domain for the Coxeter group generated by the reflections across its facets. We answer the question: when is this group arithmetic? (Joint work with Pat Devlin, Anna Felikson, Alex Kontorovich and Ian Whitehead)