I wrote the game after read the article https://discourse.threejs.org/t/360-panorama-puzzle-and-vr-version/6556.
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Nice - pretty much the same game as the one I did.
Looks like you used the same approach - make a cube map and cut it in squares.
Have you thought about cutting it in different shapes?
I have an open question over at stackoverflow about cutting an equirectangular image so I can use it on any polyhedron ( see here at link to stackoverflow) but so far no answer.
If you have any idea on how to do that that would be great.
sorry, I know that question, but my mathematics is not enough good to resolve it.