  We give a presentation for the baseleaf preserving mapping class group
$Mod(\S)$ of the punctured solenoid $\S$. The generators for our presentation
were introduced previously, and several relations among them were derived. In
addition, we show that $Mod(\S)$ has no non-trivial central elements. Our main
tool is a new complex of triangulations of the disk upon which $Mod(\S)$ acts.
