  The discovery of binary and triple asteroids in addition to the execution of
space missions to minor celestial bodies in the past several years have focused
increasing attention on periodic orbits around irregular-shaped celestial
bodies. In the present work, we adopt a polyhedron shape model for providing an
accurate representation of irregular-shaped bodies, and employ the model to
calculate their corresponding gravitational and effective potentials. We also
investigate the characteristics of periodic orbit families and the continuation
of periodic orbits. We prove a fact, which provides a conserved quantity that
permits restricting the number of periodic orbits in a fixed energy curved
surface about an irregular-shaped body. The collisions of Floquet multipliers
are maintained during the continuation of periodic orbits around the comet
1P/Halley. Multiple bifurcations in the periodic orbit families about
irregular-shaped bodies are also discussed. Three bifurcations in the periodic
orbit family have been found around the asteroid 216 Kleopatra, which include
two real saddle bifurcations and one period-doubling bifurcation.
