IPMS ( Infinite Periodic Minimal Surfaces or Triply Periodic Minimal Surfaces) belong to an important class of surface forms. Among many family of these forms, the P-surfaces, the D-surfaces, and the gyroid surfaces are the most common structures that occur in nature. Previously, we have worked out the systematic tiling rules for the P- and D-surfaces. The beaded models for these two surfaces have also been constructed by Chuang.
But the structure of Gyroid seems to be more complicated. A few months ago, when I mentioned our beaded models including the P- and D-type Schwarzites to Prof. Luh(陸駿逸), he suggested that we should try to construct gyroidal graphenoid, by which I mean a graphene embeded in a gyroidal surface. I didn't say too much at that time, since I knew only a little about this creature. Even now I still have only quite limited understanding about this surface form in particular, and IPMS in general. But this cannot prevent us to work on the construction of beaded structures of this type. Finally, Chuang has worked out how to tile graphene on a gyroid surface. The resulting gyroidal graphenoids look great on the screen of Chuang's PC. This is really remarkable. However to build a beaded model for the smallest system, we need about 120 beads per unit cell. To construct a 2x2x2 model, we need 1000 beads. The next smallest system, we need about 500 beads per unit cell. More than 4000 beads for a 2x2x2 model.
By the way, a good reference for people who are interested in the mathematics of shapes and their applications to chemistry is "The language of shape" by S. Hyde et al.