  We obtain the exhaustive list of 337 faithful spherical actions of rank two
or less on locally factorial Fano manifolds of dimension four or less. As a
preliminary step, we determine the explicit list of spherical homogeneous
spaces of dimension four or less, together with their combinatorial data. Then
we classify the possible locally factorial $G/H$-reflexive polytopes for each
such spherical homogeneous space $G/H$. From the combinatorial data gathered in
this article, one can easily read off the Picard rank (even the Picard group),
Fano index, anticanonical volume of the underlying locally factorial Fano
variety, etc.
