Tetrahedron clusters serving as a platform for foam-like structure design

There are a number of exceptional examples indicating the unique position of tetrahedral symmetry in the vast landscape of different spatial organization pathways which can be sampled by matter. This work shows that the design and analysis of relatively simple tetrahedron clusters can lead to the formulation of a new type of dendritic structure together with unique periodic frameworks resembling clathrates and foams. A simple sequential protocol leading from regular tetrahedron clusters to more complex structural motifs can be employed to determine interesting repetitive building units. Accordingly, four different hierarchical superstructures are introduced, in which the dominant population of nodes is based on tetrahedral symmetry. The introduced architectures could be of particular interest for the field of regenerative medicine and metamaterial engineering.