  The Einstein universe $\mathbf{Ein}^{p,q}$ of signature $(p,q)$ is a
pseudo-Riemannian analogue of the conformal sphere; it is the conformal
compactification of the pseudo-Riemannian Minkowski space. For $p,q \geq 1$, we
show that, up to a conformal transformation, there is only one domain in
$\mathbf{Ein}^{p,q}$ that is bounded in a suitable stereographic projection and
whose action by its conformal group is cocompact. This domain, which we call a
diamond, is a model for the symmetric space of $\operatorname{PO}(p,1) \times
\operatorname{PO}(1,q)$. We deduce a classification of closed conformally flat
manifolds with proper development.
