  Polyhedral nanocrystals are building blocks for nanostructured materials that
find applications in catalysis and plasmonics. Synthesis efforts and
self-assembly experiments have been assisted by computer simulations that
predict phase equilibra. Most current simulations employ Monte Carlo methods,
which generate stochastic dynamics. Collective and correlated configuration
updates are alternatives that promise higher computational efficiency and
generate trajectories with realistic dynamics. One such alternative involves
event-chain updates and has recently been proposed for spherical particles. In
this contribution, we develop and apply event-chain Monte Carlo for hard convex
polyhedra. Our simulation makes use of an improved computational geometry
algorithm XenoSweep, which predicts sweep collision in a particularly simple
way. We implement Newtonian event chains in the open source general-purpose
particle simulation toolkit HOOMD-blue for serial and parallel simulation. The
speed-up over state-of-the-art Monte Carlo is between a factor of 10 for nearly
spherical polyhedra and a factor of 2 for highly aspherical polyhedra. Finally,
we validate the Newtonian event-chain algorithm by applying it to a current
research problem, the multi-step nucleation of two classes of hard polyhedra.
