This is the idea
This is the idea I just got about the three dimensions as there being six levels of board with each size getting smaller by one block each level starting at thirteen by thirteen square then an eleven by eleven square above and centered the 13 board. Next I figured that the pieces would be numbers rather than pieces. One through six, six being the king and ones are pawns, twos are nights, threes are bishops and fours rooks with the queen as five. This works out obviously to sides of the dice. Now as you move up a level to exactly where you are in the board below to the board above you gain in number. There being six levels a pawn or a number one would be a number six or a king at the top level. The first person to get a pawn to the top level with out being mated wins. I believe if each move to a new level costs a turn that would A slow things down but B might make the game more playable. If each move to a higher board was done to the position directly above the piece then there would need to be movement in the board below to get to the board above it since if the playing piece were outside the bounds of the board above.