Three-dimensional chess

Kubikschach 8×8×8 gamespace

Three-dimensional chess(or3‑D chess) is anychess variantthat replaces the two-dimensionalboardwith 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 inscience fiction—theStar Trekfranchise 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 byFerdinand Maackand considered the classic 3‑D game.Chapter 25 ofDavid Pritchard'sThe Classified Encyclopedia of Chess Variantsdiscusses 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.

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.

Kubikschach

Lionel Kieseritzky(1806–1853) developed Kubikschach (German for "Cube chess" ) in 1851.He used an 8×8×8 board, labelling the third dimension withGreek lettersalpha through theta. This format was later picked up byMaackin 1907 when developing Raumschach. According toDavid 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.

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 special piece (two per player) namedunicorn.

Board

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 calledcells) alternate in color in all three dimensions.

Raumschach 5×5×5 gamespace

The horizontal levels are denoted by capital lettersAthroughE.Ranks and files of a level are denoted usingalgebraic notation.White starts on theAandBlevels and Black starts onEandD.

Rules

E	D	C
B	A
Raumschach starting position.White's pawn onBd2can move to cells with a white dot or capture on cells marked "×". Black's unicorn onDd4can move to cells with a black dot or capture the white pawn onAa2.

E	D	C
B	A
White's knight onCc3can move or capture on cells marked "×".

White moves first. The game objective, as in standard chess, ischeckmate.Rooks, bishops, and knights move as they do in chess in any given plane.

• A rook moves through the sixfacesof a cube in any rank, file, or column.
• A bishop moves through the twelveedgesof 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 unique to a 3D space: it moves through thecornersof a cube (i.e. along aspace 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 (rankE5for White, rankA1for 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 cubeedge.In Raumschach there is no pawn initialtwo-step move(and consequently no capturingen passant), and nocastling.

Star TrekTri-Dimensional Chess

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

Tri-Dimensional Chess,Tri-D Chess,orThree-Dimensional Chessis a chess variant which can be seen in manyStar TrekTV episodes and movies, starting withthe original series(TOS) and proceeding in updated forms throughout the subsequent movies and spinoff series.

The originalStar Trekprop was crafted using boards from 3D Checkers and3D Tic-Tac-Toesets available in stores at the time (games also seen in TOS episodes) and adding chess pieces from the futuristic-lookingClassicchess set designed byPeter Ganinein 1961.The design retained the 64 squares of a traditionalchessboard,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– 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 theStar Trek Star Fleet Technical ManualbyFranz 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.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 2×2attack 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 onFIDE'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

The Tri‑D chessboard

Playing Parmen

Plans for constructing a Tri‑D chessboard can be found onThe 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.

Other three-dimensional chess variants

Parallel Worlds Chess

• Alice chess– two adjacent 8×8 boards
• Cubic chess– a 6×6×6 variant
• Dragonchess– three stacked 8×12 boards, a fantasy variant
• Flying chess– two adjacent 8×8 boards
• Millennium 3D chess– an 8×8×3 variant retaining most of the rules of standard chess
• Parallel worlds chess– an 8×8×3 variant with two armies per player
• Space shogi– a 9×9×9shogi variant

In fiction

As well as inStar Trek,multi-dimensional chess games are featured in various fictional works, usually in a futuristic or science fiction setting. Examples includePebble in the SkybyIsaac Asimov,Legend of the Galactic Heroes,Nova,Blake's 7,UFO,Starman Jones,Unreal 2,theLegion of Super-Heroesfranchise,Doctor Who,The Big Bang Theory,andThe Lego Movie.The concept is parodied inFuturamaas "tridimensionalScrabble".

See also

• 5D Chess with Multiverse Time Travel

Bibliography

• Dickins, Anthony (1971) [1969].A Guide to Fairy Chess.New York:Dover PublicationsInc.ISBN0-486-22687-5.(corrected repub. of
  A Guide to Fairy Chess(2nd ed.). Richmond, UK: The Q Press. 1969.)
• Okuda, Denise; Okuda, Michael; Mirek, Debbie (1997).The Star Trek Encyclopedia.Pocket Books.ISBN0-671-53607-9.
• Pritchard, D.B.(1994).The Encyclopedia of Chess Variants.Games & Puzzles Publications.ISBN0-9524142-0-1.
• Pritchard, D.B.(2007). Beasley, John (ed.).The Classified Encyclopedia of Chess Variants(PDF).John Beasley.ISBN978-0-9555168-0-1.
• Schmittberger, R. Wayne (1992). "3D Chess Sets".New Rules for Classic Games.John Wiley & Sons Inc. pp.103–07.ISBN978-0471536215.
• Schnaubelt, Franz Joseph(1975).Star Trek Star Fleet Technical Manual.Ballantine Books.ISBN0-345-34074-4.

Further reading

• Hooper, David;Whyld, Kenneth(1987). "Three-dimensional chess".The Oxford Companion to Chess.Oxford University Press.pp. 351–52.ISBN0-19-281986-0.

External links

• "Three Dimensional (index)".The Chess Variant Pages.

Raumschach

• Balden, Bruce;Bodlaender, Hans(eds.)."Raumschach".The Chess Variant Pages.
• Moeser, David (ed.)."3‑D Chess FAQ File".The Chess Variant Pages.
• RaumschachatBoardGameGeek
• Friedlander, Ed."Raumschach".– a simple program (inJava)
• "Raumschach".Jocly.com.

Star TrekTri‑D

• Bodlaender, Hans."3‑D Chess fromStar Trek".The Chess Variant Pages.
• Bartmess, Andrew."Tridimensional Chess Rules".– commercial site; history of Standard Rules
• Roth, Charles."Star Trek3‑D Chess Rules ".– free summary of Standard Rules
• Meder, Jens."3‑D chess".– Tri‑D Chess Tournament Rules, boards, and more
• Klein, Michael."3‑D Chess".– Tournament Rules game library and more
• Three-dimensional chessatMemory Alpha
• 3-D ChessatBoardGameGeek
• "Tri‑D Chess Tracker".– Tri-Dimensional Chess Tracker; web-based Perl program