Larry Smith wrote on Fri, Nov 5, 2010 09:23 PM UTC:
Another idea about the 3x8x8 3D field. Restricting the King from translating to a similar cell which is attacked on the middle level. So that a King could not move from the bottom level to the top d4 cell if the d4 cell of the middle level was attacked by the opponent.
And a player could trap an opposing King with their own. For example, a King on the top a1 cell could pin an opposing King on the bottom b2 cell by simply translating to the b2 cell of the middle level. Neither King would directly attack the other in this position, and the King on the middle level could still 'release' this trap by translating to the top level.
This might greatly aid in the endgame.