Supplément au Journal de Physique Colloques

Sommaire

International Workshop on Geometry and Interfaces

J. Phys. Colloques 51 (1990) C7-131-C7-147
DOI: 10.1051/jphyscol:1990713

CRYSTALLOGRAPHIC ASPECTS OF MINIMAL SURFACES

W. FISCHER and E. KOCH

Institut für Mineralogie, Petrologie und Kristallographie der Universität Marburg, Hans-Meerwein-Strasse, D-3550 Marburg, F.R.G.

Abstract
Symmetry properties of 3-periodic minimal surfaces subdividing R3 into two congruent regions are discussed. The relation between the order of a flat point and its site symmetry is established. Explicit formulae are given for the calculation of the genus of such a surface depending on the kind of surface patches that build up the surface. Making use of 2-fold axes that have to be embedded in a surface with given symmetry new families of minimal balance surfaces have been derived. Corresponding lists are referred to the different kinds of surface patches.