Tetrapodal nanotube junction can be modeled by fullerene spanning and by using some operations on map. They can self-assembly in more complex structures, such as dendrimers and/or multi tori, which are structures of high genera. Eight tetrapodal units were designed and their energetics evaluated at the Hartree-Fock HF level of theory. Their stability is discussed in terms of total energy, HOMO-LUMO gap, strain energy, HOMA index of aromaticity and the Kekulé structure count. The results of this study show that the tetrapodal junctions, bearing more aromatic patches, can be a challenge for the laboratory synthesis of new nanostructures.