New families of triply periodic minimal surfaces

Abstract

The established results regarding balanced minimal surfaces of orthorhombic symmetry are analysed and supplemented here. We commence by reviewing the simplest examples, possessing a genus value (per unit cell) of 3. From this foundation we construct a generalised approach, and apply it to the next simplest cases. In particular, we derive two related families of surfaces possessing genera of 5. These two families contain, in total, three previously unrealised examples. For all 11 surfaces considered the exact mathematical equations specifying them are given, along with their space group–subgroup specifications, and illustrations of their elements are provided.