  We are interested in the development of spherically symmetric geometries in
$F(T)$ teleparallel gravity which are of physical importance. We first express
the general forms for the spherically symmetric frame and the zero curvature,
metric compatible, spin connection. We then analyse the antisymmetric field
equations (the solutions of which split into two cases, which we subsequently
consider separately), and derive and analyse the resulting symmetric field
equations. In order to further study the applications of spherically symmetric
teleparallel models, we study $3$ subcases in which there is an additional
affine symmetry so that the resulting field equations reduce to a system of
ordinary differential equations. First, we study static spherical symmetric
geometries and solve the antisymmetric field equations and subsequently derive
the full set of symmetric field equations. In particular, we investigate vacuum
spacetimes and obtain a number of new solutions. Second, we consider an
additional affine frame symmetry in order to expand the affine frame symmetry
group to that of a spatially homogeneous Kantowski-Sachs geometry. Third, we
study the special case of spherical symmetry with an additional fourth
similarity affine vector.
