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. A first-order analysis of the particle-surface energies associated with a fluid-fluid interface indicates that such enthalpic interactions will be particularly important in determining particle orientation behavior at low to intermediate concentrations.