Vertical SpacingOne problem with 3 dimensional Chess is that the squares of a full-sized board are only half the width of a hand; the pieces themselves are taller than that, and if you need to reach into the middle of a 3D board to move a piece, of course the distance between levels must be greater than the height of a piece -- quite a bit greater, considering the size of a hand, and the need to have some room to maneuver.
The reason this is a problem is that the "vertical diagonals", for example from a1 on one level to a2 on the next and a3 on the third level, won't line up at a proper angle; and so these moves will be harder to see.
The Physical Design of a Low Technology 8x8 BoardIn order to play 8x8x8 chess, you would need 8 transparent boards with a framework to hold them in place, plus 8 chess-sets worth of specially-designed pieces (designed to be not too tall); and in order to move a piece into or out of the very center of the board, you'd need to have the framework designed very cleverly.
A simple but expensive solution would be to put the 8 transparent boards on sliding supports: to move a piece from e4 on level 4 to d5 on level 5, you'd pull out level 4 like a sliding drawer, remove the piece, push level 4 back in, pull out level 5, put down the piece, slide it back in. This would be cumbersome and error-prone.
In addition, the pieces would have to stick to their squares, so that they wouldn't fall over as you slid the pieces in and out. (One advantage of this would be that you could turn the board upside down to study the angles from the other side!)
If the pieces are stuck to their squares, of course you could have the 8 boards on hinges rather than sliders. In order to move a piece on the bottom level, you'd have to lift 7 boards, which might be heavy.
The hinges could be vertical, and you'd open the board like a book.
The Physical Design of a High Technology 8x8 BoardPhysical, bah! Holographic projections to mark the squares (cubes, I mean), and tractor beams to hold the pieces in place! Easy.
The Physical Design of a Feasible 8x8 BoardMake a wire frame; the pieces hang from the wires; you use a tool to reach in and move the pieces.
When you move from 4e4 to 5d5, don't the wires still get in the way?
Okay, from a rigid side you have 64 metal rods sticking out, and each rod has 8 discrete places to attach a piece. You reach in with the tool from the side opposite the base. The pieces clamp on, the tool releases them.
This works, but I couldn't afford to buy a set. The metal rod would be visually distracting as you tried to read the board.
Might be better and cheaper to build it big, using poles rather than rods, and move the pieces by hand. A one-meter cube would be heavy.
One meter is approximately 8 hands, so you really couldn't reach all the way in bare-handed; you'd still need a tool for moving the pieces.
The Physical Design of a Cheap and Useful Low Technology 8x8 BoardMake a one-meter frame and use 64 bungee cords; now you can move the pieces by hand.
Spray-paint the bungee cords before putting them in, to get the coloring for the white and black "squares". If you can find something thinner than bungee cords, it will be easier to read the board. The cords need to be taut, to prevent sagging; and it must be possible to tighten them.
Perhaps weighted twine would be better than stretchy cords...
One side has 64 anchors, the opposite side has 64 holes. 64 lengths of twine go from the anchors through the holes, and then, having different lengths so they don't tangle, are attached to weights. The idea is that you can push things aside when you reach in to move a piece, but then they go back to their proper places.
Now, what about the pieces? Could you take 8 regular sets and tape clothespins to them? Maybe it's better to simply make ad hoc hooks from pipe cleaners.
Playing 8x8x8 ChessOnly one King of each color needs to worry about check.
Expect the game to take a long time.