Classification of spatial polygons that could possibly generate embedded triply periodic minimal surfaces (Q1429182)

The paper classifies spatial polygons that could possibly generate embedded triply periodic minimal surfaces. There are 21 types of such spatial polygons. They are listed in terms of crystallographic groups. The line symmetries of the edges of such a polygon generate a crystallographic group. In the last section a list of known results concerning the actual existence (and uniqueness) of a triply periodic minimal surface generated by the candidates is given. For many of the 21 polygons examples exist and are known to be unique. For some examples exist, but it is unknown if they are unique. For about four of the 21 cases the existence of a spanning surface is not known.