  We investigate the collapse of three inelastic particles in dimension $d \geq
2$. We obtain general results of convergence and asymptotics concerning the
variables of the dynamical system describing a collapsing system of particles.
We prove a complete classification of the singularities when a collapse of
three particles takes place, obtaining only two possible orders of collisions
between the particles. In the first case we recover that the particles arrange
in a nearly-linear chain, already studied by Zhou and Kadanoff, and in the
second case we obtain that the particles arrange in a triangle, and we show
that, after sufficiently many collisions, the particles collide according to a
unique order of collisions, which is periodic. Finally, we construct an initial
configuration leading to a nearly-linear collapse, stable under perturbations,
and such that the angle between the particles at the time of collapse can be
chosen a priori, with an arbitrary precision.
