3-D CHESS FAQ FILE
___________ 5 | r n k n r | (The top 3-D CHESS FAQ FILE 4 | p p p p p | board) EEE 3 | - - - - - | Here's a diagram of the so-called 2 | - - - - - | Level "normal" form of three dimensional 1 | - - - - - | 'E' chess, according to Anthony S.M. ~~~~~~~~~~~ Dickins in his classic book, A GUIDE a b c d e TO FAIRY CHESS. This version, using ___________ a 5x5x5 cube (five boards of 25 5 | u b q u b | black squares or "cells" each), was de- 4 | p p p p p | pieces scribed by the lengendary English DDD 3 | - - - - - | chess variants publisher T.R. Dawson 2 | - - - - - | Level in 1926. 1 | - - - - - | 'D' ~~~~~~~~~~~ Black's pieces are placed on the a b c d e uppermost two levels; White's, on ___________ the lowest two levels. All the 5 | - - - - - | pieces of regular chess are used, 4 | - - - - - | plus each side has two more pawns CCC 3 | - - - - - | Level and two pieces called Unicorns. 2 | - - - - - | 'C' 1 | - - - - - | There are no squares with special ~~~~~~~~~~~ powers. All the rules of regular a b c d e chess apply except for castling, en ___________ passant, and the pawn's initial dou- 5 | - - - - - | WHITE ble jump. 4 | - - - - - | pieces BBB 3 | - - - - - | The 5x5x5 cube has the advantages 2 | P P P P P | Level of being compact (compared to 8x8x8, 1 | B U Q B U | 'B' for example) and not needing any spe- ~~~~~~~~~~~ cial rules (like 8x8x3). It can be a b c d e fairly easily constructed, or made by ___________ modifying other game equipment (like 5 | - - - - - | (bottom 3-D tic-tac-toe sets). 4 | - - - - - | board) AAA 3 | - - - - - | A GUIDE TO FAIRY CHESS is avail- 2 | P P P P P | Level able from Dover Publications. 1 | R N K N R | 'A' ~~~~~~~~~~~
THE MOVES OF THE PIECESFirst, a few notes about dimensions. Each of the five levels pic- tured in this diagram is a plane. By definition planes are two- dimensional. There are many additional planes that can be identified in this 5x5x5 grid besides these five horizontal ones. Such addi- tional, vertical planes also consist of 25 squares. Examples: The first ranks, from level E to level A, constitute a plane. Or the 'a' files, from level E to level A, constitute a plane. These planes -- the five horizontal "boards" plus the vertical planes consisting of same-numbered ranks or same-small-lettered files -- allow the option of "3-D" or "vertical" movements by all the regular chess pieces. For some of the regular pieces -- Knights, Bishops, Rooks, and Pawns -- when the concept of their regular chess move is applied to this 5x5x5 cube, moving in these vertical planes is the only kind of "3-D" movement allowed.
Note that a 3-D move is optional. All the regular (2-D) chess pieces retain the option of moving in their usual way on any of the five horizontal planes, or levels. Pawns can move one square forward (to a higher-numbered rank) on the same level, or one cell upward (for White) or downward (for Black) to the cell of the same coordi- nates on the next level.
As mentioned, the possible so-called 3-D moves of the Rook, Bishop, Knight, and Pawn are made within any of the planes perpen- dicular to the ranks or files of any of the five horizontal planes. The Rook's "3-D" move is pretty obvious. It moves like an elevator, straight up and down. The Pawn's "3-D" move is like a Rook, but only one cell at a time. The Knight's L-shaped move must be within such a plane. In other words, the Knight's 3-D move can be measured out as two cells along either a rank or a file and then one cell along a file or rank -- but never along any diagonal.
Dickins suggests imagining the Bishop's "3-D" move as a stairway path, zigzagging its way from level to level, but always within one of these planes (composed of all five same-numbered ranks or same- small-lettered files). A Bishop on Ea5 could move to Da4, then Ca3, Ba2, and Aa1. Notice that all these cells are on the "a" file. Or it could move to Db5, then Cc5, Bd5, and Ae5. Notice that all those cells are on the fifth rank. The Pawn's possible "3-D" capturing movement is like a Bishop move, forward (to the next higher level for White pawns or next lower level for Black pawns) one cell, within one of these same planes, along a rank or file.
These Rook, Bishop, Knight, and Pawn movements just described may be called 3-D or vertical, but they're really two-dimensional in na- ture. Only two of the three coordinates change when describing the move in "algebraic" notation. This inevitably leads to a discussion of true 3-D moves, where all three coordinates change, and the nature of what might be called "3-D planes."
One might suggest a plane cutting obliquely across the cube, con- necting cells Ea5, Da4-b5, Ca3-b4-c5, etc. This is the wrong way to imagine a Bishop move because it would suggest Bishop movement from Ea5 to Cb4, which is not allowed. (In fact, a move from Ea5 to Cb4, one square along a 2-D diagonal and then two cells vertically, is a move that no piece in this game can make. A new 3-D, knightlike piece would have to be invented for that.) Then there's the idea of moving from Ea5 to Db4, Cc3, Bd2, and Ae1, along a true diagonal of the 5x5x5 cube. That is indeed a three-dimensional diagonal, and it is NOT a move that can be made by a Bishop or a Pawn capture. Does this leave Bishops and Pawns a bit weaker than one might like? Yes, it does. But that's life (or chess).
That 3-D diagonal constitutes the path of movement for the Uni- corn. A Unicorn on Cc3 on an empty cube can move to 16 cells: upward to Db4 and Ea5, Dd4 and Ee5, Db2 and Ea1, Dd2 and Ee1; downward to Bb4 and Aa5, Bd4 and Ae5, Bb2 and Aa1, and Bd2 and Ae1. The Unicorn has no two-dimensional move, leaving it substantially weaker than one would like. It's the weakest piece in the game.
The Queen and King can also move along 3-D diagonals. The Queen can move like a Rook, Bishop, or Unicorn. And a King moves similar- ly, but limited to one cell in any direction. Placed in the middle of the cube, on Cc3, a King can move to 26 cells, a Queen 52, Rook 12, Bishop 24, and Unicorn 16.
Pawns promote on the back rank of the opponent's end-level. White Pawns promote on the fifth rank of Level E; Black Pawns promote on the first rank of Level A. Dickins notes that in capturing Pawns must move toward their promotion rank. The "3-D" application of this rule means that a White Pawn on Cc3 can capture on Cb4 or Cd4 (like regular chess) or on Db3, Dd3, or Dc4, but not Db2. (Db2 is upward but backwards -- toward White's back rank instead of toward Black's back rank.)
(This FAQ file prepared by David Moeser ((email removed contact us for address) ou.com). Snailmail address: PO Box 30072, Cincinnati, OH 45230-0072.)
- The Thoroddsen board. An elegant design of a board for this game to make yourself.
- Other description of this game with pictures.
Written by David Moeser.
WWW page created: June 24, 1997.