  The vast knowledge of strong influence of quadrupole deformation $\beta_2$ of
colliding nuclei on heavy-ion subbarrier fusion reactions inspires a desire to
quest the sensitivity of fusion dynamics to higher order deformations, such as
$\beta_4$ and $\beta_6$ deformations. However, such studies have rarely been
carried out, especially for deformation of projectile nuclei. In this article,
we investigated the role of $\beta_4$ of the projectile nucleus in fusion of
the $^{28}$Si + $^{92}$Zr system. We demonstrated that the fusion barrier
distribution is sensitive to the sign and the value of the $\beta_4$ parameter
of the projectile, $^{28}$Si, and confirmed that the $^{28}$Si nucleus has a
large positive $\beta_4$. This study opens an indirect way to estimate
deformation parameters of radioactive nuclei using fusion reactions, which is
otherwise difficult due to experimental constraints.
