A Gorenstein toric singularity can be described by simple combinatorial data, namely a convex polytope $P$ in $Z^n$ with integer vertices. Different triangulations of $P$ with vertices given by integer points of $P$ give rise to different resolutions of the singularity. It has been shown that bounded derived categories of coherent sheaves on these resolutions are equivalent. It is reasonable to expect that there is in fact a continuous family of triangulated categories that includes these categories as its limit points. This is very much work in progress, and the main questions are still wide open. It is my hope that by bringing this problem to your attention I can inspire someone to find such construction.