New surface patches for minimal balance surfaces. III. Infinite strips

Abstract

Two new families of minimal balance surfaces are described. Their surface patches are not finite but have the shape of infinite strips. Such a strip is bounded by two congruent zigzag lines in one case or by a zigzag line and a meander line in the other case. In addition, certain minimal balance surfaces derived before with the aid of finite surface patches can also be generated from infinite strip-like surface patches.multiple catenoids . Each such surface patch is spanned by two flat polygons as generating circuits. These polygons may be either convex or concave with one point of self-contact.In addition, a fourth kind of surface patch is compatible with parallel flat nets of twofold axes, namely strips of infinite length. Instead of two polygons such a strip is bounded by two infinite zigzag or meander lines which play a role analogous to that of the generating circuits of finite surface patches.

3-Periodic Minimal Surfaces Derivable from Laves Nets

“…In the past it turned out that also other surface patches may be spanned between nets of 2-fold axes: multiple catenoids [17] or infinite strips [18] between equal nets and branched catenoids [16] between different nets. It seemed worth-while, therefore, to look for such kinds of surface patches between the four hexagonal Laves nets.…”