\begin{document}$\beta_\lambda$\end{document} (\begin{document}$\lambda=4,6,8,$\end{document} and 10) on the ground state properties of superheavy nuclei (SHN) near the doubly magic deformed nucleus \begin{document}$^{270}{\rm{Hs}}$\end{document} using the multidimensionally-constrained relativistic mean-field (MDC-RMF) model with five effective interactions: PC-PK1, PK1, NL3*, DD-ME2, and PKDD. The doubly magic properties of \begin{document}$^{270}{\rm{Hs}}$\end{document} include large energy gaps at \begin{document}$N=162$\end{document} and \begin{document}$Z=108$\end{document} in the single-particle spectra. By investigating the binding energies and single-particle levels of \begin{document}$^{270}{\rm{Hs}}$\end{document} in the multidimensional deformation space, we find that, among these higher-order deformations, the deformation \begin{document}$\beta_6$\end{document} has the greatest impact on the binding energy and influences the shell gaps considerably. Similar conclusions hold for other SHN near \begin{document}$^{270}{\rm{Hs}}$\end{document}. Our calculations demonstrate that the deformation \begin{document}$\beta_6$\end{document} must be considered when studying SHN using MDC-RMF."> Microscopic study of higher-order deformation effects on the ground states of superheavy nuclei around <sup>270</sup>Hs -
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