  Electrons hopping on the sites of a three-dimensional pyrochlore lattice are
shown to form topologically non-trivial insulating phases when the spin-orbit
(SO) coupling and lattice distortions are present. Of 16 possible topological
classes 9 are realized for various parameters in this model. Specifically, at
half-filling undistorted pyrochlore lattice with SO term yields a 'pristine'
strong topological insulator with Z2 index (1;000). At quarter filling various
strong and weak topological phases are obtained provided that both SO coupling
and uniaxial lattice distortion are present. Our analysis suggests that many of
the non-magnetic insulating pyrochlores should be topological insulators.

Mesoscale and Nanoscale Physics;Strongly Correlated Electrons