We propose a new convex relaxation for phase retrieval that operates in the natural domain of the signal. Therefore, the proposed method has significantly lower computational cost than the existing convex methods that rely on semidefinite programming and competes with the recent non-convex methods. In the proposed formulation the quadratic equations are relaxed to inequalities describing a "complex polytope". Then, using an anchor vector, a simple convex program estimates the ground truth as an (approximate) extreme point of the polytope. We show, using classic results in statistical learning theory, that with random measurements this convex program produces accurate estimates.