Three-dimensional chess

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Kubikschach 8x8x8 gamespace Kieseritzky Cubic Chess board.png
Kubikschach 8×8×8 gamespace

Three-dimensional chess (or 3‑D chess) is any chess variant that uses multiple boards representing different levels, allowing the chess pieces to move in three physical dimensions. In practical play, this is usually achieved by boards representing different layers being laid out next to each other.


Three-dimensional variants have existed since at least the late 19th century, one of the oldest being Raumschach (German for '"Space chess" '), invented in 1907 by Ferdinand Maack and considered the classic 3‑D game. [1] Maack founded a Raumschach club in Hamburg in 1919, which remained active until World War II.

Chapter 25 of David Pritchard's The Classified Encyclopedia of Chess Variants discusses some 50 such variations extending chess to three dimensions as well as a handful of higher-dimensional variants. 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, who are implied to be "playing" regular chess. [3]

Three-dimensional chess has often appeared in science-fiction—the Star Trek franchise in particular—contributing to the game's familiarity.


Lionel Kieseritzky (1806–1853) developed Kubikschach (German for Cube Chess) in 1851. [4] 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. [5]


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 3‑D 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 5x5x5 gamespace Raumschach gameboard.png
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.


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Raumschach starting position. [6] 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. [lower-alpha 1]
  • The queen combines the moves of a rook, bishop, and unicorn. [lower-alpha 2]
  • 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

3D chess on Star Trek (from the episode "Court Martial") StarTrekChess.jpg
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. [7] [lower-alpha 3]

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. [10] 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 [11] – 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

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. [12] 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

Star trek chessboard.JPG
The Tri‑D chessboard
Parmen graphic.jpg
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 (potentially named after a lead character in the episode "Plato's Stepchildren") 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.

Other three-dimensional chess variants

Parallel Worlds Chess Parallel Worlds Chess init config.png
Parallel Worlds Chess

In fiction

As well as in Star Trek, multi-dimensional chess games are featured in various fictional works, usually in a futuristic or science fiction setting. Examples include Nova (novel), Blake's 7 , UFO , Starman Jones , Unreal 2 , the Legion of Super-Heroes franchise, Doctor Who , The Big Bang Theory , and The Lego Movie . The concept is parodied in Futurama as “tridimensional Scrabble ”. [14]


  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 [8] or "Three-Dimensional Chess" as in The Star Trek Encyclopedia [9] 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).

Related Research Articles

Chessboard Any board used in the game chess

A chessboard is the type of gameboard used for the game of chess, on which the chess pawns and pieces are placed. A chessboard is usually square in shape, with an alternating pattern of squares in two colours. Though usually played on a surface, a tangible board is not a requirement to play the game. Traditionally wooden boards are made of unstained light and dark brown woods. To reduce cost, many boards are made with veneers of more expensive woods glued to an inner piece of plywood or chipboard. A variety of colours combinations are used for plastic, vinyl, and silicone boards. Common dark-light combinations are black and white, as well as brown, green or blue with buff or cream. Materials vary widely; while wooden boards are generally used in high-level games; vinyl, plastic, and cardboard are common for less important tournaments and matches and for home use. Decorative glass and marble boards are rarely permitted for games conducted by national or international chess federations. When they are permitted, they must meet various criteria

Alice chess Chess variant played on two boards

Alice chess is a chess variant invented in 1953 by V. R. Parton which employs two chessboards rather than one, and a slight alteration to the standard rules of chess. The game is named after the main character "Alice" in Lewis Carroll's work Through the Looking-Glass, where transport through the mirror into an alternate world is portrayed on the chessboards by the after-move transfer of chess pieces between boards A and B.

Capablanca chess is a chess variant invented in the 1920s by World Chess Champion José Raúl Capablanca. It incorporates two new pieces and is played on a 10×8 board. Capablanca believed that chess would be played out in a few decades. This threat of "draw death" for chess was his main motivation for creating a more complex version of the game.

Grand chess is a large-board chess variant invented by Dutch games designer Christian Freeling in 1984. It is played on a 10×10 board, with each side having two additional pawns and two new pieces: the marshal and the cardinal.

V. R. Parton English chess variant inventor (1897–1974)

Vernon Rylands Parton was an English chess enthusiast and prolific chess variant inventor, his most renowned variant being Alice chess. Many of Parton's variants were inspired by the fictional characters and stories in the works of Lewis Carroll. Parton's formal education background, like Lewis Carroll's, was in mathematics. Parton's interests were wide and he was a great believer in Esperanto.

Dice chess can refer to a number of chess variants in which dice are used to alter gameplay; specifically that the moves available to each player are determined by rolling a pair of ordinary six-sided dice. There are many different variations of this form of dice chess. One of them is described here.

Hexagonal chess Set of chess variants played on a board with hexagonal cells

Hexagonal chess refers to a group of chess variants played on boards composed of hexagon cells. The best known is Gliński's variant, played on a symmetric 91-cell hexagonal board.

Minichess Family of chess variants played on a smaller board

Minichess is a family of chess variants played with regular chess pieces and standard rules, but on a smaller board. The motivation for these variants is to make the game simpler and shorter than standard chess. The first chess-like game implemented on a computer was the 6×6 chess variant Los Alamos chess. The low memory capacity of early computers meant that a reduced board size and a smaller number of pieces were required for the game to be implementable on a computer.

Millennium 3D chess Three-dimensional chess variant

Millennium 3D chess is a three-dimensional chess variant created by William L. d'Agostino in 2001 which employs three vertically stacked 8×8 boards, with each player controlling a standard set of chess pieces. The inventor describes his objective as "extending the traditional chess game into a multilevel environment without distorting the basic game."

Cubic chess

Cubic chess is a chess variant invented by Vladimír Pribylinec beginning with an early version in 1977. The game substitutes cubes for the chess pieces, where four of the faces of each cube display a different chess piece, the two other faces are blank and are orientated to the players. This provides an efficient means to change a piece's type. Kings and queens have unique cubes containing only their symbol, effectively behaving as normal.

Triangular chess (game) Chess variant

Triangular chess is a chess variant for two players invented by George R. Dekle Sr. in 1986. The game is played on a hexagon-shaped gameboard comprising 96 triangular cells. Each player commands a full set of chess pieces in addition to three extra pawns and a unicorn.

Masonic chess Chess variant

Masonic chess is a chess variant invented by George R. Dekle Sr. in 1983. The game is played on a modified chessboard whereby even-numbered ranks are indented to the right—resembling masonry brickwork. The moves of the pieces are adapted to the new geometry; in other respects the game is the same as chess.


Chesquerque is a chess variant invented by George R. Dekle Sr. in 1986. The game is played on a board composed of four Alquerque boards combined into a square. Like Alquerque, pieces are positioned on points of intersection and make their moves along marked lines ; as such, the board comprises a 9×9 grid with 81 positions (points) that pieces can move to.


Tri-chess is the name of a chess variant for three players invented by George R. Dekle Sr. in 1986. The game is played on a board comprising 150 triangular cells. The standard chess pieces are present, minus the queens, and plus the chancellor and cardinal compound fairy pieces per side.

Cross chess Chess variant

Cross chess is a chess variant invented by George R. Dekle Sr. in 1982. The game is played on a board comprising 61 cross-shaped cells, with players each having an extra rook, knight, and pawn in addition to the standard number of chess pieces. Pieces move in the context of a gameboard with hexagonal cells, but Cross chess has its own definition of ranks and diagonals.

Quatrochess Chess variant

Quatrochess is a chess variant for four players invented by George R. Dekle Sr. in 1986. It is played on a square 14×14 board that excludes the four central squares. Each player controls a standard set of sixteen chess pieces, and additionally nine fairy pieces. The game can be played in partnership or all-versus-all.

Dynamo chess is a chess variant invented by chess problemists Hans Klüver and Peter Kahl in 1968. The invention was inspired by the closely related variant push chess, invented by Fred Galvin in 1967. The pieces, board, and starting position of Dynamo chess are the same as in orthodox chess, but captures are eliminated and enemy pieces are instead "pushed" or "pulled" off the board. On any given move, a player can make a standard move as in orthodox chess, or execute a "push move" or a "pull move". A move that is either a push move or a pull move is called a "dynamo move".

Chess on a really big board is a large chess variant invented by Ralph Betza around 1996. It is played on a 16×16 chessboard with 16 pieces and 16 pawns per player. Since such a board can be constructed by pushing together four standard 8×8 boards, Betza also gave this variant the alternative names of four-board chess or chess on four boards.

Chess variant Games related to, derived from or inspired by chess

A chess variant is a game related to, derived from, or inspired by chess. Such variants can differ from chess in many different ways.


  1. Pritchard (2007), p. 229.
  2. Pritchard (2007), p. 93.
  3. e.g.
    • "Obama is playing three-dimensional chess". Daily Kos . Kos Media, LLC. Retrieved 24 July 2017.
    • "The enduring appeal of seeing Trump as chess-master in chief". The New York Times Magazine . The New York Times Company. 2017-05-31. Retrieved 25 July 2017.
    • "How the Ukrainian crisis is like three-dimensional chess". Monkey Cage. Washington Post. 2015-03-15. Retrieved 2018-08-15.
  4. Dickins (1971), p. 16.
  5. Pritchard (1994), p. 305.
  6. Dickins (1971), p. 17.
  7. Pritchard (2007), p. 226.
  8. Schnaubelt (1975), p. T0:03:98:3x.
  9. Okuda, Okuda & Mirek (1997), p. 342.
  10. "Vintage Chessmen by Peter Ganine". Dansk the Night Away. 12 October 2011. Retrieved 2 June 2014.
  11. Okuda, Okuda & Mirek (1997), p. 509.
  12. Bartmess, Andrew (2005). The Federation Standard Tri‑D Chess Rules (Revision 5.0 ed.).
  13. Pritchard (2007), p. 227.
  14. "3‑D Scrabble - The Infosphere, the Futurama Wiki". Retrieved 2019-10-11.


Further reading

Star Trek Tri‑D