Regular Icosahedron - How much to rotate X, Y, Z to get from face to face?

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I have a regular icosahedron shape in Adobe After Effects. I want to start out with the one side flush with the camera, then have the rotations end with another face (adjacent) flush with the camera.

I can adjust X, Y, and Z rotation, in degrees (0-360).

What values should I put to cause a perfect rotation to flush with another face?

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The first (2-fold) is what is shown at (x=0,y=0,z=0) rotation. 3-fold is where we want to start and finish the rotation. I think I got to 3-fold with (x=70,y=0,z=0), but I am not sure it is perfect.

Thanks for being awesome!!