| 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. |
| 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 (White) | +(0,1) | +(0,1,0) +(0,1,1) |
 |
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)+(0,1,1) |
 |
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) -(0,1,1) -(0,2,2) |
 |
Travels through alternating color cells. Ends on a cell of either color. |
| Pawn (Black) | -(0,1) | -(0,1,0) -(0,1,1) |
 |
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)+(0,1,1) |
 |
Travels to a same color cell. Ends on a cell of the starting color. |