Hint 3

(a) Taking the ${\bf e}_1$ axis along a side of length $a$, ${\bf e}_2$ along $b$ and ${\bf e}_3$ along $c$, we get

$$I_{11}={M\over 12}(b^2+c^2),\qquad I_{12}=I_{23}=I_{31}=0,$$

and similar expresssions for $I_{22}$ and $I_{33}$.

(b) With a similar choice of axes, in this case we get

$$I_{11}={M\over 3}(b^2+c^2),\qquad I_{12}=-{Mab\over 4}.$$

By symmetry, the remaining components of the tensor are

$$I_{22}={M\over 3}(c^2+a^2),\qquad I_{33}={M\over 3}(a^2+b^2),\qquad I_{23}=-{Mbc\over 4},\qquad I_{31}=-{Mca\over 4}.$$