A 44-vertex triangulation of $\mathbb{RP}^{6}$

The manuscript gives an explicit centrally symmetric simplicial 7-polytope with 88 integer vertices. Its antipodal boundary quotient is a 44-vertex triangulation of real projective 6-space, with f-vector (44, 938, 7024, 22555, 34936, 25914, 7404). This improves the 45-vertex construction of Guyer, Steinerberger and Yang and gives an affirmative answer to their Question 3.2. Integer coordinates, facet lists and exact-arithmetic verification code accompany the manuscript. No claim that 44 is vertex-minimal is made.

The manuscript gives an explicit centrally symmetric simplicial 7-polytope with 88 integer vertices. Its antipodal boundary quotient is a 44-vertex triangulation of real projective 6-space, with f-vector (44, 938, 7024, 22555, 34936, 25914, 7404). This improves the 45-vertex construction of Guyer, Steinerberger and Yang and gives an affirmative answer to their Question 3.2. Integer coordinates, facet lists and exact-arithmetic verification code accompany the manuscript. No claim that 44 is vertex-minimal is made.

The supplied 44 integer vectors in $\mathbb{Z}^{7}$ and 7404 antipodal facet representatives define a centrally symmetric simplicial 7-polytope with 88 vertices whose antipodal boundary quotient is a simplicial triangulation of $\mathbb{RP}^{6}$ with $f$-vector $(44, 938, 7024, 22555, 34936, 25914, 7404)$. Thus $29 \leq \nu(\mathbb{RP}^{6}) \leq 44$ and the construction improves the prior 45-vertex bound; no claim that 44 is vertex-minimal is made.

The manuscript's exact supporting-hyperplane, ridge-incidence, antipodal-neighborhood, and quotient-face tests are the stated certificate; this draft does not independently rerun them.