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Licensed Unlicensed Requires Authentication Published by De Gruyter (O) June 30, 2011

On the continuous transformations between genus-3 minimal surfaces approximants

Stefano Leoni and Igor A. Baburin

Abstract

A continuous, genus-preserving transformation relating four minimal surfaces – P, G, D and H – 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. The mean and Gauss curvatures of PNS were calculated in order to quantify their similarity to minimal surfaces. The inhomogeneity of the Gauss curvature distributions on PNS was used to produce tilings directly on the surfaces. Such tilings on the P, G and D surfaces can be easily related to three-dimensional nets important in structural chemistry (rhr, analcime, sodalite frameworks, respectively). A tiling on the H surface gave rise to a completely new 3,4-coordinated net.


* Correspondence address: Technische Universität Dresden, In, 01062 Dresden, Deutschland,

Published Online: 2011-06-30
Published in Print: 2011-08

© by Oldenbourg Wissenschaftsverlag, Dresden, Germany

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