Moebius Chess

Moebius Chess
Menno Dekker from Haarlem, the Netherlands, invented Moebius Chess in 1992 or 1993. The rules of this game were sent to me by Rob Nierse. Moebius Chess has not been played often, asfar as I know.
It is somewhat different from the Moebius Chess which is used sometimes in fairy chess problems: the board of the game described here has 128 squares, whereas the board of fairy chessproblems Moebius chess has 64 squares.
Moebius Rings
Take a strip of paper. Twist it once, and then glue the ends together. Now you have a Moebius Ring, called after the mathematician who inventedthis concept. Note that the Moebius ring has only one side: when you start to draw a line around the strip, you will first come to the other side of the paper of where you started to draw before youcome back to the place where you started to draw.
A Moebius Chess Board
The chess board of Moebius Chess is like a Moebius strip. The idea is: consider an 8 by 8 board, that is drawn at both sides ofa piece of paper. (The paper should either be very elastic, or, better, the squares should be rectangles, e.g., with a size of 10 by 2 centimeters.) Make a Moebius ring of this board, as describedabove. Rob Nierse wrote me that he actually made a board this way (of paper, with pieces made of pieces of paper): it looks quite interesting, but is hard to use.
We have a chess board of 8 rows, and16 columns. The first eight columns form a normal chess board; the second eight columns are a chess board `mirrored'. The squares of the second board have an accent (') in their notation.
a8 | b8 |c8 | d8 | e8 | f8 | g8 | h8 | a1' | b1' | c1' | d1' | e1' | f1' | g1' | h1' |
a7 | b7 | c7 | d7 | e7 | f7 | g7 | h7 | a2' | b2' | c2' | d2' | e2' | f2' | g2' | h2' |
a6 | b6 | c6 | d6 | e6 | f6| g6 | h6 | a3' | b3' | c3' | d3' | e3' | f3' | g3' | h3' |
a5 | b5 | c5 | d5 | e5 | f5 | g5 | h5 | a4' | b4' | c4' | d4' | e4' | f4' | g4' | h4' |
a4 | b4 | c4 | d4 | e4 | f4 | g4 | h4 |...