  Fragment-fragment-$\gamma$ coincidences have been measured for $\rm ^{28}Si +
{^{28}Si}$ at an energy corresponding to the population of a conjectured
resonance in $^{56}$Ni. Fragment angular distributions as well as $\gamma$-ray
angular correlations indicate that the spin orientations of the outgoing
fragments are perpendicular to the orbital angular momentum. This differs from
the $\rm ^{24}Mg+{^{24}Mg}$ and the $\rm ^{12}C+{^{12}C}$ resonances, and
suggests two oblate $\rm ^{28}Si$ nuclei interacting in an equator-to-equator
molecular configuration.
