This might be useful, not sure:
The triangles in your mesh will be drawn in a certain order no matter which direction you view them. So in some directions it will look find because they will render back to front. In other directions that won’t because of the things in the article above.
That’s just 3D graphics. That’s not even a JME-specific thing.
Either you can rebuild your mesh every time it’s rotated so that the triangles are sorted back to front (possible but maybe a little slow) or you can find a different way to do what you are actually trying to do (which I’m not sure and you haven’t really explained why you need this).