[ddjmaops] Standard chess in a cube

Because 64 = 8*8 = 4*4*4, one can map the squares on a chessboard onto cubelets in a 4x4x4 cube.  Of course, no mapping can fully preserve the geometry of the square's rows, columns, and diagonals.  Nevertheless, are there some interesting mappings?  Try putting the 16 squares occupied by each player in the initial position on opposite faces of the cube.  With practice, a player can probably learn the mapping.  Perhaps treat the cube as an awkward UI for blindfold chess.

The next size square that is also a cube is 729 = 27*27 = 9*9*9 = 3^6.

For Shogi, 9*9 = 3*3*3*3 suggesting an order-3 hypercube.