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Rectahex Chess

Is hexagonal chess really hexagonal, or is it merely a rectangular dream?

The Diamond Board

If we rotate the chessboard 90 degrees counterclockwise, it becomes a diamond; and if the squares also become diamonds, nothing has really changed.

However, if the squares become squares, we get the following diagram:

                        +-----+
                        | h8 B|
                        |     |
                     +-----+-----+
                     | g8 W| h7 W|
                     |     |     |
                  +-----+-----+-----+
                  | f8 B| g7 B| h6 B|
                  |     |     |     |
               +-----+-----+-----+-----+
               | e8 W| f7 W| g6 W| h5 W|
               |     |     |     |     |
            +-----+-----+-----+-----+-----+
            | d8 B| e7 B| f6 B| g5 B| h4 B|     
            |     |     |     |     |     |     
         +-----+-----+-----+-----+-----+-----+
         | c8 W| d7 W| e6 W| f5 W| g4 W| h3 W|
         |     |     |     |     |     |     |
      +-----+-----+-----+-----+-----+-----+-----+
      | b8 B| c7 B| d6 B| e5 B| f4 B| g3 B| h2 B|
      |     |     |     |     |     |     |     |
   +-----+-----+-----+-----+-----+-----+-----+-----+
   | a8 W| b7 W| c6 W| d5 W| e4 W| f3 W| g2 W| h1 W|
   |     |     |     |     |     |     |     |     |
   +-----+-----+-----+-----+-----+-----+-----+-----+
      | a7 B| b6 B| c5 B| d4 B| e3 B| f2 B| g1 B|
      |     |     |     |     |     |     |     |
      +-----+-----+-----+-----+-----+-----+-----+
         | a6 W| b5 W| c4 W| d3 W| e2 W| f1 W|   
         |     |     |     |     |     |     |
         +-----+-----+-----+-----+-----+-----+
            | a5 B| b4 B| c3 B| d2 B| e1 B|     
            |     |     |     |     |     |     
            +-----+-----+-----+-----+-----+
               | a4 W| b3 W| c2 W| d1 W|
               |     |     |     |     |
               +-----+-----+-----+-----+
                  | a3 B| b2 B| c1 B|
                  |     |     |     |
                  +-----+-----+-----+
                     | a2 W| b1 W|
                     |     |     |
                     +-----+-----+
                        | a1 B|
                        |     |
                        +-----+
In the diagram, the notation "a1 B" for example, labels the square as a1, and reminds us that the square is a Black square.

This diagram is really our familiar 64 square chessboard, but there is an illusion, caused by the shape of the squares, that the lines of play are different.

For example, there appear to be three Rookwise directions in which one can move...

The Rectahex Rook

                        +-----+
                        | h8 B|
                        |     |
                     +-----+-----+
                     | g8 W| h7 W|
                     |     |     |
                  +-----+-----+-----+
                  | f8 B| g7 B| h6 B|
                  |     |     |     |
               +-----+-----+-----+-----+
               | e8 W| f7 W| g6 W| h5 W|
               |     |     |     |     |
            +-----+-----+-----+-----+-----+
            | d8 B| e7 B| f6 B| g5 B| h4 B|     
            | \\\\|     |     |     | ////|     
         +-----+-----+-----+-----+-----+-----+
         | c8 W| d7 W| e6 W| f5 W| g4 W| h3 W|
         |     | \\\\|     |     | ////|     |
      +-----+-----+-----+-----+-----+-----+-----+
      | b8 B| c7 B| d6 B| e5 B| f4 B| g3 B| h2 B|
      |     |     | \\\\|     | ////|     |     |
   +-----+-----+-----+-----+-----+-----+-----+-----+
   | a8 W| b7 W| c6 W| d5 W| e4 W| f3 W| g2 W| h1 W|
   |     |     |     | \\\\| ////|     |     |     |
   +-----+-----+-----+-----+-----+-----+-----+-----+
      | a7 B| b6 B| c5 B| d4 B| e3 B| f2 B| g1 B|
      | ====| ====| ====| Rook| ====| ====| ====|
      +-----+-----+-----+-----+-----+-----+-----+
         | a6 W| b5 W| c4 W| d3 W| e2 W| f1 W|   
         |     |     | ////| \\\\|     |     |
         +-----+-----+-----+-----+-----+-----+
            | a5 B| b4 B| c3 B| d2 B| e1 B|     
            |     | ////|     | \\\\|     |     
            +-----+-----+-----+-----+-----+
               | a4 W| b3 W| c2 W| d1 W|
               | ////|     |     | \\\\|
               +-----+-----+-----+-----+
                  | a3 B| b2 B| c1 B|
                  |     |     |     |
                  +-----+-----+-----+
                     | a2 W| b1 W|
                     |     |     |
                     +-----+-----+
                        | a1 B|
                        |     |
                        +-----+
The Rectahex Rook moves either as a Rook or as a Northwest/Southeast Bishop. Here is what it looks like with the board turned normally:

   +---+---+---+---+---+---+---+---+
 8 |   |   |   |\\\|   |   |   |   |
   +---+---+---+---+---+---+---+---+
 7 |===|   |   |\\\|   |   |   |   |
   +---+---+---+---+---+---+---+---+
 6 |   |===|   |\\\|   |   |   |   |
   +---+---+---+---+---+---+---+---+
 5 |   |   |===|\\\|   |   |   |   |
   +---+---+---+---+---+---+---+---+
 4 |///|///|///| R |///|///|///|///|
   +---+---+---+---+---+---+---+---+
 3 |   |   |   |\\\|===|   |   |   |
   +---+---+---+---+---+---+---+---+
 2 |   |   |   |\\\|   |===|   |   |
   +---+---+---+---+---+---+---+---+
 1 |   |   |   |\\\|   |   |===|   |
   +---+---+---+---+---+---+---+---+
     a   b   c   d   e   f   g   h
The Rectahex Rook has a move which is not symmetrical. From the square a1, it has no moves that a normal Rook would not have, but from the square h1, it has all the moves that a normal Queen would have.

The Rectahex Bishop

                        +-----+
                        | h8 B|
                        | |||||
                     +-----+-----+
                     | g8 W| h7 W|
                     |     |     |
                  +-----+-----+-----+
                  | f8 B| g7 B| h6 B|
                  |     | |||||     |
               +-----+-----+-----+-----+
               | e8 W| f7 W| g6 W| h5 W|
               |     |     |     |     |
            +-----+-----+-----+-----+-----+
            | d8 B| e7 B| f6 B| g5 B| h4 B|     
            |     |     | |||||     |     |     
         +-----+-----+-----+-----+-----+-----+
         | c8 W| d7 W| e6 W| f5 W| g4 W| h3 W|
         |     |     |     |     |     |     |
      +-----+-----+-----+-----+-----+-----+-----+
      | b8 B| c7 B| d6 B| e5 B| f4 B| g3 B| h2 B|
      | {{{{|     |     | |||||     |     | }}}}|
   +-----+-----+-----+-----+-----+-----+-----+-----+
   | a8 W| b7 W| c6 W| d5 W| e4 W| f3 W| g2 W| h1 W|
   |     |     | {{{{|     |     | }}}}|     |     |
   +-----+-----+-----+-----+-----+-----+-----+-----+
      | a7 B| b6 B| c5 B| d4 B| e3 B| f2 B| g1 B|
      |     |     |     |Bishp|     |     |     |
      +-----+-----+-----+-----+-----+-----+-----+
         | a6 W| b5 W| c4 W| d3 W| e2 W| f1 W|   
         |     | }}}}|     |     | {{{{|     |
         +-----+-----+-----+-----+-----+-----+
            | a5 B| b4 B| c3 B| d2 B| e1 B|     
            |     |     | |||||     |     |     
            +-----+-----+-----+-----+-----+
               | a4 W| b3 W| c2 W| d1 W|
               |     |     |     |     |
               +-----+-----+-----+-----+
                  | a3 B| b2 B| c1 B|
                  |     | |||||     |
                  +-----+-----+-----+
                     | a2 W| b1 W|
                     |     |     |
                     +-----+-----+
                        | a1 B|
                        | |||||
                        +-----+
The Rectahex Bishop moves as Northeast/Southwest Bishop, or as West-by-Northwest/East-by-Southeast Knightrider, or as North-by-Northwest/South-by-Southeast Knightrider.

This is confusing, so here is what it looks like with the normal view of the board:

   +---+---+---+---+---+---+---+---+
 8 |   |{{{|   |   |   |   |   |||||
   +---+---+---+---+---+---+---+---+
 7 |   |   |   |   |   |   |||||   |
   +---+---+---+---+---+---+---+---+
 6 |   |   |{{{|   |   |||||   |   |
   +---+---+---+---+---+---+---+---+
 5 |   |}}}|   |   |||||   |   |   |
   +---+---+---+---+---+---+---+---+
 4 |   |   |   | B |   |   |   |   |
   +---+---+---+---+---+---+---+---+
 3 |   |   |||||   |   |}}}|   |   |
   +---+---+---+---+---+---+---+---+
 2 |   |||||   |   |{{{|   |   |}}}|
   +---+---+---+---+---+---+---+---+
 1 |||||   |   |   |   |   |   |   |
   +---+---+---+---+---+---+---+---+
     a   b   c   d   e   f   g   h
Strangely enough, the Rectahex Bishop can reach squares of two different colors, but cannot reach all the squares on the board! In fact, it can reach only one third of all the squares on the board!

The Rectahex Queen

The Rectahex Queen combines the moves of the Rectahex Rook and the Rectahex Bishop, as follows:

                        +-----+
                        | h8 B|
                        | |||||
                     +-----+-----+
                     | g8 W| h7 W|
                     |     |     |
                  +-----+-----+-----+
                  | f8 B| g7 B| h6 B|
                  |     | |||||     |
               +-----+-----+-----+-----+
               | e8 W| f7 W| g6 W| h5 W|
               |     |     |     |     |
            +-----+-----+-----+-----+-----+
            | d8 B| e7 B| f6 B| g5 B| h4 B|     
            | \\\\|     | |||||     | ////|     
         +-----+-----+-----+-----+-----+-----+
         | c8 W| d7 W| e6 W| f5 W| g4 W| h3 W|
         |     | \\\\|     |     | ////|     |
      +-----+-----+-----+-----+-----+-----+-----+
      | b8 B| c7 B| d6 B| e5 B| f4 B| g3 B| h2 B|
      | {{{{|     | \\\\| ||||| ////|     | }}}}|
   +-----+-----+-----+-----+-----+-----+-----+-----+
   | a8 W| b7 W| c6 W| d5 W| e4 W| f3 W| g2 W| h1 W|
   |     |     | {{{{| \\\\| ////| }}}}|     |     |
   +-----+-----+-----+-----+-----+-----+-----+-----+
      | a7 B| b6 B| c5 B| d4 B| e3 B| f2 B| g1 B|
      | ====| ====| ====|Queen| ====| ====| ====|
      +-----+-----+-----+-----+-----+-----+-----+
         | a6 W| b5 W| c4 W| d3 W| e2 W| f1 W|   
         |     | }}}}| ////| \\\\| {{{{|     |
         +-----+-----+-----+-----+-----+-----+
            | a5 B| b4 B| c3 B| d2 B| e1 B|     
            |     | ////| ||||| \\\\|     |     
            +-----+-----+-----+-----+-----+
               | a4 W| b3 W| c2 W| d1 W|
               | ////|     |     | \\\\|
               +-----+-----+-----+-----+
                  | a3 B| b2 B| c1 B|
                  |     | |||||     |
                  +-----+-----+-----+
                     | a2 W| b1 W|
                     |     |     |
                     +-----+-----+
                        | a1 B|
                        | |||||
                        +-----+
You will not be surprised to read that the next diagram shows the moves of the Rectahex Queen in the normal view:
   +---+---+---+---+---+---+---+---+
 8 |   |{{{|   |\\\|   |   |   |||||
   +---+---+---+---+---+---+---+---+
 7 |===|   |   |\\\|   |   |||||   |
   +---+---+---+---+---+---+---+---+
 6 |   |===|{{{|\\\|   |||||   |   |
   +---+---+---+---+---+---+---+---+
 5 |   |}}}|===|\\\|||||   |   |   |
   +---+---+---+---+---+---+---+---+
 4 |///|///|///| Q |///|///|///|///|
   +---+---+---+---+---+---+---+---+
 3 |   |   |||||\\\|===|}}}|   |   |
   +---+---+---+---+---+---+---+---+
 2 |   |||||   |\\\|{{{|===|   |}}}|
   +---+---+---+---+---+---+---+---+
 1 |||||   |   |\\\|   |   |===|   |
   +---+---+---+---+---+---+---+---+
     a   b   c   d   e   f   g   h

The Rectahex Knight

The Rectahex Knight moves to the nearest 12 squares that the Rectahex Queen cannot reach:
                        +-----+
                        | h8 B|
                        |     |
                     +-----+-----+
                     | g8 W| h7 W|
                     |     |     |
                  +-----+-----+-----+
                  | f8 B| g7 B| h6 B|
                  |     |     |     |
               +-----+-----+-----+-----+
               | e8 W| f7 W| g6 W| h5 W|
               |     |     |     |     |
            +-----+-----+-----+-----+-----+
            | d8 B| e7 B| f6 B| g5 B| h4 B|     
            |     |     |     |     |     |     
         +-----+-----+-----+-----+-----+-----+
         | c8 W| d7 W| e6 W| f5 W| g4 W| h3 W|
         |     |     | nnnn| nnnn|     |     |
      +-----+-----+-----+-----+-----+-----+-----+
      | b8 B| c7 B| d6 B| e5 B| f4 B| g3 B| h2 B|
      |     | nnnn|     |     |     | nnnn|     |
   +-----+-----+-----+-----+-----+-----+-----+-----+
   | a8 W| b7 W| c6 W| d5 W| e4 W| f3 W| g2 W| h1 W|
   |     | nnnn|     |     |     |     | nnnn|     |
   +-----+-----+-----+-----+-----+-----+-----+-----+
      | a7 B| b6 B| c5 B| d4 B| e3 B| f2 B| g1 B|
      |     |     |     |Night|     |     |     |
      +-----+-----+-----+-----+-----+-----+-----+
         | a6 W| b5 W| c4 W| d3 W| e2 W| f1 W|   
         | nnnn|     |     |     |     | nnnn|
         +-----+-----+-----+-----+-----+-----+
            | a5 B| b4 B| c3 B| d2 B| e1 B|     
            | nnnn|     |     |     | nnnn|     
            +-----+-----+-----+-----+-----+
               | a4 W| b3 W| c2 W| d1 W|
               |     | nnnn| nnnn|     |
               +-----+-----+-----+-----+
                  | a3 B| b2 B| c1 B|
                  |     |     |     |
                  +-----+-----+-----+
                     | a2 W| b1 W|
                     |     |     |
                     +-----+-----+
                        | a1 B|
                        |     |
                        +-----+
Here it is in the normal view:
   +---+---+---+---+---+---+---+---+
 8 |   |   |   |   |   |   |   |   |
   +---+---+---+---+---+---+---+---+
 7 |   |nnn|nnn|   |   |   |   |   |
   +---+---+---+---+---+---+---+---+
 6 |nnn|   |   |   |nnn|   |   |   |
   +---+---+---+---+---+---+---+---+
 5 |nnn|   |   |   |   |nnn|   |   |
   +---+---+---+---+---+---+---+---+
 4 |   |   |   | N |   |   |   |   |
   +---+---+---+---+---+---+---+---+
 3 |   |nnn|   |   |   |   |nnn|   |
   +---+---+---+---+---+---+---+---+
 2 |   |   |nnn|   |   |   |nnn|   |
   +---+---+---+---+---+---+---+---+
 1 |   |   |   |   |nnn|nnn|   |   |
   +---+---+---+---+---+---+---+---+
     a   b   c   d   e   f   g   h
The Rectahex Knight moves Northeast/Southwest N (NNE Knight or ENE Knight/et cetera), or as NW/SE (1,3)-leaper or as NW/SE (2,3)-leaper.

This is a cumbersome piece, but it can reach every square of the board.

Surprise! Surprise!

The Rectahex Rook, Rectahex Bishop, Rectahex Queen, and Rectahex Knight move exactly the same way as do the R, B, Q, and N in Hexagonal Chess -- at least, as described so far they are exactly the same!

However, this page is not about Hexagonal Chess. It is about Rectahex Chess, and so some differences may turn up.

The Rectahex Pawn

The Rectahex Pawn moves exactly like a normal Pawn.

The Rectahex King

The Rectahex King moves exactly like a normal King, and may Castle.

The Rectahex Opening Position

The opening position of Rectahex Chess is exactly the same as that of FIDE Chess, except, of course, that instead of the normal Rooks, Knights, Bishops, and Queens we have Rectahex Rooks, Knights, Bishops, and Queens.

Hexarect Chess

Suppose that in the original diagram we had turned the board 90 degrees clockwise instead of 90 degrees counterclockwise.

This would flip the moves of all the pieces. There follows a series of diagrams showing how some Hexarect pieces move:

   +---+---+---+---+---+---+---+---+
 8 |   |   |   |\\\|   |   |   |===|
   +---+---+---+---+---+---+---+---+
 7 |   |   |   |\\\|   |   |===|   |
   +---+---+---+---+---+---+---+---+
 6 |   |   |   |\\\|   |===|   |   |
   +---+---+---+---+---+---+---+---+
 5 |   |   |   |\\\|===|   |   |   |
   +---+---+---+---+---+---+---+---+
 4 |///|///|///| R |///|///|///|///|
   +---+---+---+---+---+---+---+---+
 3 |   |   |===|\\\|   |   |   |   |
   +---+---+---+---+---+---+---+---+
 2 |   |===|   |\\\|   |   |   |   |
   +---+---+---+---+---+---+---+---+
 1 |===|   |   |\\\|   |   |   |   |
   +---+---+---+---+---+---+---+---+
     a   b   c   d   e   f   g   h
   +---+---+---+---+---+---+---+---+
 8 |   |   |   |   |   |{{{|   |   |
   +---+---+---+---+---+---+---+---+
 7 |||||   |   |   |   |   |   |   |
   +---+---+---+---+---+---+---+---+
 6 |   |||||   |   |{{{|   |   |}}}|
   +---+---+---+---+---+---+---+---+
 5 |   |   |||||   |   |}}}|   |   |
   +---+---+---+---+---+---+---+---+
 4 |   |   |   | B |   |   |   |   |
   +---+---+---+---+---+---+---+---+
 3 |   |}}}|   |   |||||   |   |   |
   +---+---+---+---+---+---+---+---+
 2 |   |   |{{{|   |   |||||   |   |
   +---+---+---+---+---+---+---+---+
 1 |   |   |   |   |   |   |||||   |
   +---+---+---+---+---+---+---+---+
     a   b   c   d   e   f   g   h
Hexarect Chess is, of course, an uninteresting mirror image of Rectahex Chess.

Rectahexahexarect Chess

The rules are the same as Rectahex Chess, but whenever you move a Rectahex piece you may replace it with its Hexarect equivalent, and whenever you move a Hexarect piece you may replace it with its Rectahex equivalent.

Rectahexahexarect Chess is tactically difficult; probably it is too difficult.

Summary

Hexagonal Chess can be played quite simply on a normal rectangular board, and therefore one may question whether it is as hexagonal as it ought to be.

Written by Ralph Betza.


WWW page made: January 15, 2003.