There are $xyz$ dice arranged in an $x \times y \times z$ box such that touching faces have the same value.
All dice are indistinguishable up to rotations.

Let $f(x, y, z)$ be the number of possible arrangements.

You are given $f(1, 1, 1)=24$ and $f(2, 3 , 4)=18432$.

Find $f(9,10,11)$.