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We construct a family of PL triangulations of the $d$-dimensional real projective space $\mathbb{R}P^d$ for every $d\geq 1$ on $\Theta((\frac{1+\sqrt{5}}{2})^{d+1})$ vertices. This improves a construction due to K\"{u}hnel on $2^{d+1}-1$ vertices.
