  We derive the most general homogeneous and isotropic teleparallel geometries,
defined by a metric and a flat, affine connection. We find that there are five
branches of connection solutions, which are connected via several limits, and
can further be restricted to the torsion-free and metric-compatible cases. We
apply our results to several classes of general teleparallel gravity theories
and derive their cosmological dynamics for all five branches. Our results show
that for large subclasses of these theories the dynamics reduce to that of
closely related metric or symmetric teleparallel gravity theories, while for
other subclasses up to two new scalar degrees of freedom participate in the
cosmological dynamics.
