  We present an analysis of the dynamics of the equifacial pentahedron on the
Kapovich-Millson phase space under a volume preserving Hamiltonian. The
classical dynamics of polyhedra under such a Hamiltonian may arise from the
classical limit of the node volume operators in loop quantum gravity. The
pentahedron is the simplest nontrivial polyhedron for which the dynamics may be
chaotic. We consider the distribution of polyhedral configurations throughout
the space and find indications that the borders between certain configurations
act as separatrices. We examine the local stability of trajectories within this
phase space and find that locally unstable regions dominate although extended
stable regions are present. Canonical and microcanonical estimates of the
Kolmogorov-Sinai entropy suggest that the pentahedron is a strongly chaotic
system. The presence of chaos is further suggested by calculations of
intermediate time Lyapunov exponents which saturate to non zero values.
