It is just amazing! I met Chuang unexpectedly while I was waiting for the bus home yesterday evening. Chuang told me he has figured out how to construct graphitic sheet with the structure of the Scherk's singly periodic minimal surface (SPMS) and has posted it on my group blog as shown in the following figure. It is indeed a beautiful structure. In some sense, we can view this structure as an intersection of two graphene sheets. Instead of a straight line for the intersection, here one need a chain of octagon loops to mimic this intersection.
Apparently, Chuang has worked out this when he has a shooting training in the army. I hope that he can still shoot the target in the training course.
This SPMS structure is not complicated. It is quite straightforward to make a beaded model for this kind of graphitic structure. It took me several hours to make it today.