  The Minkowski tensors are valuations on the space of convex bodies in
${\mathbb R}^n$ with values in a space of symmetric tensors, having additional
covariance and continuity properties. They are extensions of the intrinsic
volumes, and as these, they are the subject of classification theorems, and
they admit localizations in the form of measure-valued valuations. For these
local tensor valuations, restricted to convex polytopes, a classification
theorem has been proved recently, under the assumption of isometry covariance,
but without any continuity assumption. This characterization result is extended
here, replacing the covariance under orthogonal transformations by invariance
under proper rotations only. This yields additional local tensor valuations on
polytopes in dimensions two and three, but not in higher dimensions. They are
completely classified in this paper.
