  We continue to investigate the premetric teleparallel theory of gravity (TG)
with the coframe (tetrad) as gravitational potential. We start from the field
equations and a local and linear constitutive law. We create a Tonti diagram of
TG in order to disclose the structure of TG. Subsequently we irreducibly
decompose the 6th order constitutive tensor under the linear group. Moreover,
we construct the most general constitutive tensors from the metric and the
totally antisymmetric Levi-Civita symbol, and we demonstrate that they
encompass nontrivial axion and skewon type pieces. Using these tools, we derive
for TG in the geometric-optics approximation propagating massless spin 0, 1,
and 2 waves, including the special case of Einstein's general relativity.
