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Disc. Math. 6(2) (1993), 214–229. [17] U. I. Bobenko, P. M. M. ), Oberwolfach Seminars, vol. 38, Birkh¨auser, 2008, this volume, pp. 37–56. ¨ [18] E. Christoffel, Uber einige allgemeine Eigenschaften der Minimumsﬂ¨achen, J. reine angew. Math. 67 (1867), 218–228. [19] J. Cie´sli´nski, A. M. Santini, The integrable discrete analogues of orthogonal coordinate systems are multi-dimensional circular lattices, Phys. Lett. A 235(5) (1997), 480– 488. [20] U. Dierkes, S. Hildebrandt, A. K¨uster, and O. , Grundlehren der mathematischen Wissenschaften, vol.

92–125]. F IGURE 18. Schwarz’s H-surface. Boundary conditions: Take two parallel copies of an equilateral triangle as the boundary frame for a minimal surface spanned in between them, as in Figure 19. By construction this minimal surface has one plane of reﬂection symmetry parallel to the planes of the triangles and three other orthogonal planes as symmetry group of the equilateral triangle. Thus a fundamental piece is bounded by three planar curvature lines and one straight asymptotic line, as in Figure 19.

Analogously, there are two other integer parameters corresponding to the two boundary lengths of the Minimal Surfaces from Circle Patterns: Examples n m a b ˛ c 47 ˛ curvature line asymptotic line nodal point n; m integer parameters of curvature lines F IGURE 12. A generalization of Schwarz’s CLP-surface: boundary frame (left) and combinatorics of curvature lines (right). second rectangle. The pasting procedure translates into the condition that the number of curvature lines on the curvature line joining the pasted corners has to be equal on both sides.