  We construct a compact convex generating set $\mathcal{C}_n$ of the moduli
set of closed connected projective special real manifolds of fixed dimension
$n$. We show that a closed connected projective special real manifold
corresponds to an inner point of $\mathcal{C}_n$ if and only if it has regular
boundary behaviour. Our results can be used to describe deformations of 5d
supergravity theories with complete scalar geometries.
