Vertex-minimality conjecture for the triangulation of real projective 5-space from \mathcal{P}_{6,48}

Let $\mathcal{P}_{6,48}$ be the centrally symmetric simplicial $6$-polytope whose antipodal quotient of the boundary gives a triangulation of $\mathbb{R}P^5$. A triangulation is vertex minimal if no triangulation of the same space has fewer vertices. Vertex-minimality conjecture. The triangulation of $\mathbb{R}P^5$ obtained by antipodally identifying the boundary of $\mathcal{P}_{6,48}$ is vertex minimal among all triangulations of $\mathbb{R}P^5$. The construction has $24$ vertices, and the conjecture asserts that this is the fewest possible; at minimum, the authors expect minimality among triangulations arising from antipodally identifying a centrally symmetric polytope.