The triaxial dynamics of the quadrupole-deformed rotor model of both the rigid and the irrotational type have been investigated in detail. The results indicate that level patterns and E2 transitional characters of the two types of the model can be matched with each other to the leading order of the deformation parameter $beta$. Especially, it is found that the dynamical structure of the irrotational type with most triaxial deformation ($gamma=30^circ$) is equivalent to that of the rigid type with oblate deformation ($gamma=60^circ$), and the associated spectrum can be classified into the standard rotational bands obeying the rotational $L(L+1)$-law or regrouped into a new ground- and $gamma$-band with odd-even staggering in the new $gamma$-band commonly recognized as a signature of the triaxiality. The differences between the two types of the model in this case are emphasized especially on the E2 transitional characters.
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