Reflections concerning triply-periodic minimal surfaces

In recent decades, there has been an explosion in the number and variety of embedded triply-periodic minimal surfaces (TPMS) identified by mathematicians and materials scientists. Only the rare examples of low genus, however, are commonly invoked as shape templates in scientific applications. Exact analytic solutions are now known for many of the low genus examples. The more complex surfaces are readily defined with numerical tools such as Surface Evolver software or the Landau-Ginzburg model. Even though table-top versions of several TPMS have been placed within easy reach by rapid prototyping methods, the inherent complexity of many of these surfaces makes it challenging to grasp their structure. The problem of distinguishing TPMS, which is now acute because of the proliferation of examples, has been addressed by Lord & Mackay (Lord & Mackay 2003 Curr. Sci. 85, 346-362).