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14 families of minimal surfaces with straight self-intersections have been derived which subdivide R 3  into infinitely many congruent, two-periodic ‘flat labyrinths’. For eleven families, all flat labyrinths are parallel to each other. Two sets of mutual perpendicular flat lab-yrinths have been found three times. All these minimal surfaces are non-orientable. Their Euler characteristics vary between -3 and -13.

Self-intersecting three-periodic minimal surfaces forming two-periodic (flat) labyrinths