  The simplest Lorentz-nonreciprocal medium has the constitutive relations
(${\bf D} =\epso {\bf E} -{\bf \Gamma}\times {\bf H}$ and ${\bf B} =\muo {\bf
H} + {\bf \Gamma}\times{\bf E}$). Scattering by a three-dimensional object
composed of this medium was investigated using the extended boundary condition
method. Scattering by this object in free space must be attributed to non-zero
$\Gamma=\vert\bf \Gamma\vert$. The differential scattering efficiency is immune
to the transformation of the incident toroidal electric field phasor into a
poloidal electric field phasor, or \textit{vice versa}, and a consequence of
this source-invariance is the polarization-state invariance of the differential
scattering efficiency when the irradiating field is a plane wave. Both the
total scattering and forward-scattering efficiencies of an ellipsoid composed
of the simplest Lorentz-nonreciprocal medium are maximum when the plane wave is
incident in a direction {coparallel (but not antiparallel)} to $\bf \Gamma$,
and the backscattering efficiency is minimum when $\bf \Gamma$ is {parallel} to
the incidence direction. The total scattering and the forward-scattering
efficiencies are maximum when the incidence direction is parallel to the
largest semi-axis of the ellipsoid if the incidence direction is coparallel
(but not antiparallel) to $\bf \Gamma$. Lorentz nonreciprocity in an object is
thus intimately connected to the shape of that object in affecting the
scattered field.
