The strong hull property for affine irreducible Coxeter groups of rank 3

A conjecture proposed by Gaetz and Gao asserts that the Cayley graph of any Coxeter group satisfies the strong hull property. In this paper, we prove this conjecture for all affine irreducible Coxeter groups of rank 3. Our approach exploits the geometry of Coxeter complexes to reduce the analysis of convex hulls to finitely many manageable configurations.