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About 1980 I and two my friends (we were 12 or 13 years old) often played spherical chess (as well as the cylinder one) with just these rules, including rules of 'transpolar' moving of pieces, four types of castling etc. We had invented these rules independently, knowing rules of the cylinder chess. It was very interesting to play simultaneously three games on three boards between three persons (a kind of triangle) with one board of normal, one of cylinder ad one of spherical rules -- it gives a very good brain training!
The board is not actually spherical, but rather is a torus with a half-twist.
One assumes that a magnetic version (or perhaps a velcro version) exists. I have big trouble seeing the board layout. Starting position is the same as square chess. I think the polar problem is too complex. Better would be degenerate triangles perhaps.
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