Total Routhian surface calculations have been performed to investigate rapidly rotating transfermium nuclei, the heaviest nuclei accessible by detailed spectroscopy experiments. The observed fast alignment in $^{252}$No and slow alignment in $^{254}$
No are well reproduced by the calculations incorporating high-order deformations. The different rotational behaviors of $^{252}$No and $^{254}$No can be understood for the first time in terms of $beta_6$ deformation that decreases the energies of the $ u j_{15/2}$ intruder orbitals below the N=152 gap. Our investigations reveal the importance of high-order deformation in describing not only the multi-quasiparticle states but also the rotational spectra, both providing probes of the single-particle structure concerning the expected doubly-magic superheavy nuclei.
