  we investigate developable cones (d-cones) topology and mechanical
properties. We found that for a sample of a finite thickness the singularity is
never pointlike but has a spatial extension in form of a crescent. The
variations of the sheet local curvature versus the distance from the d-cone tip
for all deformations showed that the d-cone tip is rejected by a distance which
depends on the deformation and on the singularity extension. A further
deformation of the d-cone leads to a transition to a plastic deformation
equivalent to a decrease in the singularity size characterized from curvature
and profile analysis. The crescent radius of curvature is measured both at
small deformations and at large deformations. It is found that during the
buckling process, the curvature of the crescent exhibit two different scaling
versus the deformation.From the cone profile, we measured the reaction force of
the plate to deformation and from force measurements, the energy necessary to
create the singularity is characterized.
