Crab Canon
Learn surface chess
Select a piece, then a highlighted square. Every exercise keeps legal turns and king safety. Most use a small, constructed setup; the first begins from the full starting board.
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The six pieces
Their movement follows the board’s connections. A pawn’s arrow shows its forward direction; White and Black identify ownership throughout.
| Piece | Movement | On these boards |
|---|---|---|
K King | One square in any permitted direction. | Cannot move into attack. Never captured. Castles only on Möbius. |
Q Queen | Any unobstructed distance along a rank, file or diagonal. | Every clear winding route counts. A cone blocks a diagonal ray. |
R Rook | Any unobstructed distance along a rank or file. | Can continue through marked connections until blocked. |
B Bishop | Any unobstructed distance diagonally. | Keeps one checkerboard color on Möbius and Klein. Genus two has no such global coloring. |
N Knight | A long, short, long jump: two steps along one cardinal direction with a perpendicular step between them. | Ignores intermediate pieces. Directions are carried through joins. |
P Pawn | One forward step into an empty square; captures diagonally forward. An unused right allows two clear forward steps. | Its facing reverses at reflected joins. Mandatory promotion and one-reply en passant apply. |
A slider stops at the first occupied cell, its departure cell, a boundary, a blocked diagonal or a repeated directed state. A friendly piece blocks the route; an opposing non-king piece may be captured. A legal move must leave its own king safe.
Reading moves and keeping history
A square has a file and rank, such as e4. Genus-two coordinates include the chart, such as I:a4 and II:a4. Move labels use long coordinates so seam crossings remain explicit.
e2–e4- A pawn move. Other pieces add their letter, as in
Re2×e5; × denotes a capture. c8–c9=N- A pawn promotes to a knight. The alternatives are Q, R and B.
O-O / O-O-O- East / west castling on Möbius. King and rook move together.
e.p.- En passant: the pawn lands on the recorded intermediate square and removes the vulnerable pawn elsewhere.
Play keeps the game. Study this position copies its complete historical prefix into an independent study. Edit begins a setup with unknown earlier history, fresh repetition counts and rights set deliberately. Saving a study retains its complete line and the viewed position.
Checkmate wins; stalemate, bare kings, fivefold repetition, or 150 halfmoves without a pawn move or capture draw. Checkmate takes precedence. Other material combinations are not automatically declared dead.
Three connected boards
