Odd-valence subsequence conjecture for face-homogeneous tessellations

Let $\sigma$ be the valence sequence of a face-homogeneous tessellation. Suppose that $\sigma$ contains $[p,q,r]$ as a subsequence, where $q$ is odd and $p\neq r$. Odd-valence subsequence conjecture. Then $\sigma$ must contain at least three terms equal to $q$. This would constrain which cyclic valence sequences can occur in face-homogeneous tessellations; the source does not state whether the claim is known or unresolved.