A lattice structure includes multiple identical unit cells formed from joined plates. In the lattice structure, some of the plates are rectangular plates, some of the plates are triangular plates, and some of the plates are trapezoidal plates. Further, any two of the joined rectangular plates have corresponding surface normals perpendicular to each other and at least two edges of each one of the triangular plates are joined to one of a surface or an edge of one of the plurality of joined plates. Further, at least three edges of each one of the trapezoidal plates are joined to one of a surface or an edge of one of the plurality of joined plates, and any one of a plurality of surface normals for the triangular plates and the trapezoidal plates are nonparallel to any one of a plurality of surface normals of rectangular plates.