Möbius chess

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The record includes the complete move history and special-move rights.

Chess on three surfaces

White moves first. Select a piece and a highlighted destination. Captures, check and checkmate work through every marked connection. Kings are never captured.

On Möbius and Klein, crossing a side join reflects the remaining route. The small arrow shows a pawn’s forward direction. Knights jump along their transported path. Genus-two cone markers block a diagonal crossing, including a king or pawn diagonal.

Promotion: on Möbius, a pawn must promote at its final forward boundary. On Klein, White promotes on rank 15 and Black on rank 4. On genus two, White promotes on II:9 and Black on I:1. Choose queen, rook, bishop or knight.

En passant lasts for one reply and follows the previous pawn’s exact two-step route. Castling is available only on Möbius, with the original king and rooks on the short home-rank segment.

Stalemate, bare kings, fivefold repetition, or 150 consecutive halfmoves without a pawn move or capture draw. Checkmate takes precedence. Other material combinations are not automatically declared dead.

Piece ownership stays fixed through a join. Möbius and Klein support a consistent checkerboard coloring. The genus-two board does not; it uses one board color.