  We study several properties of $\ZZ_2^n$-equivariant triangulations of $\RR
P^n$. We show that a $\ZZ_2^n$-equivariant triangulation of $\RR P^n$ induces a
triangulated subdivision of the orbit space $\bigtriangleup^n$. We show that
any vertex minimum $\ZZ_2^3$-equivariant triangulation of $\RR P^3$ contains
$11$ vertices.
