Genera of minimal balance surfaces

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.