The contributions of the non-spherical interaction terms, arising due to the anisotropy, shape factor, quadrupole moment and quadrupole induced dipole interaction, to the third virial coefficient C(T) of carbon dioxide gas have been calculated over a range of temperatures by using the method suggested by Alder and Pople. The results show the importance of such contributions to C(T). The agreement with the experimental C(T) data becomes much better by including such contributions and also that due to the non-additive interactions. The conclusions drawn for carbon dioxide are expected to hold all the polyatomic gases.