Please help in this difficult math geometry quiz.

 From:  Elang
11167.4 
Hi Bem... thank you very much for the reply and link. I will definitely study them since it's kinda cool.

However, I prefer 'non-mathematical' solution with involves no calculation at all. Instead, I would like to know if using only MOI, the problem can be solved.

For a better illustration: there are many many tutorial on youtube to model a DODECAHEDRON, which most of them require us to enter some 'predefined' numbers (be it length or angle) to successfully create the geometry. However, there is one tutorial here (https://www.youtube.com/watch?v=_XDg57dO94E&t=116s), he is a friend of mine, that successfully model the geometry inside Moi WITHOUT any number inputs!.. So, I would like to know this kind of method in solving the math problem I posted before.

Hope you all can understand what I mead, and pardon for my english.

Thank you very much in advance.