  For teleparallel gravity in four dimensions, Lucas and Pereira have shown
that a generalized Hodge dual for torsion tensor can be defined with
coefficients determined by mathematical consistency. In this paper, we
demonstrate that a direct generalization to other dimensions fails and no new
generalized Hodge dual operator could be given. Furthermore, if one enforces
the definition of a generalized Hodge dual to be consistent with the action of
teleparallel gravity in general dimensions, the basic identity for any sensible
Hodge dual would require an \textit{ad hoc} definition for the second Hodge
dual operation which is totally unexpected. Therefore, we conclude that at
least for the torsion tensor, the observation of Lucas and Pereira only applies
to four dimensions.
