In this paper, we develop a hybrid controller for global asymptotic stabilization on the n-dimensional sphere (mathbb S^ n) using synergistic potential functions. These consist of a collection of potential functions on mathbb S^ n that induce a gradient descent controller during flows of the hybrid closed-loop system and a switching law that, at undesired equilibrium points of the gradient vector field, jumps to the lowest value among all the potential functions in the collection. We show that the proposed controller can be used for global reduced attitude synchronization, i.e., given a network of rigid-bodies, the proposed synergistic hybrid feedback can be used to globally synchronize a reference direction of each agent within a global but unknown inertial reference frame. We study this application for a network of three vehicles by means of simulation results.