  We derive a family of Post-Newtonian (PN) Dedekind ellipsoids to first order.
They describe non-axially symmetric, homogeneous, and rotating figures of
equilibrium. The sequence of the Newtonian Dedekind ellipsoids allows for an
axially symmetric limit in which a uniformly rotating Maclaurin spheroid is
recovered. However, the approach taken by Chandrasekhar & Elbert (1974) to find
the PN Dedekind ellipsoids excludes such a limit. In G\"urlebeck & Petroff
(2010), we considered an extension to their work that permits a limit of 1 PN
Maclaurin ellipsoids. Here we further detail the sequence and demonstrate that
a choice of parameters exists with which the singularity formerly found in
Chandrasekhar & Elbert (1974) along the sequence of PN Dedekind ellipsoids is
removed.
