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See also 'Moebius Chess', by Menno Dekker from the Netherlands. It is played on a Moebius strip.

In related news, BrainKing offers a game called Froglet, and has just introduced a variant called 'Sphere Froglet' ... played on a torus, of course.

I think we need to start teaching topology in elementary schools.

Jared is right to point out that the board is not spherical, but it's not
a torus either. It would be a torus with a half-twist if a1->d1 were
joined to e8->h8 and e1->e4 to a8->d8, and it would be a sphere if a1->d1
were joined to h1->e1 and a8->d8 to h8->e8. But instead we have a1->d1
joined to e1->h1 and a8->d8 to e8->h8. This board is a compact nonorientable manifold with Euler characteristic 0, i.e. a Klein bottle.

Of course, chess on a Klein bottle has got to be at least as cool as chess on a sphere, right?

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!

I like the idea of spherical chess; I visualize 'globular chess.' Is there a graphic representation of a board (globe?) somewhere, showing shape of cells, etc.? Seems like magnetic--steel globe with little magnets in bases of pieces would work, and you'd have to be able to rotate the globe. Paint it up like Earth and play out some ominous metaphors.

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.

Maybe a diagram of the starting position would be nice... Or at least, some notation...

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