Relative Helicity and Tiling Twist

We consider domino tilings of 3D cubiculated regions. The tilings have two invariants, flux and twist, often integer-valued, which are given in purely combinatorial terms. These invariants allow one to classify the tilings with respect to certain elementary moves, flips and trits. In this paper we present a construction associating a divergence-free vector field ξₜ to any domino tiling t, such that the flux of the tiling t can be interpreted as the (relative) rotation class of the field ξₜ, while the twist of t is proved to be the relative helicity of the field ξₜ.