Vizzini

3D Chess

Musings on 3D Chess

Introduction

Chessboards

Piece Movement

Game Variations

Conclusion

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Musings on 3D Chess

Table of Contents

  1. Introduction

  2. Chessboards

  3. Piece Movement
    4. 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
  4. Game Variations

  5. Conclusion

3.6.   Piece Movement - Slant, Constant

Piece 2D 3D Slant, Constant Comments
Vectors Vectors Illustration
Rook (±n,0)
(0,±n) 		(±n,0,0)
(0,±n,0)
±(0,n,n)
Travels through alternating color cells. Ends on a cell of either color.
Bishop (±n,±n) (±n,±n,0)
(±n,0,0)±(0,n,n)
(0,±n,0)±(0,n,n)
Travels through same color cells. Ends on a cell of the starting color.
Mace (a.k.a. Unicorn) n/a (±n,±n,±n) Triagonal move. 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)
±(0,n,n)
(±n,0,0)±(0,n,n)
(0,±n,0)±(0,n,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)
±(0,1,1)
(±1,0,0)±(0,1,1)
(0,±1,0)±(0,1,1) 		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)±(0,1,1)
(0,±2,0)±(0,1,1)

(±1,0,0)±(0,2,2)
(0,±1,0)±(0,2,2) 		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)
+(0,1,1)
+(0,2,2) 		Travels through alternating color cells. Ends on a cell of either color.
Pawn Normal and Attack (White) Normal:
+(0,1)
Attack:
+(±1,1) 		Normal:
+(0,1,0)
+(0,1,1)
Attack:
+(±1,1,0)
+(0,1,0)
+(0,1,1) 		Normal: Travels to an opposite color cell. Ends on a cell the opposite of the starting color.
Attack: 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)
-(0,1,1)
-(0,2,2) 		Travels through alternating color cells. Ends on a cell of either color.
Pawn Normal and Attack (Black) Normal:
-(0,1)
Attack:
-(±1,1) 		Normal:
-(0,1,0)
-(0,1,1)
Attack:
-(±1,1,0)
-(0,1,0)
-(0,1,1) 		Normal: Travels to an opposite color cell. Ends on a cell the opposite of the starting color.
Attack: Travels to a same color cell. Ends on a cell of the starting color.
n integer in [1,∞], in practice limited by the chessboard dimensions
a.k.a. also known as
n/a not applicable
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