Exploiting space group Pm-3m symmetry for designing isotropic lattice structures

Utilizing space group Pm -3 m symmetry, seven polyhedra with cubic symmetry are characterized. A design method for near-isotropic lattice unit cells is proposed based on nested unit cell concepts. By ingeniously incorporating the symmetry constraints of the Pm -3 m space group, this method reduces the number of tuning parameters, which contributes to more efficient parameter modulation. Based on this method, the specific geometric parameters of six near-isotropic unit cells at different relative densities are determined, and finite element simulations and experimental validation are conducted on the three configurations exhibiting relatively high specific Young’s moduli. The results demonstrate that the C-CO configuration exhibits excellent mechanical properties, confirming the engineering practicality of this lattice design methodology. This outcome further validates the feasibility and effectiveness of integrating symmetry group theory into the design of lattice metamaterials.