Valence-four vertex conjecture for Dirichlet domains of m125 and m129

Let $M$ be either of the census manifolds \texttt{m125} or \texttt{m129}, and let $D$ be a Dirichlet domain for $M$. A finite vertex of valence four is a finite vertex of $D$ incident to four edges. Valence-four vertex conjecture. Every Dirichlet domain of $M$ has a finite vertex of valence four. This conjecture concerns an obstruction to verifying Dirichlet domains with interval arithmetic, since such verification is impossible when a Dirichlet domain has a finite vertex of valence four. The source gives no resolution, so the conjecture remains open.