The Game Of Three Dimensional Eight Level Chess
Copyright (c) 1984-2000 by Ray Edward Bornert II

ray.bornert@hixoxih.com

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CONTENTS

INTRODUCTION
2D CHESS
TRUE 3D CHESS
NOTATION
LEVELS
SECTIONS
DEGREES
COLUMNS
FILES
RANKS
RECORDING MOVES
RULES OF PLAY
DEFINITIONS
SETUP
PHOTOGRAPHS



THE ROOK



THE BISHOP



THE MACE



THE ROOKBISHOP



THE ROOKMACE



THE BISHOPMACE



THE PLAIN KNIGHT



THE RED KNIGHT



THE GREEN KNIGHT



THE GRAND KNIGHT



THE QUEEN



THE KING

CASTLING


THE PAWN

FIRST MOVE
EN PASSANT
PROMOTION



INTRODUCTION

This work was originally produced and copyrighted in 1984. It is officially recorded with the Library of Congress Copyright Office under registration numbers TX-1-561-056 and VAu-73-017. This 2nd edition online version is new and updated. Various typographical errors have been corrected. And some movement analysis for some of the pieces has been corrected as well. The format has been updated and enhanced for web-content.




2D CHESS

The game of Two-Dimensional One-Level Chess hereafter referred to as 2D is the standard game of Chess that we know today.

The 2D board is 8x8 with a total of 64 squares of which 32 are white and 32 are black.

There are 32 playing pieces of which 16 are white and 16 are black, and there are exactly 6 different types of pieces as far as shape and movement are concerned.



Diagram - Standard 2D chessboard




TRUE 3D CHESS

The game of Three-Dimensional Eight-Level Chess hereafter referred to, as 3D-8L is simply Chess in three dimensions instead of two dimensions.

The 3D-8L board is 8x8x8 with a total of 512 points of which 256 are white and 256 are black. In addition to white and black, there are four colors: red, green, blue and yellow that are used 128 times each so that the playing board is further divided into fourths.

There are 256 playing pieces of which 128 are white and 128 are black, and there are exactly 13 different types of pieces as far as shape and movement are concerned.

The following rules and diagrams are recommended for those persons who are already thoroughly familiar with 2D Chess, the board and it's notation, the movement of the playing pieces, and all of the rules of play such as En passant, Castling, Priority of Check, etc.

A keen grasp of spatial relations is also highly recommended.



Diagram - The 3D-8L Board




NOTATION

The 3D-8L playing board is actually an 8x8x8 cube.

There are a total of 512 sub-cubes or points, each of which has its own unique notation.

The system notation used in 3D-8L is Three Coordinate Algebraic, which is similar to Two Coordinate Algebraic using 2D, the only difference being the third coordinate.

To better illustrate the method of three coordinate notation, the cube representation of the 3D-8L playing board will be used for diagrams.

In the Three Coordinate Algebraic System, the notation of a point is accomplished by naming the three common planes to the point.

The three common planes are Level, Section and Degree; there are 8 of each, and they should always be named in that order (L, S, D).

Every point on the board can be named in this manner.

A line, which is the intersection of two planes, can also be named this way.

There are three different kinds of lines: Columns, Files, and Ranks.

The notation of a line is accomplished by naming the two common planes to the line.



Diagram - 8 x 8 x 8 Cube




LEVELS

There are eight levels in all.

They number one to eight from the bottom to the top.

Levels are the first coordinate in three coordinate notation. (1-8, S, D)



Diagram - Levels



SECTIONS

There are eight sections in all.

They are lettered a through h from left to right.

Sections are the second coordinate in three coordinate notation. (L, a-h , D)



Diagram - Sections



DEGREES

There are eight degrees in all.

They number one to eight from the white piece side to the black piece side.

Degrees are the third coordinate in three coordinate notation. (L, S, 1-8 )



Diagram - Degrees




COLUMNS

There are 64 columns in all.

They run vertically up and down and they are the intersection of a Section and a Degree.

The notation for a column is (S, D).

The diagram highlights the b1 column.



Diagram - The b1 column



FILES

There are 64 files in all.

They run laterally from player to player, and they are the intersection of a Level and a Section.

The notation for a file is (L, S).

The diagram highlights the 3a file.



Diagram - The 3a file



RANKS

There are 64 ranks in all.

They run horizontally from side to side, and they are the intersection of a Level and a Degree.

The notation for a rank is (L, D).

The diagram highlights the 82 rank.



Diagram - The 82 rank




RECORDING MOVES

The eight corners of the playing board in the diagram are: 1a1, 1a8, 1h1, 1h8, 8a1, 8a8, 8h1, and 8h8. The three lines on the board in the diagram are the a8 column, the 3d file, and the 76 rank.

To record the moves in a 3D-8L Chess game, first, write the correct notation for the origin point. The diagram shows an origin point at 7c2. Second, write an (-) if the destination point is unoccupied, or write an (x) which means a capture, if the point contains an enemy piece. Last of all write the correct notation for the destination point.

The diagram shows a destination point at 2h2. The correct notation for the complete move would be 7c2-2h2, or 7c2x2h2 if the move was a capture. Sometimes it is possible to replace the notation for the origin point with the symbol or the abbreviation of the piece being moved. An example might be: R-8g5 or Bx7b8. This can be done only when there is no doubt as to which piece actually moved. For instance, when two Bishops can move to the same point then it becomes necessary to give more information than just B. If they are on different levels then the addition of the level number is used. If they are on the same level than the letter for the section will do provided its not the same for both. If they are on the very same file then the degree number can be used. To avoid any confusion as to which plane the number refers to (level or degree), simply put the number before the piece if it refers to a level and put it after if it refers to a degree. A few examples are: 4Bx7b8, R3-8g5, Bax7b8. Because there are 512 different points on a 3D-8L board, it is always best to give more information than what is needed and avoid the risk of recording ambiguous moves.



Diagram - Corners, column, file, rank, move 7c2-2h2




THE RULES OF PLAY

1. Players must confine all of their moves to the 512 points on the 3D-8L board. They may not move off the board at any time during the game.

2. Players move alternately beginning with white.

3. Players are obligated to move. They may not decline except for Stalemate, Checkmate, or Resignation.

4. Players must move only the pieces of their own color. They may not move their opponents pieces.

5. Players must move only one piece per turn (exception: Castling). See the rules for King

6. Players must make Valid moves.

7. Players must make Legal moves.



DEFINITIONS

1. Valid Move - Any move that is in accordance with the rules of movement for the type of piece that is moved.

2. Legal Move - Any Valid Move that does not leave the King in check.

3. Check - Any position on the board where the King is exposed to capture by an enemy piece.

4. Checkmate - Any position on the board where the King is in check and there are no legal moves for the player whose King it is.

5. Stalemate - Any position on the board where the King is not in check and there are no legal moves for the player whose King it is.

6. Resignation - When a player tips his King over and concedes defeat to his opponent.

7. End of Game - When a Checkmate, Stalemate, or Resignation occurs.



THE ROOK



The Rook is a one coordinate piece or linear piece.

It moves along the lines (Columns, Files, and Ranks) in one of six directions: (0, 0, 1), (0, 1, 0), ( 1, 0, 0).

The Rook has a minimum distance of 1 and maximum distance of 7.

The diagram shows all of the possible moves for a Rook at the point 5e4.

There are 21 possible moves for a Rook regardless of its position.

The domain of a Rook on the empty board is 100%, and it can reach any point in its domain in a maximum of 3 moves.

The Rook is a sliding piece.

For sliding pieces, all of the points between the origin point and the destination point must be unoccupied. The destination point must be unoccupied or contain an opposing piece in which case the enemy piece is captured and removed from the board for the remainder of the game



Diagram - Rook movement from 5e4




THE BISHOP



The Bishop is a two coordinate piece or diagonal piece.

It moves along the diagonals (white points or Black points) in one of twelve directions: (0, 1, 1), (1, 0, 1), (1, 1, 0).

The Bishop has a minimum distance of 1 and maximum distance of 7.

The diagram shows all of the possible moves for a Bishop at the point 5e4.

There are 21 to 39 possible moves for a Bishop depending on its position.

The domain of a bishop on the empty board is 50% (either the white or black points), and it can reach any point in its domain in a maximum of 3 moves.

The Bishop is a sliding piece.

For sliding pieces, all of the points between the origin point and the destination point must be unoccupied. The destination point must be unoccupied or contain an opposing piece in which case the enemy piece is captured and removed from the board for the remainder of the game.



Diagram - Bishop movement from 5e4




THE MACE



The Mace is a three coordinate piece or a triagonal piece.

It moves along triagonals (red points, green points, blue points, or yellow points) in one of eight directions: (1, 1, 1).

The Mace has a minimum distance of 1 and a maximum distance of 7.

The diagram shows all of the possible moves for a Mace at the point 5e4.

There are 7 to 25 possible moves for a Mace depending on its position.

The domain of a Mace on the empty board is 25% (either the red, green, blue or yellow points), and it can reach any point in its domain in a maximum of 3 moves.

The Mace is a sliding piece.

For sliding pieces, all of the points between the origin point and the destination point must be unoccupied. The destination point must be unoccupied or contain an opposing piece in which case the enemy piece is captured and removed from the board for the remainder of the game.



Diagram - Mace movement from 5e4




THE PLAIN KNIGHT



The Plain Knight is a two coordinate piece and moves in one of 24 directions: (0, 1, 2), (0, 2, 1), (1, 0, 2), (2, 0, 1), (1, 2, 0), (2, 1, 0)

The Plain Knight has a distance of 1.

The diagram shows all of the possible moves for a Plain Knight at the point 5e4.

There are 6 to 24 possible moves for a Plain Knight depending on its position.

The domain of a Plain Knight on the empty board is 100% (all points), and it can reach any point in its domain in 3 to 6 moves depending on initial placement.

The Plain Knight is a jumping piece.

For jumping pieces, the destination point must be unoccupied or contain an opposing piece in which case the enemy piece is captured and removed from the board for the remainder of the game.



Diagram - Plain Knight movement from 5e4




THE RED KNIGHT



The Red Knight is a three coordinate piece and moves in one of 24 directions: (1, 1, 2), (1, 2, 1), (2, 1, 1)

The Red Knight has a distance of 1.

The diagram shows all of the possible moves for a Red Knight at the point 5e4.

There are 3 to 24 possible moves for a Red Knight depending on its position.

The domain of a Red Knight on the empty board is 50% (either the white or black points), and it can reach any point in its domain in 3 to 5 moves depending on initial placement.

The Red Knight is a jumping piece.

For jumping pieces, the destination point must be unoccupied or contain an opposing piece in which case the enemy piece is captured and removed from the board for the remainder of the game.



Diagram - Red Knight movement from 5e4




THE GREEN KNIGHT



The Green Knight is a three coordinate piece and moves in one of 24 directions: (1, 2, 2), (2, 1, 2), (2, 2, 1)

The Green Knight has a distance of 1.

The diagram shows all of the possible moves for a Green Knight at the point 5e4.

There are 3 to 24 possible moves for a Green Knight depending on its position.

The domain of a Green Knight on the empty board is 100% (either the white or black points), and it can reach any point in its domain in six moves or less.

The Green Knight is a jumping piece.

For jumping pieces, the destination point must be unoccupied or contain an opposing piece in which case the enemy piece is captured and removed from the board for the remainder of the game.



Diagram - Green Knight movement from 5e4




THE ROOKBISHOP



The Rookbishop is the combination of a Rook and a Bishop as the name implies.

The Rookbishop moves like a Rook or like a Bishop.

However, it cannot move like one and then like the other in the same move.

The diagram shows all of the possible moves for a Rookbishop at the point 5e4.

There are 42 to 60 possible moves for a Rookbishop depending on its position.

The domain of a Rookbishop on the empty board is 100%, and it can reach any point in its domain in 3 moves or less.

The Rookbishop is a sliding piece.

For sliding pieces, all of the points between the origin point and the destination point must be unoccupied. The destination point must be unoccupied or contain an opposing piece in which case the enemy piece is captured and removed from the board for the remainder of the game.



Diagram - Rookbishop movement from 5e4




THE ROOKMACE



The Rookmace is the combination of a Rook and a Mace as the name implies.

The Rookmace moves like a Rook or like a Mace.

However, it cannot move like one and then the other in the same move.

The diagram shows all of the possible moves for a Rookmace at the point 5e4.

There are 28 to 46 possible moves for a Rookmace depending on its position.

The domain of a Rookmace on the empty board is 100%, and it can reach any point in its domain in 3 moves or less.

The Rookmace is a sliding piece.

For sliding pieces, all of the points between the origin point and the destination point must be unoccupied. The destination point must be unoccupied or contain an opposing piece in which case the enemy piece is captured and removed from the board for the remainder of the game.



Diagram - Rookmace movement from 5e4




THE BISHOPMACE



The Bishopmace is the combination of a Bishop and a Mace as the name implies.

The Bishopmace moves like a Bishop or like a Mace.

However, it cannot move like one and then the other in the same move.

The diagram shows all of the possible moves for a Bishopmace at the point 5e4.

There are 28 to 64 possible moves for a Bishopmace depending on its position.

The domain of a Bishopmace on the empty board is 100%, and it can reach any point in its domain in 3 moves or less.

The Bishopmace is a sliding piece.

For sliding pieces, all of the points between the origin point and the destination point must be unoccupied. The destination point must be unoccupied or contain an opposing piece in which case the enemy piece is captured and removed from the board for the remainder of the game.



Diagram - Bishopmace movement from 5e4




THE QUEEN



The Queen is a combination of a Rook and a Bishop and a Mace.

It could be called a Rookbishopmace but the name Queen implies a combination of all of the element coordinate pieces.

The Queen moves like a Rook or like a Bishop or like a Mace.

However, it cannot move like one and then either or both of the other in the same move.

The diagram shows all of the possible moves for a Queen at the point 5e4.

There are 49 to 85 possible moves for a Queen depending on its position.

The domain of a Queen on the empty board is 100%, and it can reach any point in its domain in 3 moves or less.

The Queen is a sliding piece.

For sliding pieces, all of the points between the origin point and the destination point must be unoccupied. The destination point must be unoccupied or contain an opposing piece in which case the enemy piece is captured and removed from the board for the remainder of the game.



Diagram - Queen movement from 5e4




THE GRAND KNIGHT



The Grand Knight is a combination of a Plain Knight and a Red Knight and a Green Knight.

The Grand Knight moves like a Plain Knight or like a Red Knight or like a Green Knight.

However, it cannot move like one and then either or both of the other in the same move.

The diagram shows all of the possible moves for a Grand Knight at the point 5e4.

There are 12 to 72 possible moves for a Grand Knight depending on its position.

The domain of a Grand Knight on the empty board is 100% (all points), and it can reach any point in its domain in a maximum of 3 to 5 moves depending on its position.

The Grand Knight is a jumping piece.

For jumping pieces, the destination point must be unoccupied or contain an opposing piece in which case the enemy piece is captured and removed from the board for the remainder of the game.



Diagram - Grand Knight movement from 5e4




THE KING



The King is identical in movement to the Queen except that it has a distance of one (exception: Castling). The diagram shows all of the possible moves for a King at the point 6c6. There are 7 to 26 possible moves for a king depending on initial placement. The domain for a King on the empty board is 100% and it can reach any point in its domain in a maximum of 7 moves.

Castling

The rules for castling the King in 3D-8L are the same as the 2D rules except the King can castle in six different ways instead of two. The diagram shows the Kings' origin point to be 5e1. The six darkened points at 7e1, 7g1, 5g1, 5c1, 3c1, and 3e1 are the six points that the King may castle to. The six dark-magenta points at 8e1, 8h1, 5h1, 5a1, 1a1 and 1e1 respectively, are the origin points for the six corresponding Rooks and Rookbishops with which the King may castle. The six light-magenta points at 6e1, 6f1, 5f1, 5d1, 4d1, and 4e1 respectively, are the destination points for the six corresponding Rooks and Rookbishops after castling occurs. Castling is the only time in the game when the King moves two instead of one, and it is the only time when there are two pieces moved in the turn.

Castling may occur only if all of the following conditions are met:
1) All of the points between the King and the corresponding Rook or Rookbishop must be unoccupied.
2) Castling must be the Kings' first move of the game.
3) Castling must be the corresponding Rooks' or Rookbishops' first move of the game.
4) The King must not be in check.
5) The point(s) through which the King passes must not be in check
6) The destination point where the King is castling to must not be in check.

The notation for the six castling moves is:
O|O, O/O, O-O, O-O-O, O/O/O, O|O|O.

The O's correspond to the number of points between the King and the corresponding Rook or Rookbishop. The slashes refer to the direction in which the King castled. The King may castle only once for the entire game



Diagram - King movement from 6c6, castling from 5e1




THE PAWN



A Pawn moves like a Rook or like a Bishopmace with these restrictions:
1) A Pawn has a distance of 1. (like the King)
2) A Pawn moves forward 1 degree toward the opponent. Pawns cannot move backward or directly sideways.
3) When moving directly forward on the file like a Rook the destination point must be unoccupied.
4) When moving along the diagonals or triagonals like a Bishopmace the destination point must be occupied by an enemy piece in which case the enemy piece is captured and removed from the board for the remainder of the game.

The diagram shows all of the moves for a Pawn at the point 5e4. There are eight possible capture moves and one non-capture move.

First Move - Double Advance Option

If a Pawn is moving for the very first time in the game and it is moving like a Rook, then it may slide directly forward a distance of 2 instead of just 1. Since this is Rook-style movement, both the destination point and the intervening point must be unoccupied as in restriction 3 above.

The diagram shows an example of a pawn first move double advance at 2e2-2e4.

En Passant

When a Pawn makes a first move double advance, any enemy pawn that currently attacks the intervening point through which the first pawn passed gains the temporary option to capture the first pawn en passant. The option is only available for the turn immediately following the double advance.

The diagram shows an example of the en passant capture option. A Black pawn on a magenta point can capture en passant at 2e3 immediately after a White pawn on 2e2 double advances to 2e4.

Promotion

If a White Pawn reaches the 8th degree or a Black pawn reaches the 1st degree, it must be immediately promoted to any piece type the player chooses except a King.



Diagram
Pawn movement from 5e4
first move double advance from 2e2 to 2e4
enemy pawn en passant capture options at 2e3




THE SETUP

The 3D-8L initial setup is as follows:

The point 1a1, a black point, should be at the White players' lower left hand corner

The point at 8h8, a white point, should be at the Black players' upper left hand corner.

The diagram shows the set up of the pieces for both sides at the start of the game.

The White pieces are set up on the 1st Degree; the pawns are set up on the 2nd degree directly in front of the pieces.

The Black pieces are setup up on the 8th degree; the pawns are setup on the 7th degree directly in front of the pieces.

When all the pieces for both sides are setup they are a mirror image of each other.

                  W   B
-----------------------
K - King          1   1
Q - Queen         2   2
G - Grand Knight  1   1
Rb- Rookbishop    4   4
Rm- Rookmace      4   4
Bm- Bishopmace    4   4
R - Rook          8   8
B - Bishop        8   8
M - Mace          8   8
N - Plain Knight  8   8
Nr- Red Knight    8   8
Ng- Green Knight  8   8
P - Pawn         64  64
-----------------------
                128 128



Diagram - Initial setup for White pieces
(white pieces are intentionally dark for better image contrast only)


Copyright (c) 1984-2000, Ray Edward Bornert II. All Rights Reserved.
ray.bornert@hixoxih.com

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