An improved protective shell for a helmet, where the shell has angled panels forming pyramid-like surface structures covering the surface of the helmet. Each pyramid-like structure has three or more panels conjoining to form an apex. In one embodiment, each of the panels is a triangle having a base and a point that conjoins adjacent panels, thereby forming the apex. The limited number of apex points and the orientation of the angled panels reduce the probability that an impacting object will deliver a square blow to the helmet. The probability is increased that such blows will be only glancing in nature, thereby reducing the severity of the blow and head injury to the wearer.