Parametrization of triply periodic minimal surfaces. III. General algorithm and specific examples for the irregular class

Abstract

The construction algorithm of the first two papers of this series [Fogden & Hyde (1992). Acta Cryst. A48, 442–451, 575–591] is extended to a general treatment of triply periodic minimal surfaces (containing as a special case the `regular' class analysed previously). A detailed outline of the parametrization procedure for an arbitrary `irregular' class surface is provided and verified via a systematic rederivation of the C(P) surface described by Neovius [Bestimmung Zweier Speciellen Periodische Minimalflächen (1883), Helsinki: Frenckel]. The method is further employed in parametrizing various empirically generated surfaces.