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 $f(9,10,11)$.