The best constants of two kinds of discrete Sobolev inequalities on the C60 fullerene buckyball are obtained. All the eigenvalues of discrete Laplacian $A$ corresponding to the buckyball are found. They are roots of algebraic equation at most degree
$4$ with integer coefficients. Green matrix $G(a)=(A+a I)^{-1} (0<a<infty)$ and the pseudo Green matrix $G_*=A^{dagger}$ are obtained by using computer software Mathematica. Diagonal values of $G_*$ and $G(a)$ are identical and they are equal to the best constants of discrete Sobolev inequalities.
