  We provide a comprehensive overview of metric-affine geometries with
spherical symmetry, which may be used in order to solve the field equations for
generic gravity theories which employ these geometries as their field
variables. We discuss the most general class of such geometries, which we
display both in the metric-Palatini formulation and in the tetrad / spin
connection formulation, and show its characteristic properties: torsion,
curvature and nonmetricity. We then use these properties to derive a
classification of all possible subclasses of spherically symmetric
metric-affine geometries, depending on which of the aforementioned quantities
are vanishing or non-vanishing. We discuss both the cases of the pure rotation
group $\mathrm{SO}(3)$, which has been previously studied in the literature,
and extend these previous results to the full orthogonal group $\mathrm{O}(3)$,
which also includes reflections. As an example for a potential physical
application of the results we present here, we study circular orbits arising
from autoparallel motion. Finally, we mention how these results can be extended
to cosmological symmetry.
