Three dimensional chess

the most popular 3-D board amongst inventors, and at the same time the most mentally indigestible for the players [...] Less demanding on spatial vision, and hence more practical, are those games confined to three 8×8 boards and games with boards smaller than 8×8.

Three-dimensional chess (or 3D chess) refers to any of various chess variants that use multiple boards at different levels, allowing the chess pieces to move in three physical dimensions. Three-dimensional variants have existed since the late 19th century, one of the oldest being Raumschach (German for "Space chess"), invented in 1907 by Dr. Ferdinand Maack and considered the classic 3D game. Maack founded a Raumschach club in Hamburg in 1919, which remained active until World War II.

Chapter 25 of Pritchard's The Classified Encyclopedia of Chess Variants discusses games using boards with three or more dimensions and contains some 50 such variations. Chapter 11 covers variants using multiple boards normally set side by side which can also be considered to add an extra dimension to chess.

The inventor contended that for chess to be more like modern warfare, attack should be possible not only from a two-dimensional plane but also from above (aerial) and below (underwater). Maack's original formulation was for an 8×8×8 board, but after experimenting with smaller boards eventually settled on 5×5×5 as best. Other obvious differences from standard chess include two additional pawns per player, and a special piece (two per player) named unicorn.

The Raumschach 3D board can be thought of as a cube sliced into five equal spaces across each of its three major coordinal planes. This sectioning yields a 5×5×5 (125-cube) gamespace. The cubes (usually represented by squares and often called cells) alternate in color in all three dimensions.

The horizontal levels are denoted by capital letters A through E. Ranks and files of a level are denoted using algebraic notation. White starts on the A and B levels and Black starts on E and D.

White moves first. The game objective, as in standard chess, is checkmate. Rooks, bishops, and knights move as they do in chess in any given plane.

Probably the most familiar 3D chess variant to the general public is the game of Tri-Dimensional Chess (or Tri-D Chess), which can be seen in many Star Trek TV episodes and movies, starting with the original series (TOS) and proceeding in updated forms throughout the subsequent movies and spinoff series.

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