  We study the path $\Gamma=\{ C_{6,x}\ \vert\ x\in [0,1]\}$ in the moduli
space of configurations of 6 equal cylinders touching the unit sphere. Among
the configurations $C_{6,x}$ is the record configuration $C_{\mathfrak{m}}$ of
\cite{OS}. We show that $C_{\mathfrak{m}}$ is a local sharp maximum of the
distance function, so in particular the configuration $C_{\mathfrak{m}}$ is not
only unlockable but rigid. We show that if $\frac{(1 + x) (1 + 3 x)}{3}$ is a
rational number but not a square of a rational number, the configuration
$C_{6,x}$ has some hidden symmetries, part of which we explain.
