Probability of rolling a cuboid dice

Question

It's easy to count the probability of events on a regular dice because we know the probabilities ($P(1)$, $P(2)$, $P(3)$, $P(4)$, $P(5)$, $P(6)$) of all the basic outcomes ($P(i)=\frac{1}{6}$).

But... Is there any (simple) way how to determine the probabilities of basic outcomes of a cuboid dice? Let's suppose for example a cuboid of sizes 1 cm, 1.1 cm, 1.2 cm...

Answer 1

Diaconis, Holmes, and Montgomery have shown that when you look closely at the actual dynamics, taking angular momentum, etc., into account, even a coin toss is rather complicated.

Answer 2

The system can be best modeled by creating an analogy with thermodynamics or considering an integral over the solid angle. Either way this question that has been answered elsewhere:

http://www.riemer-koeln.de/mathematik/quader/cuboid.metrika.pdf

https://physics.stackexchange.com/questions/41297/how-to-determine-the-probabilities-for-a-cuboid-die