  Particle shape plays an important role in the phase behavior of colloidal
self-assembly. Recent progress in particle synthesis has made particles of
polyhedral shapes and dimpled spherical shapes available. Here using computer
simulations of hard particle models, we study face-centered cubic to
body-centered cubic (FCC-to-BCC) phase transitions in a convex 432 polyhedral
shape family and a concave dimpled sphere family. Particles in both families
have four-, three-, and two-fold rotational symmetries. Via free energy
calculations we find the FCC-to-BCC transitions in both families are first
order. As a previous work reports the FCC-to-BCC phase transition is first
order in a convex 332 family of hard polyhedra, our work provides additional
insight into the FCC-to-BCC transition and how the convexity or concavity of
particle shape affects phase transition pathways.
