  In this paper, we give a formula for the number of rational points on the
Dwork hypersurfaces of degree six over finite fields by using Greene's
finite-field hypergeometric function, which is a generalization of Goodson's
formula for the Dwork hypersurfaces of degree four. Our formula is also a
higher-dimensional and a finite field analogue of Matsumoto-Terasoma-Yamazaki's
formula. Furthermore, we also explain the relation between our formula and
Miyatani's formula.
