  We exhibit the traceless $SU(2)$ character variety of a 6-punctured 2-sphere
as a 2-fold branched cover of ${\mathbb{C}}P^3$, branched over the singular
Kummer surface, with the branch locus in $R(S^2,6)$ corresponding to the binary
dihedral representations. This follows from an analysis of the map induced on
$SU(2)$ character varieties by the 2-fold branched cover $F_{n-1}\to S^2$
branched over $2n$ points, combined with the theorem of Narasimhan-Ramanan
which identifies $R(F_2)$ with ${\mathbb{C}} P^3$. The singular points of
$R(S^2,6)$ correspond to abelian representations, and we prove that each has a
neighborhood in $R(S^2,6)$ homeomorphic to a cone on $S^2\times S^3$.
