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| White to move and mate in 4 by Udo Marks |
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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.[1] 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. And chapter 11 covers variants using multiple boards normally set side by side ("such games can also be considered as examples of three-dimensional chess" — Beasley).[2]
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| This article uses algebraic notation to describe chess moves. |
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| Raumschach starting position. An inverted knight is used to represent the unicorn. The pawn on square Bd2 can move to squares marked "●" and capture on squares marked "×". | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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 (air) 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 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) playing volume. The cubes (usually represented by squares) 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. (So, the kings begin on squares Ac1 and Ec5.)
Rooks, bishops, and knights move as they do in chess in any given plane. Rooks, for example, move through the six walls of the cubes in any rank, file, or column. Bishops move through the twelve edges of the cubes, and knights make a (0,1,2) leaping move (the same effect as one step as a rook and one as a bishop) enabling it to control 24 different cubes from the board's center. Unicorns move in a manner special to a 3D space (called triagonal movement) through the corners of the cubes. (Thus each unicorn can reach only 30 cubes; each player's pair, 60.) The queen combines the moves of a rook, bishop, and unicorn, giving it a total of 26 different directions to move (6 faces plus 12 edges plus 8 corners). The king moves the same as a queen but one step at a time. Pawns move forward as in chess, or one step directly upward (for White) or downward (for Black). Pawns capture diagonally as in chess, including one step upward (White) or downward (Black), through a front or side cube edge. Promotion occurs where pawns cannot move further, namely the rank E5 (for White's pawns) and rank A1 (Black's pawns). There is no pawn initial two-square advance, no en passant capture, and no castling. White moves first, and the object is still to checkmate the opposing king.
Probably the most familiar 3D[note 1] chess variant to the general public in the middle 20th and early 21st centuries 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.[3][note 2] The game even assumed a fairly significant role in the TOS episode "Court Martial". (Captain Kirk is put on trial for negligence in the death of a crew member. Spock, who had programmed the Enterprise's computer to be unbeatable at the game, plays five matches with the computer and easily wins each one, proving the machine—the source of seemingly irrefutable evidence confirming Kirk's guilt—had been tampered with, thereby destroying its credibility in its account of the incident.)
The original Star Trek prop was crafted using boards from 3D Checkers and 3D Tic-Tac-Toe sets available in stores at the time (games also seen in TOS episodes) and adding futuristic-looking chess pieces. The design retained the 64 squares of a traditional chessboard, but distributed them onto separate platforms in a hierarchy of spatial levels, implying to audiences how chess evolved by the time of a 23rd century predominated by space travel. Rules for the game were never invented within the series[6] – in fact, the boards are sometimes not even aligned consistently from one shot to the next within a single episode.
The Tri-D chessboard was further realized by its inclusion in the Star Trek Star Fleet Technical Manual by Franz Joseph, who created starting positions for the pieces and short, additional rules.
The complete Standard Rules for the game were originally developed in 1976 by Andrew Bartmess (with encouragement from Joseph) and were subsequently expanded by him into a commercially-available booklet.[7] A Creative Commons-licensed manual by Marco Bresciani gives a translation in Italian of the latest version of Bartmess's Standard Rules, and is available through the Star Trek Italian Club (for members only). A free summary in English of the Standard Rules is contained on Charles Roth's website, including omissions and ambiguities regarding piece moves across the four Tri-D gameboard 2×2 attack boards.
A complete set of tournament rules for Tri-Dimensional Chess written by Jens Meder is available on his website. Meder's rules are based on FIDE's rules more than Andrew Bartmess's Standard Rules, with some deviations too. A repository of Tournament Rules games can be found on the website of Michael Klein.
There are some software programs for playing Tri-D Chess, most notably Parmen, a Windows application written by Doug Keenan and available free on his website.
Plans for constructing a Tri-D chessboard can be found on The Chess Variant Pages, as well as in Bartmess's Tri-D Chess Rules and in Bresciani's manual. Details for building a travel-size board are included on Meder's website.