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Knowing the symobls positions out of a stopping angle

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I have a 3D Slot Reel, that I'm trying to simulate a 3D Slot Machine. I have 3D Cylinder that is composed out of 36 meshes ( symbols ) as shown in the figure. There are only 12 symbols, and I'm repeating it 3 times around the cylinder.

 

When the reel is spinning, I can get the stopping angle, but giving the above information, I would like to change the 3 symbols, that are behind the three symbols which will be appeared to the viewer or the player. My problem is, I can not find the symbol or the meshes indices, at any desired stop angle when its spinning at any time

 

 

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