  Efimov physics at $p$-wave unitarity for three equal mass fermions in
multiple symmetries interacting via Lennard-Jones potentials is predicted to
modify the long range interaction potential energy, but without producing a
true Efimov effect. This analysis treats the following total orbital angular
momenta and parities, $J^{\Pi}=0^{+}, 1^{+}, 1^{-}$ and $2^{-}$, for either
three spin-polarized fermions ($\uparrow \uparrow \uparrow $), or two spin-up
and one spin-down fermion ($\downarrow \uparrow \uparrow $). Our results for
the long range interaction in some of those cases agree with previous work by
Werner and Castin and by Blume {\it et al.}, namely in cases where the $s$-wave
scattering length goes to infinity. The present results extend those calculated
interaction energies to small and intermediate hyperradii comparable to the van
der Waals length, and we consider additional unitarity scenarios where the
$p$-wave scattering volume approaches infinity. The crucial role of the
diagonal hyperradial adiabatic correction term is identified and characterized.
