  A teleparallel geometry is an n-dimensional manifold equipped with a frame
basis and an independent spin connection. For such a geometry, the curvature
tensor vanishes and the torsion tensor is non-zero. A straightforward approach
to characterizing teleparallel geometries is to compute scalar polynomial
invariants constructed from the torsion tensor and its covariant derivatives.
An open question has been whether the set of all scalar polynomial torsion
invariants, $\mathcal{I}_T$ uniquely characterize a given teleparallel
geometry. In this paper we show that the answer is no and construct the most
general class of teleparallel geometries in four dimensions which cannot be
characterized by $\mathcal{I}_T$. As a corollary we determine all teleparallel
geometries which have vanishing scalar polynomial torsion invariants.
