  We will discuss fundamental domains for actions of discrete groups on the
3-dimensional Einstein Universe. These will be bounded by crooked surfaces,
which are conformal compactifications of surfaces that arise in the
construction of Margulis spacetimes. We will show that there exist pairwise
disjoint crooked surfaces in the 3-dimensional Einstein Universe. As an
application, we can construct explicit examples of groups acting properly on an
open subset of that space.
