J. Phys. I France
Volume 2, Numéro 12, December 1992
Page(s) 2207 - 2220
DOI: 10.1051/jp1:1992102
J. Phys. I France 2 (1992) 2207-2220

The T and CLP families of triply periodic minimal surfaces. Part 3. The properties and computation of CLP surfaces

Djurdje Cvijovic and Jacek Klinowski

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, G.B.

(Received 17 June 1992, accepted 24 August 1992)

Parametric equations for normalized CLP minimal surfaces provide the solution of the problem of finding the coordinates of the CLP saddle surface inscribed in a given tetragonal parallelepiped (right tetragonal prism). This is crucial for the matching of specific surfaces to real structures. The geometry of a CLP surface depends only on the ratio c/a of the tetragonal axes, and can be described in terms of a single free parameter. We offer a choice of two such parameters, both related to surface geometry, and derive analytical expressions for their relationships to the axes ratio and the normalization factor. Parametric equations for normalized CLP surfaces enable us, for the first time, to find the surface corresponding to any given value of the c/a ratio. Straightforward physical applications are therefore possible. A CLP surface is perfectly self-adjoint only when the free parameter $\lambda=0$. We list exact coordinates of CLP surfaces corresponding to prescribed value of the c/a ratio

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