  The self-assembly of hard polyhedral particles confined to a flat interface
is studied using Monte Carlo simulations. The particles are pinned to the
interface by restricting their movement in the direction perpendicular to it
while allowing their free rotations. The six different polyhedral shapes
studied in this work are selected from a family of truncated cubes defined by a
truncation parameter, s, which varies from cubes (s = 0) via cuboctahedra (s =
0.5) to octahedra (s = 1). Our results suggest that shapes with small values of
s show square-like behavior whereas shapes with large values of s tend to show
more disc-like behavior. At an intermediate value of s = 0.4, the phase
behavior of the system shows both square-like and disc-like features. The
results are also compared with the phase behavior of 3D bulk polyhedra and of
2D rounded hard squares. Both comparisons reveal key similarities in the number
and sequence of mesophases and solid phases observed. These insights on 2D
entropic self-assembly of polyhedral particles is a first step toward
understanding the self-assembly of particles at fluid-fluid interfaces, which
is driven by a complex interplay of entropic and enthalpic forces.
