View source for Three-dimensional chess

{{Short description|Variants of chess with multiple boards at different levels}}
[[File:Kieseritzky Cubic Chess board.png|thumb|upright=1.3|right|Kubikschach 8×8×8 gamespace]]

'''Three-dimensional chess''' (or '''3‑D chess''') is any [[chess variant]] that replaces the two-dimensional [[chessboard|board]] with a three-dimensional array of cells between which the pieces can move. In practice, this is usually achieved by boards representing different layers being laid out next to each other. Three-dimensional chess has often appeared in [[science fiction]]—the ''[[Star Trek]]'' franchise in particular—contributing to the game's familiarity.

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.{{sfnp |Pritchard |2007 |p=229}} Chapter&nbsp;25 of [[David Pritchard (chess writer)|David Pritchard]]'s ''The Classified Encyclopedia of Chess Variants'' discusses some 50&nbsp;such variations extending chess to three dimensions as well as a handful of higher-dimensional variants. Chapter&nbsp;11 covers variants using multiple boards normally set side by side which can also be considered to add an extra dimension to chess.{{sfnp |Pritchard |2007 |p=93}}

The expression "three-dimensional chess" is sometimes used as a colloquial metaphor 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.<ref>e.g. 
*{{cite news |title=Obama is playing three-dimensional chess |website=[[Daily Kos]] |publisher=Kos Media, LLC |url=https://www.dailykos.com/stories/2009/2/9/695264/- |access-date=24 July 2017}}
*{{cite magazine |title=The enduring appeal of seeing Trump as chess-master in chief |date=2017-05-31 |magazine=[[The New York Times Magazine]] |publisher=The New York Times Company  |url=https://www.nytimes.com/2017/05/31/magazine/the-enduring-appeal-of-seeing-trump-as-chess-master-in-chief.html|access-date=25 July 2017}}
*{{cite news |title=How the Ukrainian crisis is like three-dimensional chess |date=2015-03-15 |department=Monkey Cage |newspaper=Washington Post |language=en |url=https://www.washingtonpost.com/news/monkey-cage/wp/2015/03/15/the-ukrainian-crisis-and-the-western-response-is-complicated-by-the-fact-that-three-different-games-are-being-played-simultaneously/ |access-date=2018-08-15}}</ref>

==Kubikschach==
[[Lionel Kieseritzky]] (1806–1853) developed Kubikschach (German for "Cube chess") in 1851.{{sfnp|Dickins|1971|p=16}} He used an 8×8×8 board, labelling the third dimension with [[Greek alphabet|Greek letters]] alpha through theta. This format was later picked up by [[Ferdinand Maack|Maack]] in 1907 when developing Raumschach. According to [[David Pritchard (chess player)|David Pritchard]], this format is: <blockquote>[...] 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.{{sfnp|Pritchard|1994|p=305}}</blockquote>

==Raumschach==
[[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 [[Fairy chess piece|special piece]] (two per player) called the [[List of fairy chess pieces#U|''unicorn'']].

===Board===
The Raumschach 3‑D&nbsp;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&nbsp;cube) gamespace. The cubes (usually represented by squares and often called ''cells'') alternate in color in all three dimensions.

[[File:Raumschach gameboard.png|thumb|upright=1.0|left|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 chess notation|algebraic notation]]. White starts on the '''A''' and '''B''' levels and Black starts on '''E''' and '''D'''. 

{{Raumschach diagram
 |tright
 |
 |rd|nd|kd|nd|rd
 |pd|pd|pd|pd|pd
 |  |  |  |  |
 |  |  |  |  |
 |  |  |  |  |
<!-- E -->
 |Ud|bd|qd|Ud|bd
 |pd|pd|pd|pd|pd
 |  |  |  |  |
 |  |  |  |  |
 |  |  |  |  |
<!-- D -->
 |  |  |  |  |
 |  |  |xo|  |xo
 |  |  |  |ox|
 |  |  |ox|oo|ox
 |  |  |  |  |
<!-- C -->
 |  |  |  |  |
 |  |  |  |  |
 |  |xo|ox|oo|ox
 |pl|pl|pl|pl|pl
 |bl|Ul|ql|bl|Ul
<!-- B -->
 |  |  |  |  |
 |  |  |  |  |
 |  |  |  |  |
 |pl|pl|pl|pl|pl
 |rl|nl|kl|nl|rl
<!-- A -->
 |Raumschach starting position.{{sfnp|Dickins|1971|p=17}} Unicorns are on Bb1, Be1, Da5, and Dd5. White's pawn on '''Bd2''' can move to cells with a white dot or capture on cells marked "<big>×</big>". Black's unicorn on '''Dd5''' can move to cells with a black dot or capture the white pawn on '''Aa2'''.
}}

===Rules===
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.
{{unordered list|style=list-style-position:inside 
 |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 [[Fairy chess piece#Leapers|(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 unique to a 3D space: it moves through the ''corners'' of a cube (i.e. along a [[space diagonal]]), any number of steps in a straight line. Each unicorn can reach a total of 30 cells of the 125-cell gamespace; each player's pair can reach 60.
 |The queen combines the moves of a rook, bishop, and unicorn. The queen has a total of 26 different directions to move: 6 faces plus 12 edges plus 8 corners.
 |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 [[Pawn (chess)#Placement and movement|two-step move]] (and consequently no capturing ''[[en passant]]''), and no [[castling]].
}}
{{Raumschach diagram
 |tleft
 |
 |  |  |  |  |
 |  |  |ox|  |
 |  |ox|  |ox|
 |  |  |ox|  |
 |  |  |  |  |
<!-- E -->
 |  |  |ox|  |
 |  |  |  |  |
 |ox|  |  |  |ox
 |  |  |  |  |
 |  |  |ox|  |
<!-- D -->
 |  |ox|  |ox|
 |ox|  |  |  |ox
 |  |  |nl|  |
 |ox|  |  |  |ox
 |  |ox|  |ox|
<!-- C -->
 |  |  |ox|  |
 |  |  |  |  |
 |ox|  |  |  |ox
 |  |  |  |  |
 |  |  |ox|  |
<!-- B -->
 |  |  |  |  |
 |  |  |ox|  |
 |  |ox|  |ox|
 |  |  |ox|  |
 |  |  |  |  |
<!-- A -->
 |White's knight on '''Cc3''' can move or capture on cells marked "<big>×</big>".
}}
{{-}}

==''Star Trek'' Tri-Dimensional Chess== <!-- This section is linked from [[Chess]] and [[List of games in Star Trek]] -->
<!-- Please note, the following REDIRECTS link to this section name:
     [[Tri-D Chess]],
     [[Tri-Dimensional Chess]],
     [[Star Trek chess]],
     [[Star Trek 3D chess]],
     [[Star Trek 3-D Chess]],
     [[Star Trek Tri-D Chess]], and
     [[Star Trek Trk-Dimensional Chess]] -->
[[File:StarTrekChess.jpg|thumb|240px|right|3D chess on ''[[Star Trek: The Original Series|Star Trek]]'' (from the episode "[[Court Martial (Star Trek: The Original Series)|Court Martial]]")]]

''Tri-Dimensional Chess'', ''Tri-D Chess'', or ''Three-Dimensional Chess''{{efn|There is some discussion whether this game should be called "Tri-Dimensional Chess" as in the ''[[Star Trek Star Fleet Technical Manual]]''{{sfnp|Schnaubelt|1975|p=T0:03:98:3x}} or "Three-Dimensional Chess" as in ''[[The Star Trek Encyclopedia]]''{{sfnp|Okuda|Okuda|Mirek|1997|p=342}} and as on [[Memory Alpha]].}} is a chess variant which can be seen in many ''[[Star Trek]]'' TV episodes and movies, starting with [[Star Trek: The Original Series|the original series]] (TOS) and proceeding in updated forms throughout the subsequent movies and spinoff series.{{sfnp|Pritchard|2007|p=226}}

The original ''Star Trek'' prop was crafted using boards from 3D Checkers and [[Qubic|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.<ref>{{cite web |title=Vintage Chessmen by Peter Ganine |date=12 October 2011 |website=Dansk the Night Away |url=http://danskthenightaway.blogspot.com/2011/10/vintage-chessmen-by-peter-ganine.html |access-date=2 June 2014}}</ref> 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{{sfnp|Okuda|Okuda|Mirek|1997|p=509}} – 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 (artist)|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.<ref>{{cite book |last=Bartmess |first=Andrew |title=The Federation Standard Tri‑D Chess Rules |edition=Revision 5.0 |year=2005}}</ref> 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===
{{multiple image |caption_align = center |total_width = 364 |align = right
 |image1 = Star trek chessboard.JPG
 |width1 = 574 |height1 = 582
 |caption1 = The Tri‑D chessboard
 |image2 = Parmen_graphic.jpg 
 |width2 = 450 |height2 = 461
 |caption2 = 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.

===Software===
There is software for playing Tri‑D Chess. ''Parmen'' (possibly 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.{{cn |date=August 2024}}

==Other three-dimensional chess variants==
[[File:Parallel Worlds Chess init config.png|thumb|upright=1.8 |right|<small>[[Parallel Worlds Chess]]</small>]]

*[[Alice chess]] – two adjacent 8×8 boards{{efn|"Alice Chess, a well-considered variant, may also be classified as a 3‑D game."<ref>{{harvcol|Pritchard|1994|p=305}}</ref> "In a sense, it is a three-dimensional game, since the board can be thought of as measuring 8×8×2 (in squares)."<ref>{{harvcol|Schmittberger|1992|p=197}}</ref>}}
*[[V. R. Parton#Cubic chess|Cubic chess]] – a 6×6×6 variant
*[[Dragonchess]] – three stacked 8×12 boards, a fantasy variant
*[[List of chess variants#Other 2D layouts|Flying chess]] – two adjacent 8×8 boards
*[[Millennium 3D chess]] – an 8×8×3 variant retaining most of the rules of standard chess{{sfnp|Pritchard|2007|p=227}}
*[[Parallel worlds chess]] – an 8×8×3 variant with two armies per player
*[[Space shogi]] – a 9×9×9 [[shogi variant]]
==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 ''[[Pebble in the Sky]]'' by [[Isaac Asimov]], ''[[Legend of the Galactic Heroes]]'',<ref>{{cite web |title=3D Chess - Gineipaedia, a Legend of the Galactic Heroes wiki |website=gineipaedia.com |url=https://gineipaedia.com/wiki/3D_chess |access-date=2023-07-22}}</ref> [[Nova (novel)|''Nova'']], ''[[Blake's 7]]'', [[UFO (British TV series)|''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]]''".<ref>{{cite web |title=3‑D Scrabble - The Infosphere, the Futurama Wiki |website=theinfosphere.org |url=https://theinfosphere.org/3-D_Scrabble |access-date=2019-10-11}}</ref>

==See also==
* ''[[5D Chess with Multiverse Time Travel]]''

==Notes==
{{notelist}}

==References==
{{reflist}}

==Bibliography==
* {{cite book
 |last=Dickins |first=Anthony
 |year=1971
 |title=A Guide to Fairy Chess
 |publisher=[[Dover Publications]] Inc
 |location=New York
 |isbn=0-486-22687-5
 |orig-year=1969
}} (corrected repub. of<br/>{{cite book |title=A Guide to Fairy Chess |year=1969 |edition=2nd |publisher=The Q Press |place=Richmond, UK}})
* {{cite book
 |last1=Okuda |first1=Denise
 |last2=Okuda |first2=Michael
 |last3=Mirek |first3=Debbie
 |year=1997
 |title=[[The Star Trek Encyclopedia]]
 |publisher=[[Pocket Books]]
 |isbn=0-671-53607-9
}}
* {{cite book
 |last=Pritchard |first=D.B.
 |author-link=David Pritchard (chess player)
 |year=1994
 |title=The Encyclopedia of Chess Variants
 |publisher=Games & Puzzles Publications
 |isbn=0-9524142-0-1
}}
* {{cite book
 |last=Pritchard |first=D.B.
 |author-link=David Pritchard (chess player)
 |year=2007
 |editor-last=Beasley |editor-first=John
 |title=The Classified Encyclopedia of Chess Variants
 |publisher=John Beasley 
 |isbn=978-0-9555168-0-1
 |url=https://www.jsbeasley.co.uk/encyc/encyc.pdf
}}
* {{cite book
 |last=Schmittberger |first=R. Wayne
 |year=1992
 |contribution=3D Chess Sets
 |title=New Rules for Classic Games
 |publisher=John Wiley & Sons Inc
 |isbn=978-0471536215
 |pages=[https://archive.org/details/newrulesforclass00rway/page/103 103–07]
 |url-access=registration
 |url=https://archive.org/details/newrulesforclass00rway/page/103
}}
* {{cite book
 |last=Schnaubelt |first=Franz Joseph |author-link=Franz Joseph (artist)
 |year=1975
 |title=[[Star Trek Star Fleet Technical Manual]]
 |publisher=[[Ballantine Books]]
 |isbn=0-345-34074-4
}}

==Further reading==
* {{cite book
 |last1=Hooper |first1=David |author-link1=David Vincent Hooper
 |last2=Whyld |first2=Kenneth |author-link2=Kenneth Whyld
 |year=1987
 |title=[[The Oxford Companion to Chess]]
 |publisher=[[Oxford University Press]]
 |contribution=Three-dimensional chess
 |pages=351–52
 |isbn=0-19-281986-0
}}

==External links==
* {{cite web |title=Three Dimensional (index) |website=[[The Chess Variant Pages]] |url=http://www.chessvariants.org/index/mainquery.php?type=Any&category=3d&orderby=LinkText&displayauthor=1&displayinventor=1&usethisheading=Three+Dimensional}}

;Raumschach:
*  {{cite web |title=Raumschach |editor1=Balden, Bruce |editor2=[[Hans Bodlaender|Bodlaender, Hans]] |website=[[The Chess Variant Pages]] |url=http://www.chessvariants.org/3d.dir/3d5.html}}
*  {{cite web |title=3‑D Chess FAQ File |editor1=Moeser, David |website=[[The Chess Variant Pages]] |url=http://www.chessvariants.org/3d.dir/555.html}}
* {{bgg|34848|Raumschach}}
*  {{cite web |title=Raumschach |author=Friedlander, Ed |url=http://www.pathguy.com/chess/Chess3D.htm}} – a simple program (in [[Java (programming language)|Java]])
*  {{cite web  |title=Raumschach |website=Jocly.com |url=https://www.chessvariants.org/play/jocly/raumschach}}

;''Star Trek'' Tri‑D:
* {{cite web |title=3‑D Chess from ''Star Trek'' |author=[[Hans Bodlaender|Bodlaender, Hans]] |website=[[The Chess Variant Pages]] |url=http://www.chessvariants.org/3d.dir/startrek.html}}
* {{cite web |title=Tridimensional Chess Rules |author=Bartmess, Andrew |url=http://www.yestercade.net/tactical.htm}} – commercial site; history of Standard Rules
* {{cite web |title=''Star Trek'' 3‑D Chess Rules |author=Roth, Charles |url=http://www.thedance.net/~roth/TECHBLOG/chess.html}} – free summary of Standard Rules
* {{cite web |url=http://meder.spacechess.org/3dschach/indexe.html |title=3‑D chess |author=Meder, Jens}} – Tri‑D Chess Tournament Rules, boards, and more
* {{cite web |author=Klein, Michael |title=3‑D Chess |url=http://www.3dschach.de/start_.asp}} – Tournament Rules game library and more
{{Memory Alpha |Three-dimensional chess}}
* {{bgg|3499|3-D Chess}}
* {{cite web |title=Tri‑D Chess Tracker |url=http://trekpropzone.com/tdchess/tdchess_loginform.htm |url-access=registration}} – Tri-Dimensional Chess Tracker; web-based Perl program

{{Chess variants|state=collapsed}}

[[Category:Chess variants]]
[[Category:1907 in chess]]
[[Category:Board games introduced in 1907]]
[[Category:Fictional games]]
[[Category:Three-dimensional board games]]
[[Category:Star Trek]]