  Among the family of hard convex lens-shaped particles (lenses), the one with
aspect ratio equal to 2/3 is `optimal' in the sense that the maximally random
jammed (MRJ) packings of such lenses achieve the highest packing fraction
$\phi_{\rm MRJ} \simeq 0.73$. This value is only a few percent lower than
$\phi_{\rm DKP} = 0.76210\dots$, the packing fraction of the corresponding
densest-known crystalline (degenerate) packings. By exploiting the appreciably
reduced propensity that a system of such optimal lenses has to positionally and
orientationally order, disordered packings of them are progressively generated
by a Monte Carlo method-based procedure from the dilute equilibrium isotropic
fluid phase to the dense nonequilibrium MRJ state. This allows one to closely
monitor how the (micro)structure of these packings changes in the process of
formation of the MRJ state. The gradual changes undergone by the many
structural descriptors calculated can coherently and consistently be traced
back to the gradual increase in contacts between the hard particles until the
isostatic mean value of 10 contact neighbors per lens is reached at the
effectively hyperuniform MRJ state. Compared to the MRJ state of hard spheres,
the MRJ state of such optimal lenses is denser (less porous), more disordered,
and rattler-free. This set of characteristics makes them good glass formers. It
is possible that this conclusion may also hold for other hard convex uniaxial
particles with a correspondingly similar aspect ratio, be they oblate or
prolate, and that, by using suitable biaxial variants of them, that set of
characteristics might further improve.
