On the Compressive Behavior of Platonic- and Pacioli-Inspired Lattice Structures via FEA

Shapes and topologies of lattice materials have been extensively studied, yet very few studies have dealt with shapes inspired by ancient mathematicians, such as the Platonic solids discovered by Plato in 360 BC or the mathematical behavior of the unexplored “semi-regular” solids of Pacioli (1445–1517). Using the finite element analysis method, the buckling and post-buckling behavior of Platonic and Paciolian cells subjected to a compressive load were analyzed. In these solids, the energy absorbed per unit mass is an increasing function with the number of faces, similar to porosity, which reaches a maximum value for solids comprised of 90–100 surfaces.