On the continuous transformations between genus-3 minimal surfaces approximants

Abstract

AbstractA continuous, genus-preserving transformation relating four minimal surfaces –P,G,DandH– was suggested within a common trigonal group-subgroup pair (P-3c1–P321). Periodic nodal surfaces (PNS) were used as approximants of minimal surfaces to illustrate the transition path. ThemeanandGausscurvatures of PNS were calculated in order to quantify their similarity to minimal surfaces. Theinhomogeneityof the Gauss curvature distributions on PNS was used to producetilingsdirectly on the surfaces. Such tilings on theP,GandDsurfaces can be easily related to three-dimensional nets important in structural chemistry (rhr, analcime, sodalite frameworks, respectively). A tiling on theHsurface gave rise to a completely new 3,4-coordinated net.