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 * Not to be confused with chess software with a 3D rendering

Three-dimensional chess, or 3D chess, are examples of chess variants. Three-dimensional variants have existed since the late 19th century. One of the oldest versions is Raumschach (German for "Space chess"), invented in 1907 by Ferdinand Maack and played on a 5x5x5 board. Maack founded a Raumschach club in Hamburg in 1919, which remained active until the Second World War.

Raumschach
The 3D board is actually a cube sliced into 5 equal spaces across each of its three major coordinal planes. This sectioning yields a 125-cell playing volume.

Each floor is marked with a capital letter, A, B, C, D or E. Ranks and files are as in chess. So, the kings start on Ac1 and Ec5. White starts on the A level (the ground floor) and black starts on the roof.

Rooks, bishops, and knights move as they do in Chess in any given plane. Rooks, for example, move through the walls of the cubes in any rank, file, or column. Bishops move along the edges of the cubes, and knights make a (0,1,2) leaping move. Unicorns move through the vertices of the cube, each of the two can only reach 30 cubes. The queen combines the moves of rooks, bishops, and unicorns. The king moves just like a queen but one step at a time. Pawns move in two directions, forward like a Chess pawn, and may move one step upward (if white) or downward (if black) and capture diagonally upward (or downward). Promotion occurs where pawns can't move any more, that is the rank E5 for white pawns and A1 for black pawns. There is no double move, en passant nor castling.

Tri-Dimensional Chess
right|thumb|3D chess on Star Trek Probably the most familiar 3D chess variant to the general public in the early 21st century is the game of Tri-Dimensional Chess (Tri-D Chess), which can be seen in many Star Trek TV episodes and movies, starting with the original series and proceeding in updated forms throughout the subsequent movies and spinoff series.

The original Star Trek prop was assembled using boards from 3-D Checkers and 3-D Tic Tac Toe games available in stores at the time (also visible being played in the original series episodes) and adding futuristic chess pieces. Rules for the game were never invented within the series; in fact, the boards are sometimes not even aligned consistently from one shot to the next within a single episode. The Tri-D chessboard set was made popular by its inclusion in The Star Trek Star Fleet Technical Manual by Franz Joseph, who invented starting positions for the playing pieces and short additional rules. The complete Standard Rules of this game were originally developed in 1976 by Andrew Bartmess (with approval from Joseph), and he has subsequently expanded and fine-tuned them.

There also is a Creative Commons-licensed manual written in Italian by Marco Bresciani, which presents a complete and faithful translation of the latest version of Bartmess' Standard Rules, with instructions on how to build a chessboard and many other things. This manual is available through the Star Trek Italian Club (for members only, see external links, below). Marco Bresciani also made a software project as an Information Technology Laurea Degree final thesis, that allows playing Tri-D Chess with Bartmess' Standard Rules full support. There are various computer applications for playing Tri-D Chess.

A set of tournament rules for Tri-Dimensional Chess written by Jens Meder is available on his website, However, Meder's rules are based on FIDE's Rules more than Andrew Bartmess's Standard Rules, with some deviations too.

Matrixchess
Matrixchess is a new 3D chess program for Windows (released jan, 2009), with 3D rendering and interactive playing. The program contains 5 variants of 3D chess in itself, all derived from the massive 8x8x8 (8 full chess boards) matrix. The other variants are 8x8x2 (2 full chess boards), 8x4x2 (2 half-sized chess boards), 8x4x4 and 5x5x5 (as for Raumschach). Classic 8x8 chess is also included.

In Matrixchess, all chess boards have 2 rows of white pieces and 2 rows of black pieces, as in 2D chess. This means the 8x8x8 set-up has 8 times the number of chess pieces of the 2D chess game. The playing time needed for a game turns out to be linear with the number of chess pieces. This makes the 8x4x2 game quite playable, as well as the 8x8x2, 8x4x4 and 5x5x5 games, if you take some more time. The 8x8x8 game is for the real enthousiasts.

The initial piece positions and the 3D-chess rules are an attempt to extrapolate from 2D chess as much as possible, while retaining a balance in the strength of the pieces. The rules for castling, pawn promotion, in passing capturing of pawns (en passant) are all included, adapted for the 3D situation. For the Knight and the Bishop there are a "2D" and a "3D" piece: the 2D Knight and Bishop always move within one plane at the time, while the 3D Knight and Bishop never stay within one plane when moving. The initial set-up of the pieces for the smaller game matrices can all be seen as cutting out a rectangular block from the 8x8x8 game matrix.

The Matrixchess program contains a chess engine which is pretty tough to beat. On-line playing against opponents is also possible, after finding an opponent on the web site, www.matrixchess.eu

The program helps the player to cope with the increased complexity of 3D chess, compared to 2D chess (there are more possible moves in 3D chess). The Matrixchess program allows only valid moves. By using coloured fields and pieces, it shows the player the valid moves, the defending pieces, the attacking pieces, undefended and attacked pieces. Undo/redo allows exploring what-if scenarios. The boards can be moved and rotated to get a better view.

Asimovian Hyperchess
Isaac Asimov's science fiction short story "A Perfect Fit" refers to a 3D chess game which is effectively eight chessboards stacked upon each other, making the playing area cubic (see also Cubic chess) rather than square (that is, exactly one dimension more than ordinary 2D chess). The same variant is also mentioned in Pebble in the Sky, during the early Galactic Imperial period on Earth.

Asimovian Hyperchess has two lineal variants :


 * Roseate Formation : The King is surrounded by a 'ring' of Queens, and the Bishops etc, ending in a ring of Rooks. Both sides possess a 'wall' of pawns in the 2nd rank.


 * Cruciformation : The King is central, with a ring of Queens, and then a ring of Bishops interspersed with Knights, a tertiary ring interspersed with bishops on diagonals, and ultimately Rooks interspersed with Knights at their tertiary move points (assuming a central quadrant L-movement)

Asimovian Hyperchess is not easily played. Asimov himself imagined a chess set being quite compact, but even with standard boards and pieces it is highly unlikely that tracking pieces and their movements is easy.

Mobility of pieces is the same as other three-dimensional chess forms, in that a pawn may move forward, and take a piece in the third dimension. The same rules apply to other pieces, and in Asimovian Hyperchess, Knights possess a remarkable ability, when acting in concert to permit a player to achieve a checkmate in less than 20 moves.

For effective playing of the game, it is theorised that a chess display computer program would be of the most use, but that it is highly unlikely that a computer would be able to play Hyperchess efficiently, as move prediction more than 8 moves ahead is likely to tax even an IBM Bluegene Mainframe beyond its standard abilities.

To date, Asimovian hyperchess has only had sporadic application, and there are few recorded instances of it being played.

Other variants
Another variant of 3D chess is that simulated by the 3dchess program for GNU/Linux. This variant is played on three standard 8&times;8 boards, stacked vertically. The middle board features the standard pieces, while the following new pieces populate the other two boards:


 * Prince (King)
 * Princess (Queen)
 * Abbey (Bishop)
 * Cannon (Knight)
 * Galley (Rook)

The movements of various pieces have been modified to allow them to move across boards (for example the Cannon must move three spaces in one direction, two in a perpendicular direction and one in the remaining perpendicular).

This version was developed and produced in a plastic board game format by Mind Games Manufacturing Limited, a company incorporated in Ireland in 1992. Although about 2,000 copies were manufactured, the company closed after a year and a half.

A variant possibly similar to Star Trek 's Tri-Dimensional Chess is seen in Legend of the Galactic Heroes, a Japanese science fiction novel. Another SF 3D chess game is Cheops or Pyramid chess, mentioned in the Dune novels of Frank Herbert, which has the object of simultaneously placing one's opponent in checkmate and one's own Queen at the apex of the pyramidal board.

A highly specialized three-dimensional chess variant is Gary Gygax's dragon chess.

Millennium 3D Chess is a similar 3D chess variant which is also played on three standard 8 by 8 chess boards (3x8x8). Millennium 3D Chess rules were written with the objective of extending the traditional chess game into a multilevel environment without distorting the basic game. To this end, Millennium 3D Chess has not "created" new chess rules, but instead extended the traditional rules to allow for multiboard play. Other than the concept of moving between chess boards (levels), all traditional two (2D) chess rules apply. A free PDF copy of the rules can be downloaded from Millennium 3D Chess Rules.

Popular culture

 * Spock and James T. Kirk can be seen playing 3-D chess on Star Trek. The game is later seen on other Star Trek series.
 * Leonard and Sheldon can be seen playing 3-D chess in the beginning of Episode 11 in Season 1 of The Big Bang Theory. Sheldon points out to Leonard that he is good at losing "on so many different levels."
 * A three-dimensional chess variant may be seen in the Blakes 7 fourth season episode, "Games".
 * 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, including a three-dimensional Scrabble game in "Fry and the Slurm Factory" and, in "The Beast with a Billion Backs", a version of three-dimensional Pac-Man.
 * In the computer game Unreal 2, Aida, one of the main heroes, is called a 3D chess champion. A board is present in her quarters, seemingly identical to a Star Trek board.
 * In the Recess episode "Big Brother Chad", you can see Vince's big brother Chad beat himself in 3-D chess.

Raumschach

 * Raumschach by Bruce Balden and Hans L. Bodlaender.
 * 3D Chess FAQ File, by David Moeser

Matrixchess

 * www.matrixchess.eu – The web site for Matrixchess, where Matrixchess can be downloaded, with rules and descriptions and a portal for on-line playing

Star Trek three-dimensional chess

 * Tri-Dimensional Chess Rules – Standard Rules by Andrew Bartmess
 * 3-D Chess Site of Jens Meder – in English; Tri-D Chess rules, boards and more
 * Scacchi Tridimensionali – The primary reference for the Italian Tri-D Chess manual; the website also includes game software²
 * Parmen – Free Tri-D Chess for Windows, from HempTrek (supports standard and tournament rulesets according to posted sample games)
 * Vulcan Open source Tri-D chess game (inspired by a certain well-known science fiction TV series)

¹The manual is written in Italian and fully based on Bartmess' Standard Rules. It is Creative Commons-licensed but available to Star Trek Italian Club members only: see above links. ²This Tri-D Chess game has been completed but is available for testing and debugging purposes to Java programming language programmers only.

Other variants of three-dimensional chess

 * Millennium 3D Chess – A 3x8x8 variant of 3D chess by William L. D'Agostino
 * 3D Chess Board – by Dan Beyer
 * 3dchess – open-source 3D chess for X11, with Debian package
 * Chess - The Next Generation – by Paul Glover[[Image:Chess2board sml.gif|thumb|3D Chess - The Next Generation]] (see also Chess - The Future Generation ©1990)
 * 3D Chess Concept, Info and Features
 * 3D Eight Level chess – by Ray Edward Bornert II
 * Spherical Chess 400 by Derek Nalls
 * Cubic chess by Vladimir Pribylinec

3D-Schach Ajedrez tridimensional Échecs cubiques Scacchi tridimensionali 三次元チェス