Chess in a Klein Bottle
Take the Moebius Variant, and join columns a and h . This creates a Klein Bottle. This can't be done in our three-dimensional space! The board becomes like this:
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 Each line rolls around +---+---+---+---+---+---+---+---+ itself, so that a White 3| | | | | | | | | 3 Pawn at a11 is attacking +---+---+---+---+---+---+---+---+ h12 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 WhiteAll other rules (castling, en-passant, promotion, etc) apply; contrary to the Torus Chess , where all columns are equivalent, the torsion in the board create a kind of non-symmetry: the a-h column is equivalent to the d-e column, but they are different to the b-g and c-f columns
Like in the Moebius Chess , along the 8-9-10-11-12-13-14-15 board, each King is facing the opponent's Queen; and the Bishops don't have a fixed colour
Since in an empty board in the Torus Chess a Bishop may reach, in one movement, all squares of the same colour, it's expected that in the Klein Chess a Bishop might reach all squares. Let's check this property: a Bishop starting at f1 might move in the diagonal f1- a6- h7- d11- f12- h14- a1- h8- a9- c11- e12 -c14 -b1 -a2-... -e1 -h4 ... -f1 -a6; or it might move in the other diagonal f1 -h3 ... f1. So, the Bishop can only reach 3/8 of the Board in one movement
This variant can lead to subvariants, or similar games:
- Torus Chess , if there is no twist between the 11th/12th lines
- Moebius Chess , if the a and h columns are separated
Written by Alberto Monteiro, (email removed contact us for address) troin.com.br.
WWW page created: October 6, 1997.