  The central region of NGC 1068 is one of the closest and most studied Active
Galactic Nucleus. It is known to be of type 2, meaning that its accretion disk
is obscured by a large amount of dust and gas. The main properties of the
obscuring structure are still to be determined. We model the inner edge of this
structure, where the hot dust responsible for the near-infrared emission
reaches its sublimation temperature. At first, we use simple geometrical models
in image reconstructions to determine the main 2D geometrical properties of the
source. In a second step, we try to reproduce the observables with K-band
images produced by 3D radiative transfer simulations of a heated dusty disk. We
explore various parameters to find an optimal solution and a model consistent
with all the observables. The three methods indicate an elongated structure
with 4 x 6 mas dimensions and its major axis along the NW/SE direction. All
three of them suggest that the object looks like an elongated ring rather than
an elongated thin disk, with its northeast edge less luminous than the
South-West one. The best 3D model is a thick disk with an inner radius r=0.21
+/- 0.03 pc and a half-opening angle $\alpha_{1/2}=21\pm8\degree$ observed with
an inclination $i=44_{-6}^{10}$\,$\degree$ and $PA=150_{-13}^{8}$\,$\degree$. A
high density of dust $n=5_{-2.5}^{+5}\ M_{\odot}.pc^{-3}$ is required to
explain the contrast between the two edges by self-absorption from the closer
one. The overall structure is obscured by a large foreground obscuration $A_V
\sim 75$. The hot dust is not responsible for the obscuration of the central
engine. The geometry and the orientation of the structure are different from
those of the previously observed maser and molecular disks. A single disk is
unable to account for these differences, and we favor a description of the
source where multiple rings are entangled around the central mass.
