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