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Tetrapodal junctions are used to construct diamond-like networks and dodecahedral architectures. They can be associated with the already synthesized spongy carbon, consisting only of sp2 covalent carbon atoms, and the zeolites, periodic structures in the Euclidean space. In this paper, the structure and stability of two zigzag tetrapodal junctions are discussed. Series of objects are built up by connecting a various number of junctions. Geometry optimization and single point computations (total energy E(tot) and HOMO-LUMO gap energy E(gap)) were performed at the Hartree-Fock level of theory in view of evaluating their stability. The genus of such nanostructures was calculated from the number of consisting tetrapodal junctions.