Three-dimensional chess

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Kubikschach 8×8×8 gamespace
King / Queen
Maack's unicorn
Chess pieces in three dimensions

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 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. Chapter 11 covers variants using multiple boards normally set side by side which can also be considered to add an extra dimension to chess.[2]

Three-dimensional chess is used colloquially to describe complex, dynamic systems with many competing entities and interests, including politics, diplomacy and warfare. To describe an individual as "playing three-dimensional chess" implies a higher-order understanding and mastery of the system beyond the comprehension of their peers or ordinary observers.[3][4]


Lionel Kieseritzky (1806-1853) developed Kubikschach (German for Cube Chess) in 1851.[5] He used an 8×8×8 board, labelling the third dimension with Greek letters alpha through theta. This format was later picked up by Maack in 1907 when developing Raumschach. According to David Pritchard, this format is:

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.[6]


Ferdinand Maack (1861–1930) developed Raumschach (German for Space Chess) in 1907. He 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.

Raumschach 5×5×5 gamespace

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.


Ea5 black rook Eb5 black knight Ec5 black king Ed5 black knight Ee5 black rook
Ea4 black pawn Eb4 black pawn Ec4 black pawn Ed4 black pawn Ee4 black pawn
Ea3 Eb3 Ec3 Ed3 Ee3
Ea2 Eb2 Ec2 Ed2 Ee2
Ea1 Eb1 Ec1 Ed1 Ee1
Da5 N d Db5 black bishop Dc5 black queen Dd5 N d De5 black bishop
Da4 black pawn Db4 black pawn Dc4 black pawn Dd4 black pawn De4 black pawn
Da3 Db3 Dc3 Dd3 De3
Da2 Db2 Dc2 Dd2 De2
Da1 Db1 Dc1 Dd1 De1
Ca5 Cb5 Cc5 Cd5 Ce5
Ca4 Cb4 Cc4 black circle Cd4 Ce4 black circle
Ca3 Cb3 Cc3 Cd3 white cross Ce3
Ca2 Cb2 Cc2 white cross Cd2 white circle Ce2 white cross
Ca1 Cb1 Cc1 Cd1 Ce1
Ba5 Bb5 Bc5 Bd5 Be5
Ba4 Bb4 Bc4 Bd4 Be4
Ba3 Bb3 black circle Bc3 white cross Bd3 white circle Be3 white cross
Ba2 white pawn Bb2 white pawn Bc2 white pawn Bd2 white pawn Be2 white pawn
Ba1 white bishop Bb1 N l Bc1 white queen Bd1 white bishop Be1 N l
Aa5 Ab5 Ac5 Ad5 Ae5
Aa4 Ab4 Ac4 Ad4 Ae4
Aa3 Ab3 Ac3 Ad3 Ae3
Aa2 white pawn Ab2 white pawn Ac2 white pawn Ad2 white pawn Ae2 white pawn
Aa1 white rook Ab1 white knight Ac1 white king Ad1 white knight Ae1 white rook
Raumschach starting position.[7] White's pawn on Bd2 can move to cells with a white dot and capture on cells marked "×". Black's unicorn on Dd5 can move to cells with a black dot or capture the white pawn on Aa2.

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.

  • A rook moves through the six faces of a cube in any rank, file, or column.
  • A bishop moves through the twelve edges of a cube.
  • A knight makes a (0,1,2) leap (the same effect as one step as a rook followed by one step as a bishop in the same outward direction) enabling it to control 24 different cells from the board's center.
  • A unicorn moves in a manner special to a 3D space (i.e. triagonal movement) through the corners of a cube, any number of steps in a straight line.[a]
  • The queen combines the moves of a rook, bishop, and unicorn.[b]
  • The king moves the same as the queen but one step at a time.
  • A pawn, as in chess, moves and captures always forward toward the promotion rank (rank E5 for White, rank A1 for Black). This includes moving one step directly upward (for White) or downward (for Black), and capturing one step diagonally upward (White) or diagonally downward (Black), through a front or side cube edge. In Raumschach there is no pawn initial two-step move (and consequently no capturing en passant), and no castling.

Star Trek Tri-Dimensional Chess[edit]

3D chess on Star Trek (from the episode "Court Martial")

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.[8][c]

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 chess pieces from the futuristic-looking Classic chess set designed by Peter Ganine in 1961.[11] The design retained the 64 squares of a traditional chessboard, but distributed them onto separate platforms in a hierarchy of spatial levels, suggesting to audiences how chess adapted to a future predominated by space travel. Rules for the game were never invented within the series[12] – in fact, the boards are sometimes not even aligned consistently from one scene 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.

Rules development[edit]

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.[13] 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' Standard Rules, with some deviations too. A repository of Tournament Rules games can be found on the website of Michael Klein.

Board details[edit]

The Tri-D chessboard
Playing Parmen

Plans for constructing a Tri-D chessboard can be found on The Chess Variant Pages, as well as in Bartmess' Tri-D Chess Rules. Details for building a travel-size board are included on Meder's website.


There is software for playing Tri-D Chess. Parmen is a Windows application written by Doug Keenan and available free on his website. A free Android version of Tri D Chess is offered by AwfSoft.

Millennium 3D Chess[edit]

Millennium 3D Chess, created by William L. D'Agostino in 2001, employs three stacked 8×8 boards.[14] The inventor describes his objective as "extending the traditional chess game into a multilevel environment without distorting the basic game."

In popular culture[edit]

  • The 1966 Batman episode "The Purr-fect Crime" has Bruce Wayne and Dick Grayson playing a four-level chess variant.
  • On the TV show The Big Bang Theory, characters Leonard and Sheldon can be seen playing Tri-D chess in the beginning of Episode 11 in Season 1. Sheldon and Penny also play in "The Hofstadter Insufficiency".
  • A three-dimensional chess variant may be seen in the Blake's 7 fourth-season episode "Games".
  • A non-Star Trek type of three-dimensional chess set is used as a recurring prop in the lounge of the SHADO Moonbase in the British TV series UFO.
  • A space-themed version of three-dimensional chess is played by the titular character in Robert A. Heinlein's 1953 novel Starman Jones.
  • Four-dimensional chess is played in Arkady and Boris Strugatsky's 1961 science fiction collection Noon: 22nd Century.
  • The game is parodied in episodes of Futurama as tridimensional Scrabble.
  • In the computer game Unreal 2, Aida, one of the main heroes, is called an international 3D chess-master. A board is present in her quarters, identical in appearance to a Star Trek board.
  • In the Recess episode "Big Brother Chad", Vince's big brother Chad beats himself in 3D chess.
  • In a 2013 Audi commercial, Leonard Nimoy and Zachary Quinto are seen playing three-dimensional chess on iPads.
  • Three Dimensional Chess is mentioned as being played by the Legion of Super-Heroes in Superboy and the Legion of Super-Heroes #236.
  • In the third part of the Doctor Who serial Frontier In Space, prisoners are playing three-dimensional chess.
  • In The Lego Movie, after Batman's very short travel on the Star Wars starship Millennium Falcon (equipped with a Dejarik table), Batman says Han Solo, Chewbacca, Lando Calrissian and C-3PO play three-dimensional chess.
  • The game can be seen being played in the latest Star Trek videogame.[specify]
  • In episode 17 of Legend of Galactic Heroes, Yang Wenli and Julian are shown playing a version of 3D chess

See also[edit]


  1. ^ Thus each unicorn can reach a total of 30 cells of the 125-cell gamespace; each player's pair, 60.
  2. ^ Thus giving the queen a total of 26 different directions to move (6 faces plus 12 edges plus 8 corners).
  3. ^ There is some discussion whether this game should be called "Tri-Dimensional Chess" as in the Star Trek Star Fleet Technical Manual[9] or "Three-Dimensional Chess" as in The Star Trek Encyclopedia[10] and as on Memory Alpha.
  4. ^ "Alice Chess, a well-considered variant, may also be classified as a 3-D game." (Pritchard 1994:305). "In a sense, it is a three-dimensional game, since the board can be thought of as measuring 8×8×2 (in squares)." (Schmittberger 1992:197).


  1. ^ Pritchard (2007), p. 229.
  2. ^ Pritchard (2007), p. 93.
  3. ^ "Obama Is Playing Three-Dimensional Chess". Daily Kos. Kos Media, LLC. Retrieved 24 July 2017. 
  4. ^ "The Enduring Appeal of Seeing Trump as Chess Master in Chief". The New York Times Magazine. The New York Times Company. Retrieved 25 July 2017. 
  5. ^ Dickins (1971), p. 16.
  6. ^ Pritchard (1994), p. 305.
  7. ^ Dickins (1971), p. 17.
  8. ^ Pritchard (2007), p. 226.
  9. ^ Schnaubelt (1975), p. T0:03:98:3x.
  10. ^ Okuda (1997), p. 342.
  11. ^ "Vintage Chessmen by Peter Ganine". Dansk the Night Away. 12 October 2011. Retrieved 2 June 2014. 
  12. ^ Okuda (1997), p. 509.
  13. ^ Bartmess, Andrew (2005). The Federation Standard Tri-D Chess Rules (Revision 5.0 ed.). 
  14. ^ Pritchard (2007), p. 227.


Further reading[edit]

External links[edit]


Star Trek Tri-D