How to select remote faces on a complex mesh?

Hello the community and thank you in advance for the help.

On a snowy roof, I would like to select the remote faces : the six faces that are the most apart from one another. I have read the Select Mode page of the manual and did not find anything about it.

My goal is then to create a simplified physics shape, from these remote faces, that will cover the native shape, for a game that needs to have physics enabled.

On the picture bellow, I highlighted the remote X+ and Y+ faces I found seeking manually and randomly. I did it also for the X-, Y-, Z+ and Z- remote faces but it takes time. So my question is :

Is there a tip to find those faces easily ?

English is not my native, I apologize for the misspellings, Pierre