Regular Dodecahedron-Based Network Structures

Abstract

The packing and assembly of Platonic solids have fascinated mathematicians for ages. Recently, this fundamental geometrical problem has also attracted the attention of physicists, chemists, and engineers. This growing interest is due to the rapid advancements in various related fields, ranging from the formation of colloidal crystals and the design of metal–organic frameworks to the development of ultra-lightweight metamaterials, which are closely tied to the fast-evolving 3D printing technology. Numerous reports have focused on the assembly of Platonic polyhedra, particularly tetrahedra, for which an optimal packing strategy remains unidentified to this day. However, less attention has been given to the dodecahedron and its networks. This work introduces a new type of framework, designed from regular dodecahedra combined with icosahedron-based binders. The relatively simple design protocol employed here results in a remarkable variety of intriguing networks, which could be potentially useful in fields such as architecture, regenerative medicine, or aeronautics. Additionally, the dodecahedral networks presented in this study led to the discovery of intriguing structures resembling distorted graphene sheets. These structures exhibit features characteristic of both graphene and diamond.