Chess on a Tesseract
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Way back in the 1970s, while I was playing the 3D variant called Strato Chess, I started to wonder (as others here have done) if the dimensions of the game couldn't be extended to four or even five. It took some time to figure out, so I set the idea aside.
Eventually, upon learning about such figures as the tesseract and penteract, I started to think about how we three-dimensional beings would interact with such things. I even started writing a story about a group of people trapped in a structure built around a pentaract (with similar effects to what I'm about to describe).
It was only relatively recently that I managed to put the two ideas together. The play is, at one level of thought, as two-dimensional as orthodox chess; but on another level, it still uses four dimensions of movement.
The Geometric Concept
This game is played, ostensibly, on the two-dimensional "faces" of a tesseract. To help understand how that works, let's subtract one dimension, and consider the edges of a cube.
Suppose this game were to be played in such a way (and I wouldn't put it past the contributors of this site to come up with one). When a piece reaches a corner, there are two other edges that it continue onto. How does one choose which to go to?
The principle is the same here. Each edge of a face meets an edge of two other faces; when a piece goes off the edge of a face, the player chooses which of the two connecting faces it goes to.
Numbering the 24 faces of the tesseract should help players keep track; the figures below show (somewhat) how I prefer to order them. (Click on the pictures for a larger view.)
I've also made a PDF document showing the connections in a two-dimensional way; that may be easier (or at least less confusing) for most.
Setup
Boards
The 24 Faces of the tesseract are each made up of a 5x5 board. The corner spots of each board are blacked out; no piece may enter or pass through them.
In a physical game, the boards can be laid out however you wish. Each should have an indicator as to which Face it represents, and a guide on each edge as to which two Faces it leads to.
Pieces
In the figure above, White sets up on and around Face 1 (the front of the large cube), while Black sets up on and around Face 24 (the back of the small cube); these are their respective "Home Faces." The setup is identical for both, so only White is illustrated.
(Don't worry; I'm only calling them "large" and "small" because they look that way in the illustration. On an actual tesseract, all 8 cubes are the exact same size.)
On each Home Face, the King goes in the center. Orthogonally adjacent, he's flanked by two Nightriders; each has a Queen clockwise from it, and a Bishop counterclockwise. The remaining two spaces next to the King are filled by an Archbishop and a Chancellor. The outer spaces, going clockwise from the corner next to each Bishop, are filled by a Rook, Knight, Bishop, Archer, Knight, and another Rook.
These may be rotated however the player prefers.
Adjacent to each side of the Home Face are two more Faces; these eight are the Territory Faces. (For White, these are Faces 2, 3, 4, 5, 7, 8, 9, and 10; for Black, they're 15, 16, 17, 18, 20, 21, 22, and 23.) On the edge of the Face adjacent to the Home Face, each player has a Berolina Spear, flanked by two Arabian Spears. The next row over has three Standard Pawns, one in the center and one at each end, with Berolina Pawns filling the other two spaces.
The remaining six Faces (6, 11, 12, 13, 14, and 19) are termed "Open Faces."
Pieces
Each player is equipped with the following:
- 1 King
- 1 Archbishop
- 1 Chancellor
- 2 Queens
- 2 Nightriders
- 2 Archers
- 4 Bishops
- 4 Knights
- 4 Rooks
- 8 Berolina Spears
- 16 Arabian Spears
- 16 Berolina Pawns
- 24 Standard pawns
The pieces with links are either orthodox Chess pieces, or pieces familiar to most chess variant aficionados; the articles explain the moves. The other three pieces:
Archer: Moves two spaces diagonally, or "rifle-captures" (captures without moving) a Knight's move away.
Arabian Spear: A sort of "Pawnrider," moves without capture directly forward like a Rook, or captures forward like a Bishop.
Berolina Spear: Moves without capture forward diagonally like a Bishop, or captures directly forward like a Rook.
For Pawns and Spears, moving forward means whatever direction takes the piece closer to the opponent's Home Face. This means that those pieces will rarely, if ever, move to any of the Open Faces; the shorter route from any Territory Face (where the Pawns and Spears start) to the opponent's Home Face always is always through an opponent's Territory Face.
Rules
As noted above, when a piece reaches the edge of a Face, the player chooses which of two neighboring Faces it continues to. The move is as seamless as if the boards for the two Faces were set against one another.
The board setup makes Castling impractical, if not impossible. However, en passant is used with the Pawns (Standard and Berolina), though not the Spears.
In terms of the endgame (checkmate, stalemate, etc.), all standard rules are observed.
Both types of Pawn and both types of Spear promote upon entering the opponent's Home Face. They may promote to any type of piece that's used in the game, except of course for the King and other Pawns or Spears.
Notes
As a person on the autistic spectrum, one of the "plusses" I experience is the (generally useless) ability to, with some effiort, visualize four-dimensional space (or, with much effort and if the geometry is simple, even five; six is beyond me). Thus, I can visualize the actual tesseract in this game, while few if any other people could not.
This is presented not so much as an actual, playable game (though there's nothing really preventing that, especially if smaller equipment is used), but as an exercise to help others visualize and understand higher spatial dimensions.
About That Story
The short story I mentioned in the Introduction got started, and I knew the ending as well as most of the plot points but never actually completed it past Page 2. It really was a story meant to explore the concept of moving around the three-dimensional aspects of five-dimensional space in the same way that this game explores two-dimensional aspects of four-dimensional space; one added feature was that, depending on the route one took, one could re-enter a room with "up" in a different direction than when one left, leading to some rather Escher-esque moments.
This 'user submitted' page is a collaboration between the posting user and the Chess Variant Pages. Registered contributors to the Chess Variant Pages have the ability to post their own works, subject to review and editing by the Chess Variant Pages Editorial Staff.
By Bob Greenwade.
Last revised by Bob Greenwade.
Web page created: 2023-09-12. Web page last updated: 2023-12-16