Schwarz's P and D and Schoen's Gyroid surfaces are canonical, triply periodic, minimal surfaces widely recognized in nature and in the scientific community. Here we present theoretical chemical analogies of these three surfaces in the context of nano-carbon structures. Based on the traditional beading techniques that we have previously shown to be suited for creating various chemical structures, we constructed the beaded models of these chemical structures and thus the underlying mathematical surfaces. Moreover, due to the intricacies of the surfaces's geometries and topologies, especially for the G surface, we developed a useful technique of dividing these surfaces into one dimensional strips, whose beading procedures are much easier to follow and can be parallelized.