Musings on 3D Chess
Introduction
Chessboards
Piece Movement
Game Variations
Conclusion

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Musings on 3D Chess

Introduction

Chessboards

Piece Movement

3.1  Straight Line Piece Moves
3.2.  Knight Moves
3.3.  Pawn Moves
3.4.  Piece Movement - Upright, Varying
3.5.  Piece Movement - Cant, Constant
3.6.  Piece Movement - Slant, Constant
3.7.  Piece Movement - Skew, Varying

Game Variations

Conclusion

last modified: 03.07.09

3 Piece Movement - Cant, Constant

This chessboard is a strange variation which is my least favorite.

Piece 2D 3D Cant Comments

Vectors Vectors Illustration

Rook (±n,0)
(0,±n) (±n,0,0)
(0,±n,0)
±(n,0,n)
Travels through alternating color cells. Ends on a cell of either color.

Bishop (±n,±n) (±n,±n,0)
(±n,0,0)±(n,0,n)
(0,±n,0)±(n,0,n)
Travels through same color cells. Ends on a cell of the starting color.

Queen (±n,0)
(0,±n)
(±n,±n) (±n,0,0)
(0,±n,0)
(±n,±n,0)
±(n,0,n)
(±n,0,0)±(n,0,n)
(0,±n,0)±(n,0,n)
Makes all possible straight line moves. Ends on a cell of either color.

King (±1,0)
(0,±1)
(±1,±1) (±1,0,0)
(0,±1,0)
(±1,±1,0)
±(1,0,1)
(±1,0,0)±(1,0,1)
(0,±1,0)±(1,0,1) Moves the same as a Queen but only for a distance of one. Ends on a cell of either color.

Knight (±1,±2)
(±2,±1) (±1,±2,0)
(±2,±1,0)

(±2,0,0)±(1,0,1)
(0,±2,0)±(1,0,1)

(±1,0,0)±(2,0,2)
(0,±1,0)±(2,0,2) Travels through alternating color cells. Ends on a cell the opposite of the starting color.

Pawn First Move (White) +(0,1)
+(0,2) +(0,1,0)
+(0,2,0)
+(1,0,1)
+(2,0,2) Travels through alternating color cells. Ends on a cell of either color.

Pawn (White) +(0,1) +(0,1,0)
+(1,0,1) Travels to an opposite color cell. Ends on a cell the opposite of the starting color.

Pawn Attack (White) +(±1,1) +(±1,1,0)
+(0,1,0)+(1,0,1) Travels to a same color cell. Ends on a cell of the starting color.

Pawn First Move (Black) -(0,1)
-(0,2) -(0,1,0)
-(0,2,0)
-(1,0,1)
-(2,0,2) Travels through alternating color cells. Ends on a cell of either color.

Pawn (Black) -(0,1) -(0,1,0)
-(1,0,1) Travels to an opposite color cell. Ends on a cell the opposite of the starting color.

Pawn Attack (Black) -(±1,1) -(±1,1,0)
-(0,1,0)+(1,0,1) Travels through alternating color cells. Ends on a cell of either color.

Piece	2D	3D Cant
Vectors	Vectors	Illustration
Rook	(±n,0) (0,±n)	(±n,0,0) (0,±n,0) ±(n,0,n)	Travels through alternating color cells. Ends on a cell of either color.
Bishop	(±n,±n)	(±n,±n,0) (±n,0,0)±(n,0,n) (0,±n,0)±(n,0,n)	Travels through same color cells. Ends on a cell of the starting color.
Queen	(±n,0) (0,±n) (±n,±n)	(±n,0,0) (0,±n,0) (±n,±n,0) ±(n,0,n) (±n,0,0)±(n,0,n) (0,±n,0)±(n,0,n)	Makes all possible straight line moves. Ends on a cell of either color.
King	(±1,0) (0,±1) (±1,±1)	(±1,0,0) (0,±1,0) (±1,±1,0) ±(1,0,1) (±1,0,0)±(1,0,1) (0,±1,0)±(1,0,1)	Moves the same as a Queen but only for a distance of one. Ends on a cell of either color.
Knight	(±1,±2) (±2,±1)	(±1,±2,0) (±2,±1,0) (±2,0,0)±(1,0,1) (0,±2,0)±(1,0,1) (±1,0,0)±(2,0,2) (0,±1,0)±(2,0,2)	Travels through alternating color cells. Ends on a cell the opposite of the starting color.
Pawn First Move (White)	+(0,1) +(0,2)	+(0,1,0) +(0,2,0) +(1,0,1) +(2,0,2)	Travels through alternating color cells. Ends on a cell of either color.
Pawn (White)	+(0,1)	+(0,1,0) +(1,0,1)	Travels to an opposite color cell. Ends on a cell the opposite of the starting color.
Pawn Attack (White)	+(±1,1)	+(±1,1,0) +(0,1,0)+(1,0,1)	Travels to a same color cell. Ends on a cell of the starting color.
Pawn First Move (Black)	-(0,1) -(0,2)	-(0,1,0) -(0,2,0) -(1,0,1) -(2,0,2)	Travels through alternating color cells. Ends on a cell of either color.
Pawn (Black)	-(0,1)	-(0,1,0) -(1,0,1)	Travels to an opposite color cell. Ends on a cell the opposite of the starting color.
Pawn Attack (Black)	-(±1,1)	-(±1,1,0) -(0,1,0)+(1,0,1)	Travels through alternating color cells. Ends on a cell of either color.

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