  We uncover an infinite family of time-reversal symmetric 3d interacting
topological insulators of bosons or spins, in time-periodically driven systems,
which we term Floquet topological paramagnets (FTPMs). These FTPM phases
exhibit intrinsically dynamical properties that could not occur in thermal
equilibrium, and are governed by an infinite set of $Z_2$-valued topological
invariants, one for each prime number. The topological invariants are
physically characterized by surface magnetic domain walls that act as
unidirectional quantum channels, transferring quantized packets of information
during each driving period. We construct exactly solvable models realizing each
of these phases, and discuss the anomalous dynamics of their topologically
protected surface states. Unlike previous encountered examples of Floquet SPT
phases, these 3d FTPMs are not captured by group cohomology methods, and cannot
be obtained from equilibrium classifications simply by treating the discrete
time-translation as an ordinary symmetry. The simplest such FTPM phase can
feature anomalous $Z_2$ (toric code) surface topological order, in which the
gauge electric and magnetic excitations are exchanged in each Floquet period,
which cannot occur in a pure 2d system without breaking time reversal symmetry.
