  The planar Hall effect (PHE), wherein a rotating magnetic field in the plane
of a sample induces oscillating transverse voltage, has recently garnered
attention in a wide range of topological metals and insulators. The observed
twofold oscillations in $\rho_{yx}$ as the magnetic field completes one
rotation are the result of chiral, orbital and/or spin effects. The
antiperovskites $A_3B$O ($A$ = Ca, Sr, Ba; $B$ = Sn, Pb) are topological
crystalline insulators whose low-energy excitations are described by a
generalized Dirac equation for fermions with total angular momentum $J = 3/2$.
We report unusual sixfold oscillations in the PHE of Sr$_3$SnO, which persisted
nearly up to room temperature. Multiple harmonics (twofold, fourfold and
sixfold), which exhibited distinct field and temperature dependencies, were
detected in $\rho_{xx}$ and $\rho_{yx}$. These observations are more diverse
than those in other Dirac and Weyl semimetals and point to a richer interplay
of microscopic processes underlying the PHE in the antiperovskites.
