  A Coxeter $n$-orbifold is an $n$-dimensional orbifold based on a polytope
with silvered boundary facets. Each pair of adjacent facets meet on a ridge of
some order $m$, whose neighborhood is locally modeled on ${\mathbb R}^n$ modulo
the dihedral group of order $2m$ generated by two reflections. For $n \geq 3$,
we study the deformation space of real projective structures on a compact
Coxeter $n$-orbifold $Q$ admitting a hyperbolic structure. Let $e_+(Q)$ be the
number of ridges of order $\geq 3$. A neighborhood of the hyperbolic structure
in the deformation space is a cell of dimension $e_+(Q) - n$ if $n=3$ and $Q$
is weakly orderable, i.e., the faces of $Q$ can be ordered so that each face
contains at most $3$ edges of order $2$ in faces of higher indices, or $Q$ is
based on a truncation polytope.
