Minimal surfaces with self-intersections along straight lines. II. Surfaces forming three-periodic labyrinths.
47 families of minimal surfaces with straight self-intersections have been derived which subdivide R3 into a finite number of congruent three-periodic labyrinths. In most of these cases, namely for 42 families, the number of labyrinths is two. Four congruent labyrinths have been found three times and eight congruent labyrinths twice. Minimal surfaces with three or six labyrinths seem not to exist. Most of these minimal surfaces are non-orientable. The surfaces of three families only are orientable ones.
Koch
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Institut fur Mineralogie, Petrologie und Kristallographie, Universitat Marburg, Germany. kochelke@mailer.uni-marburg.de