[kecchtiu] Physical constructions of higher dimensional chess

Previously, higher dimensional chess.

3D: 8 chess boards stacked on top of each other with stilts.  Need to rotate alternating boards by 90 degrees to maintain checkerboard coloring up and down.  The separation between boards needs to be wide enough to allow reaching into the center squares.  Maybe use short pieces.

4D: 8 of the 3D laid out in a row, similar in style to a simul.  The opponents can be on opposite sides of the row.

5D: 64 of the 3D laid out in a 8x8 array.  Need space between individual tables to walk around.

6D becomes ridiculous: 8 levels of 5D, accessed by a mobile cherry picker or some other means of going up and down, perhaps ladders.  With ladders, it becomes serious exercise to play the game.

7D: 8 separate rooms of 6D, in a row.  Or, for a virtual reality implementation, 8 alternate realities indexed in a line.

8D: 64 rooms of 6D arranged in a 8x8 array.

9D: 8 floors of 8D.

10D: 8 buildings of 9D.

11D: 64 buildings of 9D.

These could in principle be built, at extremely high cost.  Probably want electronic boards which can sense what piece is where.  Of course, the game quickly becomes so large as to be unplayable by humans, maybe even unplayable by computers.

Build it in virtual 3D.