Torus Chess (The Shape of Space)

This variant of chess on a torus was proposed by Jeffrey R. Weeks in his book "The Shape of Space" as a tool for teaching the geometry of a torus. It can be played as one of the Torus Games on his website. It is one of several variants that make use of the torus-shaped board:

• Torus Chess. Large chess variant on torus shaped board. (16x8, Cells: 128) By Köksal Karakus.
• Torus Chess on a Standard Board. Torus Chess on a standard board with a unique setup. (8x8, Cells: 64) By Karl Fischer.
• Chess in a Toroidal Board. 8 by 14 board with sides glued together. (8x14, Cells: 112) By Alberto Monteiro.
• Toroidal Byzantine Chess. Circular chess modified to also be toroidal. (Cells: 64) By Anatoly Khalfine and Ernst Saperow.

Setup

The setup differs from standard chess, and is chosen such that the only pieces which are under attack are the pawns of each player. This will become more clear in the move diagram below.

Pieces

The following pieces are used:

	Pawn (omnipawn / steward) Instead of an ordinary pawn, the omnipawn moves one square orthogonally to an empty square or captures the enemy piece one square diagonally. It cannot be promoted to any other piece. mWcF in Betza notation.
	Knight As in standard chess.
	Bishop As in standard chess.
	Rook As in standard chess.
	Queen As in standard chess.
	King As in standard chess, except that there is no castling.

To illustrate their motion on the torus, this is their motion from the starting position.

The rook slides orthogonally as in standard chess. Note that since the board wraps around, once it leaves the board on one side, it will enter on the opposite side and continue to slide in the same direction. In the initial position, each rook can thus move until there are friendly pieces in the way.

The bishop slides diagonally as in standard chess. Since the board wraps around on each side,it means that it attacks both enemy pawns.

The queen slides orthogonally or diagonally as in standard chess. From its initial position, it threatens both enemy pawns.

The knight leaps as in standard chess. Note that the "knight's wheel" continues across the edge of the board to the other side.

The pawn can only step to one square from its initial position, since all other neighboring squares are occupied by friendly pieces. It could capture diagonally, if there were any enemy pieces diagonally adjacent (but there are no pieces on the marked square in the initial positions, and so they cannot).

The king cannot move in its initial position, since all neighboring squares are ocupied by friendly pieces.

Rules

The main difference from standard chess is the fact that the board is wrapped on a torus, i.e., the left side is glued to the right side, and the top is glued to the bottom. This means that any rank, file or diagonal wraps around the board, so that it spans a full circle of 8 squares length. Most of the pieces move as in standard chess, with the only exception of the pawn, which moves differently and does not promote, and the absence of a castling rule.

As a consequence of the different board geometry, also the initial setup of the pieces is changed: with the standard setup both kings would be in check, since the top and bottom are glued to each other. In the proposed setup, the only pieces which immediately threaten any enemy pieces are the bishops and queens, and they threaten only the two pawns.

Notes

There also exists an implementation for Zillions of Games.

Last revised by Manuel Hohmann.