I. The topology

The standard 8×8 board is mapped onto the surface of a sphere, after the variant recorded at chessvariants.com.1 Two identifications do all the work.

First, the files wrap: the a-file and the h-file are adjacent, so ranks become circles, as on a cylinder.

Second, the poles. A piece leaving the top of the board does not fall off; it crosses the north pole and re-enters on rank 8, four files over, now heading south. The eighth rank is stitched to itself —

a8 ↔ e8   b8 ↔ f8   c8 ↔ g8   d8 ↔ h8

— and rank 1 does the same at the south pole. The shift of four files is even, so a bishop crossing a pole stays on its own colour. There are no edges anywhere on this board, and no corners.

II. Consequences

Every square has the full complement of neighbours, which quietly rewrites the strategy handed down for the flat board.

• A knight has eight moves from every square. There is nowhere to trap it against a rim that does not exist.
• Bishops can reach any square of their colour through the poles, and are correspondingly stronger.
• A rook's file is a closed loop around the whole sphere.
• The back rank can be attacked from behind, through the pole. Castling for safety in a corner is not merely disabled2 — there are no corners to castle into.

III. The game as played

This is not a sketch of the idea but a complete, working game.

Every rule survives the wrapping: check and checkmate arrive through the poles, en passant works across the a–h seam, pawns promote, and a sliding piece may not lap the sphere back onto its own square.3

The board is a sphere you spin and zoom by hand. Play online in real time — quick matchmaking, or private rooms by code; play a bot opponent that looks a few moves ahead and can be dialled down to lose gracefully;4 or hand the screen back and forth for a local game. Ranked play has Elo ratings, a leaderboard, and Google sign-in. Ten-minute clocks are kept by the house, so they cannot be cheated.