J. Phys. France
Volume 48, Numéro 9, septembre 1987
Page(s) 1585 - 1590
J. Phys. France 48, 1585-1590 (1987)
DOI: 10.1051/jphys:019870048090158500

A construction algorithm for minimal surfaces

S. Lidin1 et S.T. Hyde2

1  Inorganic Chemistry 2, Chemical Centre, P.O. Box 124, S-22100 Lund, Sweden
2  Department of Applied Mathematics, Research School of Physical Sciences, P.O. Box 4, Canberra 2601, Australia

Infinite periodic minimal surfaces are constructed from complex functions, which are simply related to the orientation of flat points on the surface. Two tetragonal families of surfaces are generated, which are shown to reduce in special cases to classical minimal surfaces : the cubic diamond surface (D surface) and the Scherk surface. In all cases the construction algorithm for the complex functions yields the expected results, supporting the validity of the procedure. The algorithm can be used to determine new periodic minimal surfaces.

Nous construisons des surfaces minimales périodiques infinies à partir de fonctions complexes qui sont simplement reliées à l'orientation des points plats sur la surface. Nous engendrons deux familles tétragonales de surface, dont nous montrons qu'elles se réduisent dans des cas particuliers à des surfaces minimales classiques : la surface du diamant cubique (surface D) et la surface de Scherk.

6130 - Liquid crystals.
6150 - Crystalline state.

Key words
crystal structure -- crystal symmetry -- liquid crystals