  Using, for the first time, configuration-constrained potential-energy-surface
calculations with the inclusion of $\beta_6$ deformation, we find remarkable
effects of the high order deformation on the high-$K$ isomers in $^{254}$No,
the focus of recent spectroscopy experiments on superheavy nuclei. For shapes
with multipolarity six, the isomers are more tightly bound and,
microscopically, have enhanced deformed shell gaps at $N=152$ and $Z=100$. The
inclusion of $\beta_6$ deformation significantly improves the description of
the very heavy high-$K$ isomers.
