The present shock absorbing layer for a helmet includes a base plate and a plurality of spaced apart, independently and elastically collapsible, shock absorbing members. These hollow shock absorbing members define a closed perimeter wall extending upwardly from the base plate to an open top end sized to cause negligible reduction of fluid flow exiting the shock absorbing member. The closed perimeter wall includes a first portion with opposed inner and outer surfaces each having the shape of a frustum, and a second portion with opposed inner and outer surfaces each also having the shape of a frustum. These inner surfaces are interconnected through relatively radially wider ends of their respective frustums to define an inner angle therebetween of less than 180 degrees. These outer surfaces are interconnected through relatively radially wider ends of their respective frustums to define an outer angle therebetween of greater than 180 degrees.