  We study three-body recombination of fully spin-polarized ${}^6$Li atoms that
are interacting resonantly in relative p-waves. Motivated by a recent
experiment, we focus on negative scattering volumes where three atoms recombine
into a deep dimer and another atom. We calculate the three-body recombination
rate using a Faddeev equation derived from effective field theory. In
particular, we study the magnetic field and temperature dependences of the loss
rate and use the recombination data to determine the effective range of the
p-wave atom-atom interaction. We also predict the existence of a shallow
three-body bound state that manifests itself as a prominent feature in the
energy-dependent three-body recombination rate.
