This article reports on a nature-inspired, ultra-lightweight structure designed to optimize rigidity and density under bending loads. The structure's main features were conceived by observing the scales of the butterflies' wings. They are made of a triply periodic minimal surface geometry called gyroid and further reinforced on their outer regions with a series of ribs. In this work, the ribs were substituted with carbon fiber-reinforced bars that were connected to the main structure with an innovative concept. Stereolithography was used to print a plastic component in one piece that comprised the core and the connection system. Bending tests were performed on the structures along with a Finite Element Method optimization campaign to achieve the optimum performance in terms of stiffness and density. Results show that these architectures are among the most effective mechanical solutions in respect to their weight because of their particular arrangement of material in space.