  In teleparallel gravity and, in particular, in $F(T)$ teleparallel gravity,
there is a challenge in determining an appropriate (co-)frame and its
corresponding spin connection to describe the geometry. Very often, the
"proper" frame, the frame in which all inertial effects are absent, is not the
simplest (e.g, diagonal) (co-)frame. The determination of the frame and its
corresponding spin connection for $F(T)$ teleparallel gravity theories when
there exist affine symmetries is of much interest. In this paper we present the
general form of the coframe and its corresponding spin connection for
teleparallel geometries which are invariant under a $G_6$ group of affine
symmetries. The proper coframe and the corresponding $F(T)$ field equations are
also shown for these Teleparallel Robertson Walker (TRW) geometries. Further,
with the addition of an additional affine symmetry, it is possible to define a
Teleparallel de Sitter (TdS) geometry.
