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The asymptotic behavior of open plane sections of triply periodic surfaces isdictated, for an open dense set of plane directions, by an integer secondhomology class of the three-torus. The dependence of this homology class on thedirection can have a rather rich structure, leading in special cases to afractal. In this paper we present in detail the results for the skew polyhedron{4,6|4} and in particular we show that in this case a fractal arises and thatsuch a fractal can be generated through an elementary algorithm, which in turnallows us to verify for this case a conjecture of S.P.Novikov that suchfractals have zero measure.

Geometry of plane sections of the infinite regular skew polyhedron {4,6|4}