  Properly embedded simplices in a convex divisible domain $\Omega \subset
\mathbb{R} \textrm{P}^d$ behave somewhat like flats in Riemannian manifolds, so
we call them flats. We show that the set of codimension-$1$ flats has image
which is a finite collection of disjoint virtual $(d-1)$-tori in the compact
quotient manifold. If this collection of virtual tori is non-empty, then the
components of its complement are cusped convex projective manifolds with type
$d$ cusps.
