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Loopover is a torus, not a sphere, and you'd have trouble building a physical version because the inner radius and outer radius are different, which would mean that some pieces would have to be different sizes and you wouldn't be able to do moves along one of the axes.
(and a whole bunch more; you can see the whole list on Jaap's Puzzle Page)
However, these don't have the topology of the standard Loopover game (which is a torus), and it's simply not possible to embed a torus into a sphere. (A sphere's sides do "wrap around", but they wrap around in a different and incompatible way from how the torus's sides "wrap around".)