We are motivated by an optimization problem arising in computational scaling for optical lithography that reduces to finding the point of minimum radius that lies outside of the union of a set of diamonds centered at the origin of Euclidean space of arbitrary dimension. A decomposition of the feasible region into convex regions suggests a heuristic sampling approach to finding the global minimum. We describe a technique for decomposing the surface of a hypersphere of arbitrary dimension, both exactly and approximately, into a specific number of regions of equal area and small diameter. The decomposition generalizes to any problem posed on a spherical domain where regularity of the decomposition is an important concern. We specifically consider a storage-optimized decomposition and analyze its performance. We also show how the decomposition can parallelize the sampling process by assigning each processor a subset of points on the hypersphere to sample. Finally, we describe a freely available C++ software package that implements the storage-optimized decomposition.