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The genus of a three-periodic intersection-free surface in R3 refers to a primitive unit cell of its symmetry group. Two procedures for the calculation of the genus are described: (1) by means of labyrinth graphs; (2) via the Euler characteristic derived from a tiling on the surface. In both cases new formulae based on crystallographic concepts are given. For all known minimal balance surfaces the genera and the labyrinth graphs are tabulated.
Fischer et al. (Sun,) studied this question.