Bisztriczky's separation conjecture for totally sewn neighbourly 4-polytopes

Let $\mathbf{P}$ be a totally sewn neighbourly $4$-polytope in $\mathbb{E}^4$, and let $\mathbf{o}$ be an interior point of $\mathbf{P}$. Bisztriczky's separation conjecture. There exist $9$ hyperplanes in $\mathbb{E}^4$ such that every face of $\mathbf{P}$ can be strictly separated from $\mathbf{o}$ by at least one of them. The paper records a bound of $16$ for this class and attributes the stronger conjectured bound to Bisztriczky; its status is open.