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Michael D. Ward designed this three dimensional chess variant, and sent the following text about it:


This is a 3-D chess variant I have been working on. I have found numerous flaws in other 3-D chess games and this attempts to correct them. However, these rules have not been properly tested. Any comments on this game and possible ways of improving it would be appreciated. If anyone has any comments, please send them to:

Michael D. Ward
(email removed contact us for address) .uky.edu


Octahedral Chess

A 3-Dimensional Chess Variant

by Michael D. Ward

Lexington, KY

(email removed contact us for address) .uky.edu

Rules

The Board

The board is made of nine square levels. The lowest level being level one (I) and the highest being level nine (IX) with levels two through eight between them. The center level, level five (V), is a 10x10 grid and is where all of the pieces begin. Either level directly above or below level 5, levels four and six, is an 8x8 grid; levels three and seven are 6x6 grids; levels two and eight are 4x4; and levels one and nine are 2x2: a total of 340 squares. The levels are positioned so that the center of each level is directly above the center of the level below it.

Side view of board.

Notation

The files are designated on level five by lower case letters from left to right on the side of the board where the white player sits, beginning with "a" and following alphabetically to "j". Files are extended straight up and down to the other levels so files "a" and "j" ar found only on level 5 while "e" and "f" extend down to level 1 and up to level 9. Ranks are labelled in a similar fashion from "1" to "10" beginning on the side of the white player. Levels are labelled with capital roman numerals "I" for level one and so on. When identifying a square the level is given first followed by the file and the rank. For example, the square in the lower left hand corner of level one on white's side is Ie5. The notations for the pieces are given in the next section.

The Pieces

The pieces are meant to be as analogous to there two dimensional counterparts as is practical.

The King (K) moves one square in any direction. The King may not move into check and may castle as explained below. If unobstructed the King can move to any one of 26 squares.

The Rook (R) moves any distance in any straight direction as long as it is not obstructed. The Rook may move in up to six directions. It always remains in two of the same planes it was before. A Rook on Ve5 can move to any square on level "V" and file "e", or to any square of level "V" and rank "5", or to any square on level "e" and rank "5".

The Bishop (B) moves diagonally simultaneously in two directions while remaining in one plane. This is probably the hardest to visualize. A Bishop at Ve5 must remain in one of the planes it is on: either V, e, or 5. If it remains on V it can move to any square along to diagonals it is on in that plane. In this instance it would move precisely like its 2-D counterpart. If it remains on e it can move diagonally up or down the board as if it was walking on a staircase--remember in this instance it would change level and rank but was always remain on file "e". Similarly the Bishop could remain on 5 and move diagonally through the levels and files. A bishop can move in twelve directions, but like it 2-D counterpart is confined to half the squares on the board.

The Elephant (E) is a piece with now counterpart in standard chess, but it fills a necessary position that does not exist in two dimensions and may be thought of as another variation on the Bishop (for this reason I chose the name Elephant since the modern Bishop evolved from the Elephant of chess's predecessors). The Elephant moves diagonally with respect to all planes simultaneously. So that when an Elephant is moved in will always be on a different level, rank, AND file from which it began. The Elephant can move in any of eight directions. Just as the Bishop is limited to half of the squares on the board, the Elephant is limited to a quarter of the squares, and the four elephants run on different circuits and can never threaten or guard one another. (Note that the moves of the Rook, the Bishop, and the Elephant do not overlap in any way.)

The Queen (Q) has the combined moves of the Rook, the Bishop, and the Elephant. She can move in any of 26 directions like a King, but is, of course, not limited to a move of one square.

The Knight (N) moves two square straight (like a Rook) and on square straight in any perpendicular direction (forming an "L") and jumps over any intervening pieces so that it cannot be blocked. A Knight at the center of the board can move to any one of 24 squares.

Pawns (P) present a bit of a problem since they are the only piece in chess whose move does not demonstrate radial symmetry. Since pawns in chess move forward, confined to their one-dimensional file, pawns in Octahedral Chess move forward confined to their two-dimensional file: they may move forward one space or they may move to the either square which is forward one plus up or down one.

Additionally Pawns may move straight up or down one square. Pawns attack the ten squares directly to the left and right of the five squares they can move to. Therefore a pawn a Ve5 could move to IVe5, IVe6, Ve6, VIe6, or VIe5. The pawn could attack IVd5, IVf5, IVd6, IVf6, Vd6, Vf6, VId6, VIf6, VId5, VIf5. On its first move a pawn may make a double step in any direction but may not combine two moves in different directs. His opponent may capture by en passant subject to the restrictions of standard chess. A pawn may not move to a square on the same rank and file as another pawn of either color, nor may a pawn move through such a square with its initial two step move (i.e. a pawn may not pass over or under another pawn) with a non-capturing move. When capturing a pawn may not be blocked in this way.
The moves for the pawn may seem a poor analogy to standard chess, but they attempt to create piece that not only moves like a 2-D pawn but also behaves like one in terms of strategy and game play.

Other Pieces

Listed above are all of the pieces used in this game. However, there are other 3-D pieces which are possible and could be used in variants of this game or in other 3-D chess games.

The Camel is a variation on the Knight; the Knight described above moves two spaces straight, then one space straight in a perpendicular direction (2,1,0). The Camel moves two spaces straight, then one space straight in a perpendicular direction, and finally one space perpendicular to the first two directions (2,1,1). Like the Knight, the Camel jumps over any intervening pieces.

The General is another variation on the Knight/Camel but it moves (2,2,1) rather than (2,1,0) or (2,1,1).

Another piece with power comparable to the Queen can be made by combining the Knight, the Camel, and the General.

Still other 3-D pieces may be made by combining the moves of other pieces. Such as 3-D versions of Capablanca's Cardinal (R+N) and Archbishop (B+N, or B+E+N in 3-D).

Initial Setup

rnbqkbnr
pppppppppp






PPPPPPPPPP
RNBQKBNR

Setup on Level V:

White:
King g1; Queen d1; Elephant e1, f1; Rook a1, j1; Knight b1, i1; Bishop c1, h1; Pawn a2, b2, c2, d2, e2, f2, g2, h2, i2, j2.

Black:
King g10; Queen d10; Elephant e10, f10; Rook a10, j10; Knight b10, i10; Bishop c10, h10; Pawn a9, b9, c9, d9, e9, f9, g9, h9, i9, j9.

The black pieces sit opposite the white on level V and mirror white's pieces as they do in standard chess.

Castling

A player may castle King's side by moving his king two spaces toward the King's Rook and moving to Rook to the other side of the King. A player may castle Queen's side buy moving five space toward the Queen's Rook and moving to Rook to the other side of the King. All restriction on castling from standard chess still apply.

This is slightly different than stand chess because Queen's side castle is a much longer move and the result leaves to king only one space from the vertical edge of the board unlike standard chess where it is two spaces.

Promotion

Pawns promote as in standard chess when reaching rank 10 if white or rank 1 if black.

Remaining Rules

In all other ways Octahedral Chess is identical to standard chess. For the rules of capture, check, and checkmate or any thing else which is omitted follow the rules for standard chess.

Rule Variation

Pyramid Chess

If the board seems to large simply discard the lower 4 levels, leaving a pyramid shaped board. This reduces the boards size from 340 squares to 220 squares.

Side view for Pyramid Chess.


Written by Michael D. Ward. Webpage made by Hans Bodlaender. Revised image by Mark J. Reed.
WWW page created: August 19, 1996.