A polyatomic ideal gas has 24 vibrational modes.

(1)

Since each vibrational mode has 2 degrees of freedom hence total vibrational degrees of 

freedom $=48$

$\mathrm{f}=3+3+48=54$

$\gamma=1+\frac{2}{\mathrm{f}}=\frac{28}{27}=1.03$