  We study the scaling limit of essentially simple triangulations on the torus.
We consider, for every $n\geq 1$, a uniformly random triangulation $G_n$ over
the set of (appropriately rooted) essentially simple triangulations on the
torus with $n$ vertices. We view $G_n$ as a metric space by endowing its set of
vertices with the graph distance denoted by $d_{G_n}$ and show that the random
metric space $(V(G_n),n^{-1/4}d_{G_n})$ converges in distribution in the
Gromov-Hausdorff sense when $n$ goes to infinity, at least along subsequences,
toward a random metric space. One of the crucial steps in the argument is to
construct a simple labeling on the map and show its convergence to an explicit
scaling limit. We moreover show that this labeling approximates the distance to
the root up to a uniform correction of order $o(n^{1/4})$.
