Architected metamaterials exhibit unique properties bestowed by their engineered structure rather than their chemical composition. Extrinsic material properties have been achieved as a result of advances in additive manufacturing. Contemporary fabrication techniques, such as multiphoton lithography and digital light processing, have enabled the fabrication of complex structures with inherent hierarchies at length scales ranging from nanometers to micrometers. However, despite significant insight into the role of buckling in the mechanical behavior of materials reported in earlier studies, particularly strength and energy dissipation, the structural and design principles responsible for the improved mechanical performance were not fully elucidated, thus limiting the design space of these structures. The principal objective of this study was to investigate how controlled three-dimensional assembly and orientation of intertwined lattice members influence localized buckling and the overall mechanical response of such metamaterial structures. The novelty of the present design approach stems from a mechanical metamaterial inspired by the three-compound octahedron and the symmetry variance observed during phase change of crystalline solids. For a specific orientation and tactical joining of the unit cells, this geometry demonstrates unprecedented resilience to large deformations and high energy dissipation capacity. The selective shape modification of specific lattice members is shown to greatly improve the structural integrity of ultralight structures undergoing large deformation. Results from finite element simulations and in situ scanning electron microscopy-microindentation experiments reveal the actual deformation of metamaterial structures with straight and curved lattice members and elucidate the effects of anisotropy and orientation characteristics on the dominant mechanisms affecting the mechanical performance of intertwined lattice structures.