We present a method for discovering dense packings of general convex hard
particles and apply it to study the dense packing behavior of a one-parameter
family of particles with tetrahedral symmetry representing a deformation of the
ideal mathematical tetrahedron into a less ideal, physical, tetrahedron and all
the way to the sphere. Thus, we also connect the two well studied problems of
sphere packing and tetrahedron packing on a single axis. Our numerical results
uncover a rich optimal-packing behavior, compared to that of other continuous
families of particles previously studied. We present four structures as
candidates for the optimal packing at different values of the parameter,
providing an atlas of crystal structures which might be observed in systems of
nano-particles with tetrahedral symmetry