These tiny structures could offer architectural designs for the cities of the future. The authors explore the foam-like carbon structures, which relate to 'schwarzites' and which are infinite periodic minimal surfaces of negative curvature. They show that the periodicity of close repeat units of such structures is evident not only in these formations but also in all of the carbon allotropes. The text provides literature and data on the field of nanostructure periodicity and the authors' own results on nanostructure building and energy calculations.