  We study the topological properties of 3D Floquet bandstructures, which are
defined using unitary evolution matrices rather than Hamiltonians. Previously,
2D bandstructures of this sort have been shown to exhibit anomalous topological
behaviors, such as topologically-nontrivial zero-Chern-number phases. We show
that the bandstructure of a 3D network model can exhibit Weyl phases, which
feature "Fermi arc" surface states like those found in Weyl semimetals. Tuning
the network's coupling parameters can induce transitions between Weyl phases
and various topologically distinct gapped phases. We identify a connection
between the topology of the gapped phases and the topology of Weyl point
trajectories in k-space. The model is feasible to realize in custom
electromagnetic networks, where the Weyl point trajectories can be probed by
scattering parameter measurements.
