Two special tetrahedra packing clusters were analytically calculated and discussed. Diamond and double-diamond, periodic superstructures emerge. Both structures exemplify an efficient, congruent tetrahedra space tiling strategy. The diamond superstructure exhibits a remarkable packing density of φ ∼ 0.76 exceeding maximal density for the packing of equal spheres. The presented architectures display long range order with specific, repetitive structural motifs. Due to their simple tetrahedral symmetry, the investigated clusters have the potential to become interesting, unique sub-units both in construction technology and in self-assembled systems design. The modified structure of presented cluster can entirely tile three-dimensional Euclidean space through periodic tessellations. Moreover, detailed analysis of the cluster enables definition of a new plesiohedron.