  We consider dimer models on graphs which are bipartite, periodic and satisfy
a geometric condition called {\em isoradiality}, defined in \cite{Kenyon3}. We
show that the scaling limit of the height function of any such dimer model is
$1/\sqrt{\pi}$ times a Gaussian free field. Triangular quadri-tilings were
introduced in \cite{Bea}; they are dimer models on a family of isoradial graphs
arising form rhombus tilings. By means of two height functions, they can be
interpreted as random interfaces in dimension 2+2. We show that the scaling
limit of each of the two height functions is $1/\sqrt{\pi}$ times a Gaussian
free field, and that the two Gaussian free fields are independent.
