  We theoretically investigate a tight binding model of fermions hopping on the
square-octagon lattice which consists of a square lattice with plaquette
corners themselves decorated by squares. Upon the inclusion of second neighbor
spin-orbit coupling or non-Abelian gauge fields, time-reversal symmetric
topological Z_2 band insulators are realized. Additional insulating and gapless
phases are also realized via the non-Abelian gauge fields. Some of the phase
transitions involve topological changes to the Fermi surface. The stability of
the topological phases to various symmetry breaking terms is investigated via
the entanglement spectrum. Our results enlarge the number of known exactly
solvable models of Z_2 band insulators, and are potentially relevant to the
realization and identification of topological phases in both the solid state
and cold atomic gases.
