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Spherical chess. Sides of the board are considered to be connected to form a sphere. (8x8, Cells: 64)
half sick of shadows wrote on 2008-07-08 UTCGood ★★★★
```Contrary to what some have written, this game is indeed spherical. Firstly,
the right and left edges are connected to each other, making a cylinder (or
annulus for the mathematically pedantic). Then imagine shrinking the top
and bottom circles on this cylinder until they become mere points. This
means that the top eight 'squares' are really triangles, all joining at
the top edge of the board, which is now a point. The same goes for the
bottom. The black pieces are then in a circle around the north pole and
the white ones around the south pole. For examples of what this looks
like, see:

http://69.90.174.250/photos/thumb_small/69461/69461,1165605152,1.jpg
http://www.cs.unc.edu/~olano/papers/primitive/sphere_check.gif

(although they all have too many squares, it should be eight from pole to
pole and eight around the equator)

For reference, the ranks become lines of latitude and the files lines of
longitude. A rook travelling up a file comes back down the 'opposite'
file four squares to the side. The other pieces are harder to work out,
but I assure you that this entry has got the geometry correct.

I independently invented the rules about five years ago and made my own
board out of a 10cm diameter polystyrene ball, with pins as pieces. This
worked quite well and only took a few hours to make with a black marker
and a piece of string for measurements. Before making it, I determined the
rules by drawing the board as a series of concentric circles (roughly like
circular chess, but 8x8 not 4x16), then make them go all the way into the
center point, which is one of the poles. This can give a playable flat
board for the game, and help you see how going through the poles works
(although it is pretty poor for helping with the colour that begins around
the outside of the circle).

As to the game, it is quite similar to cylindrical chess. Indeed, it is
identical until you go through a pole, which cannot happen until at least
a few pieces leave the home squares. The end is quite different as the
poles become vacated and are convenient for travel.

My only rules quibble would be that you don't need to modify the castling
rule. Indeed, I would play this and cylindrical chess without any castling
as the entire point of it is void when there are no corners of the board,
and it would never have been invented on such a board.```

Roberto Lavieri wrote on 2005-12-12 UTC
See also 'Moebius Chess', by Menno Dekker from the Netherlands. It is played on a Moebius strip.

Thomas McElmurry wrote on 2005-12-12 UTC
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.

Thomas McElmurry wrote on 2005-12-07 UTC
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?

v1adis1av wrote on 2005-12-06 UTCExcellent ★★★★★
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!

James Spratt wrote on 2004-11-27 UTC
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.

Jared McComb wrote on 2004-11-24 UTCPoor ★
The board is not actually spherical, but rather is a torus with a half-twist.

Mark wrote on 2004-11-24 UTCPoor ★
```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.```

Matthew Paul wrote on 2004-05-14 UTC
```Maybe a diagram of the starting position would be nice...
Or at least, some notation...```