  We exhibit an infinite family of discrete subgroups of ${Sp}_4(\mathbb R)$
which have a number of remarkable properties. Our results are established by
showing that each group plays ping-pong on an appropriate set of cones. The
groups arise as the monodromy of hypergeometric differential equations with
parameters $\left(\tfrac{N-3}{2N},\tfrac{N-1}{2N}, \tfrac{N+1}{2N},
\tfrac{N+3}{2N}\right)$ at infinity and maximal unipotent monodromy at zero,
for any integer $N\geq 4$. Additionally, we relate the cones used for ping-pong
in $\mathbb R^4$ with crooked surfaces, which we then use to exhibit domains of
discontinuity for the monodromy groups in the Lagrangian Grassmannian.
