  Hexaquark wave function with the quantum numbers $I(J^P)=0(3^+)$, which might
be relevant for $d^*(2380)$, is constructed under an assumption that this is
composed only of $u,d$ quarks in an $S$-wave. By combining three diquarks of
either type, ($\bm{\bar{3}}_c, I=1$) or ($\bm{6}_c, I=0$), we demonstrate that
there are five possible configurations for the six-quark state. The fully
antisymmetric wave function is constructed by linearly combining the five
configurations on an equal footing. We then take this wave function as well as
the five configurations to calculate the hexaquark mass using the contact type
effective potential consisting of the color-spin, color electric and constant
shift. The mass is found to be the same regardless of the configurations being
used including the fully antisymmetric one. This result can be traced to the
fact that the hexaquark system has a freedom in choosing three diquarks in the
construction of its wave function. The calculated hexaquark mass using the
empirical parameters independently fixed from the baryon spectroscopy is found
to be around $2342$ MeV, which is indeed very close to the experimental mass of
$d^*(2380)$. Therefore, the hexaquark picture is promising for $d^*(2380)$ as
far as the mass is concerned.
