Chess in a Moebius Strip

Take the Cylindrical 8 x 14 Variant. Why should the board be glued so nicely? Why not twist it before the glue? The board would still look like the picture below, however, along the 11th/12th (or -3rd/-2nd) junction, there would be a "inversion", so that a11 would join h12, b11 would join g12, and so on:

	       Black
    a   b   c   d   e   f   g   h
  +---+---+---+---+---+---+---+---+
14| P | P | P | P | P | P | P | P | 0
  +---+---+---+---+---+---+---+---+
13|   |   |   |   |   |   |   |   |-1        The 15th line is identical
  +---+---+---+---+---+---+---+---+          to the 1st, in other words,
12|   |   |   |   |   |   |   |   |-2        the 9th line is the -5th.
  +***+***+***+***+***+***+***+***+
11|   |   |   |   |   |   |   |   |-3        White's pawns in the 2nd line
  +---+---+---+---+---+---+---+---+          or Black's pawns in the 9th
10|   |   |   |   |   |   |   |   |-4        (or -5th) move forward.
  +---+---+---+---+---+---+---+---+
 9| p | p | p | p | p | p | p | p |-5        White's pawns in the 0th
  +---+---+---+---+---+---+---+---+          (14th) or Black's pawns in
 8| r | n | b | q | k | b | n | r | 8        the 7th line move backwards.
  +---+---+---+---+---+---+---+---+
 7| p | p | p | p | p | p | p | p | 7        The 11th/12th (or -3rd/-2nd)
  +---+---+---+---+---+---+---+---+          junction is done after a
 6|   |   |   |   |   |   |   |   | 6        rotation of the board, so
  +---+---+---+---+---+---+---+---+          that the a11 is in front of
 5|   |   |   |   |   |   |   |   | 5        h12, and so on.
  +---+---+---+---+---+---+---+---+   
 4|   |   |   |   |   |   |   |   | 4
  +---+---+---+---+---+---+---+---+   
 3|   |   |   |   |   |   |   |   | 3
  +---+---+---+---+---+---+---+---+   
 2| P | P | P | P | P | P | P | P | 2
  +---+---+---+---+---+---+---+---+   
 1| R | N | B | Q | K | B | N | R | 1
  +---+---+---+---+---+---+---+---+
    a   b   c   d   e   f   g   h
	     White

All other rules (castling, en-passant, promotion, etc) apply.

An interesting aspect of this board is that, while on most standard variants, the King is facing the other King, here, along the 8-9-10-11-12-13-14-15 board, each King is facing the opponent's Queen.

The Moebius Strip is a non-oriented surface. While this concept can hardly apply to chess, a minor consequence is that the Bishops don't have a fixed colour: a bishop that starts in a "White" square (say, f1) can chance to a "Black" square (f1-a6-b12).

A sample game could be:

1-   d12    e11 [actually in front of the d12 pawn]
2-   c12    [White is playing a Queen's Gambit, while
	     Black is playing a King's Gambit!]
2-   ...    exc12
3-   e12    g11 [defending the c12 pawn]

This variant can lead to subvariants, or similar games:

Cylindrical Chess, if there is no twist before glueing.
Klein Chess, if the Moebius Strip is glued again, along the a and h columns.

Written by Alberto Monteiro, (email removed contact us for address) troin.com.br.

WWW page created: October 6, 1997.

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Created on: October 06, 1997. Last modified on: October 06, 1997.

Chess in a Moebius Strip

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