the monge-ampere equation det$(d^2u) = 1$ arises in prescribed curvature problems and in optimal transport. an interesting feature of the equation is that it admits singular solutions. we will discuss new examples of convex functions on $r^n$ that solve the monge-ampere equation away from finitely many points, but contain polyhedral and y-shaped singular structures. along the way we will discuss geometric motivations for constructing such examples, as well as their connection to a certain obstacle problem.