The Chess Variant Pages




Trans-Dimensional Chess

By L. Lynn Smith

TABLE OF CONTENTS

0.      INTRODUCTION
1.      THE PLAYING FIELD
2.      THE PLAYING PIECES
2.1.    PAWN
2.1.1.  CUBIC MOVEMENT OF THE PAWN
2.1.2.  FIELD MOVEMENT OF THE PAWN
2.1.3.  COMBINATION MOVEMENT OF THE PAWN
2.1.4.  PROMOTION OF THE PAWN
2.2.    ROOK
2.2.1.  CUBIC MOVEMENT OF THE ROOK
2.2.2.  FIELD MOVEMENT OF THE ROOK
2.2.3.  COMBINATION MOVEMENT OF THE ROOK
2.3.    BISHOP
2.3.1.  CUBIC MOVEMENT OF THE BISHOP
2.3.2.  FIELD MOVEMENT OF THE BISHOP
2.3.3.  COMBINATION MOVEMENT OF THE BISHOP
2.4.    UNICORN
2.4.1   CUBIC MOVEMENT OF THE UNICORN
2.4.2.  FIELD MOVEMENT OF THE UNICORN
2.4.3.  COMBINATION MOVEMENT OF THE UNICORN
2.5.    FAVOURITE
2.5.1.  CUBIC MOVEMENT OF THE FAVOURITE
2.5.2.  FIELD MOVEMENT OF THE FAVOURITE
2.5.3.  COMBINATION MOVEMENT OF THE FAVOURITE
2.6.    ARCHBISHOP
2.6.1.  CUBIC MOVEMENT OF THE ARCHBISHOP
2.6.2.  FIELD MOVEMENT OF THE ARCHBISHOP
2.6.3.  COMBINATION MOVEMENT OF THE ARCHBISHOP
2.7.    DRAGON
2.7.1.  CUBIC MOVEMENT OF THE DRAGON
2.7.2.  FIELD MOVEMENT OF THE DRAGON
2.7.3.  COMBINATION MOVEMENT OF THE DRAGON
2.8.    QUEEN
2.8.1.  CUBIC MOVEMENT OF THE QUEEN
2.8.2.  FIELD MOVEMENT OF THE QUEEN
2.8.3.  COMBINATION MOVEMENT OF THE QUEEN
2.9.    KING
2.9.1.  CUBIC MOVEMENT OF THE KING
2.9.2.  FIELD MOVEMENT OF THE KING
2.9.3.  COMBINATION MOVEMENT OF THE KING
2.10.   KNIGHT
2.10.1. CUBIC MOVEMENT OF THE KNIGHT
2.10.2. FIELD MOVEMENT OF THE KNIGHT
2.10.3. COMBINATION MOVEMENT OF THE KNIGHT
2.11.   HIPPOGRIFF
2.11.1. THE CUBIC MOVEMENT OF THE HIPPOGRIFF
2.11.2  THE FIELD MOVEMENT OF THE HIPPOGRIFF
2.11.3  COMBINATION MOVEMENT OF THE HIPPOGRIFF
2.12.   WYVERN
2.12.1. THE CUBIC MOVEMENT OF THE WYVERN
2.12.2. THE FIELD MOVEMENT OF THE WYVERN
2.12.3. THE COMBINATION MOVEMENT OF THE WYVERN
2.13.   GARGOYLE
2.13.1. THE CUBIC MOVEMENT OF THE GARGOYLE
2.13.2. THE FIELD MOVEMENT OF THE GARGOYLE
2.13.3. THE COMBINATION MOVEMENT OF THE GARGOYLE
3.      THE OBJECT OF TRANS-DIMENSIONAL CHESS
4.      JUSTIFICATION OF TRANS-DIMENSIONAL CHESS
4.1.    JUSTIFICATION OF THE PLAYING FIELD
4.2.    JUSTIFICATION OF PIECE MOVEMENT
4.2.1.  JUSTIFICATION OF THE PAWN
4.2.2.  JUSTIFICATION OF THE ROOK
4.2.3.  JUSTIFICATION OF THE BISHOP
4.2.4.  JUSTIFICATION OF THE UNICORN
4.2.5.  JUSTIFICATION OF THE FAVOURITE
4.2.6.  JUSTIFICATION OF THE ARCHBISHOP
4.2.7.  JUSTIFICATION OF THE DRAGON
4.2.8.  JUSTIFICATION OF THE QUEEN
4.2.9.  JUSTIFICATION OF THE KING
4.2.10. JUSTIFICATION OF THE KNIGHT
4.2.11. JUSTIFICATION OF THE HIPPOGRIFF
4.2.12. JUSTIFICATION OF THE WYVERN
4.2.13. JUSTIFICATION OF THE GARGOYLE
4.3.    JUSTIFICATION OF THE INITIAL SET-UP
4.3.1.  JUSTIFICATION OF THE NUMBER OF PIECES
4.3.2.  JUSTIFICATION OF THE PLACEMENT OF PIECES
5.      SUMMARY




0. INTRODUCTION

I wish to first acknowledge the works of V. R. Parton as having greatly contributed to the conception of this game.
At first glance, the game may appear daunting.  I assure the reader that not only the rules but also the strategy of
the game will readily become apparent.

1. THE PLAYING FIELD

The basic component of the playing FIELD is the 3x3x3 CUBE.  Each of the 27 CELLS within the CUBE will be referenced thus:

Level 3

[3a3][3b3][3c3]
[3a2][3b2][3c2]
[3a1][3b1][3c1]

Level 2

[2a3][2b3][2c3]
[2a2][2b2][2c2]
[2a1][2b1][2c1]

Level 1

[1a3][1b3][1c3]
[1a2][1b2][1c2]
[1a1][1b1][1c1]





The entire playing FIELD consists of 20 separate 3x3x3 CUBES arranged and referenced in the following pattern:


Level 3

[3a3][3b3][3c3]
[3a2]     [3c2]
[3a1][3b1][3c1]

Level 2

[2a3]     [2c3]

[2a1]     [2c1]

Level 1

[1a3][1b3][1c3]
[1a2]     [1c2]
[1a1][1b1][1c1]


Each 3x3x3 CUBE will have 27 CELLS and the entire playing FIELD will consist of 540 CELLS.

Each CELL will be referred to first by its CUBE then by its particular point within that CUBE

So the term (2a3,1a1) would denote the CELL located in the middle left back CUBE of the overall playing FIELD,
at the bottom left front point within that particular CUBE.

Some would jump to the conclusion that this game represents game play above 3D, in actuality it plays on the
concept of subsets.  Each CUBE is merely a subset of the overall playing FIELD.  Pieces will play in and through
these various subsets, all according to strict and logical rules.

-------------------------------------------------------------------------------------------

2. THE PLAYING PIECES

All pieces in Trans-Dimensional Chess not only move within each 3x3x3 CUBE by particular rules but they also are allowed to
move between each 3x3x3 CUBE by particular rules.  Moves within each 3x3x3 CUBE will be referred to as CUBIC MOVES,
moves between the 3x3x3 CUBES will be referred to as FIELD MOVES.  COMBINATION MOVES are those moves which utilize both
CUBIC and FIELD MOVES.

2.1. PAWN

There are 24 Pawns for each player. 

Initial positions:

White
(1a2,1a2)
(1a2,1b1)(1a2,1b2)
(1a2,2a2)
(1a2,2b1)(1a2,2b2)
(1a2,3a1)
(1a2,3b1)(1a2,3b2)

(1b1,1a2)
(1b1,1b1)(1b1,1b2)
(1b1,2a2)
(1b1,2b1)(1b1,2b2)
(1b1,3a1)
(1b1,3b1)(1b1,3b2)

(2a1,1a2)
(2a1,1b1)(2a1,1b2)
(2a1,3a2)
(2a1,3b1)(2a1,3b2)



Black

(2c3,1b2)(2c3,1b3)
(2c3,1c2)
(2c3,2b2)(2c3,2b3)
(2c3,2c2)
(2c3,3b2)(2c3,3b3)
(2c3,3c2)

(3b3,1b2)(3b3,1b3)
(3b3,1c2)
(3b3,2b2)(3b3,2b3)
(3b3,2c2)
(3b3,3b2)(3b3,3b3)
(3b3,3c2)

(3c2,1b2)(3c2,1b3)
(3c2,1c2)
(3c2,3b2)(3c2,3b3)
(3c2,3c2)


2.1.1. CUBIC MOVEMENT OF THE PAWN

The Pawn may NOT move without capturing within its CUBE.  It performs a capture move by stepping to any adjacent diagonal 
CELL within its CUBE.  The following diagram should suffice to demonstrate.  The 'o' refers to the Pawn itself, the 'x' 
denotes the CELLS it may capture.


[ ][x][ ]
[x][ ][x]  Level 3
[ ][x][ ]

[x][ ][x]
[ ][o][ ]  Level 2
[x][ ][x]

[ ][x][ ]
[x][ ][x]  Level 1
[ ][x][ ]


2.1.2. FIELD MOVEMENT OF THE PAWN

The White Pawn is restricted to 'positive' travel from CUBE to CUBE, while the Black Pawn is restricted to 'negative' travel.

Examples:  Movement from CUBE 1a2 to CUBE 1a3 is 'positive' travel.  Movement from CUBE 1a2 to CUBE 1a1 would be considered
'negative' travel.  CUBE 2a3 to CUBE 3a3 is 'positive' travel.  CUBE 3c1 to CUBE 2c1 is 'negative'.

The Pawn moves without capturing by translating to an empty CELL of the identical position within an adjacent orthogonal 
CUBE.

So, a White Pawn on 2b1 of CUBE 2a3(2a3,2b1) could move without capturing to an empty 2b1 position within CUBE 3a3(3a3,2b1).

The Pawn captures by translating to an enemy-occupied CELL of the identical position within an adjacent diagonal CUBE.

A Black Pawn on 3a1 of CUBE 3b1(3b1,3a1) could capture the 3a1 position within CUBE 2a1(2a1,3a1).  But not in CUBE 2c1, 
since this would result in the Black Pawn performing 'positive' travel.

2.1.3. COMBINATION MOVEMENT OF THE PAWN

The Pawn may make only a capture move when performing a COMBINATION move.  The White Pawn begins a COMBINATION with a
'positive' orthogonal FIELD MOVE, the Black Pawn begins with a 'negative' orthogonal FIELD MOVE, both then follow with 
any orthogonal CUBE MOVE.  The first CELL of this two-step move need not be empty, since effectively the Pawn does not
actually translate through it but leaps to the adjacent orthogonal CELL.


Example:

Starting CUBE      Destination CUBE

[ ][ ][ ]          [ ][ ][ ]
[ ][ ][ ] Level 3  [ ][x][ ]
[ ][ ][ ]          [ ][ ][ ]

[ ][ ][ ]          [ ][x][ ]
[ ][o][ ] Level 2  [x][ ][x]
[ ][ ][ ]          [ ][x][ ]

[ ][ ][ ]          [ ][ ][ ]
[ ][ ][ ] Level 1  [ ][x][ ]
[ ][ ][ ]          [ ][ ][ ]

The 'o' represents the Pawn and the 'x' represents those CELLS which are eligible for immediate capture.


2.1.4. PROMOTION OF THE PAWN

When the White Pawn reaches any position within CUBE 3c3, or the Black Pawn reaches any position within CUBE 1a1, they may
promote to any one of their previously captured pieces.  If there are no available captured pieces to perform the promotion,
the Pawn is not promoted and must remain unpromoted.  A player may opt not to promote the Pawn, if so the Pawn will remain
unpromoted.

2.2. ROOK

There are 2 Rooks for each player

Initial positions:

White
(1a1,2a2)(1a1,2b1)

Black
(3c3,2b3)(3c3,2c2)


2.2.1. CUBIC MOVEMENT OF THE ROOK

The Rook moves within its 3x3x3 CUBE by sliding through one or two adjacent orthogonal empty CELLS. It must stop before 
encountering one its own, but it may continue and capture an opponent piece.

Example:

[o][x][x]
[x][ ][ ]  Level 3
[x][ ][ ]

[x][ ][ ]
[ ][ ][ ]  Level 2
[ ][ ][ ]

[x][ ][ ]
[ ][ ][ ]  Level 1
[ ][ ][ ]

2.2.2. FIELD MOVEMENT OF THE ROOK

The Rook may move through any orthogonally connected CUBES.  It does this by translating from its position in its starting
CUBE to the same position in an adjacent CUBE.  If that new position is empty, it may then continue to the next CUBE.  A
Rook may capture any one of those positions.

Example:

A Rook at (2a1,1a2) can make a FIELD MOVE to (1a1,1a2) or (3a1,1a2), but NOT to (2a3,1a2) or (2c1,1a2) since there are no
inter-connecting CUBES.

2.2.3. COMBINATION MOVEMENT OF THE ROOK

There is no COMBINATION movement of the Rook.  Since the normal move of the Rook involves translation along a single axis,
there are no possible COMBINATION moves available.

2.3. BISHOP

There are 2 Bishops for each player.

Initial positions:

White
(1a1,1b2)(1a1,2b2)

Black
(3c3,2b2)(3c3,3b2)

2.3.1. CUBIC MOVEMENT OF THE BISHOP

The Bishop moves within its 3x3x3 CUBE by sliding through one or two adjacent diagonal empty CELLS. It must stop before 
encountering one its own pieces, but it may continue and capture an opponent piece.

Example:

[o][ ][ ]
[ ][x][ ]  Level 3
[ ][ ][x]

[ ][x][ ]
[x][ ][ ]  Level 2
[ ][ ][ ]

[ ][ ][x]
[ ][ ][ ]  Level 1
[x][ ][ ]

2.3.2. FIELD MOVEMENT OF THE BISHOP

The Bishop may move through any diagonally adjacent CUBE.  It does this by translating from its position in its starting
CUBE to the same position in an diagonally adjacent CUBE.

Example:

A Bishop located at (1b1,2a1) can perform a FIELD move to either (1a2,2a1), (2a1,2a1), (1c2,2a1) or (2c1,2a1).

The player may have noticed that a Bishop located in the 1a1, 1a3, 1c1, 1c3, 3a1, 3a3, 3c1, and 3c3 CUBES cannot perform
a simple FIELD move.  The COMBINATION move solves this.

2.3.3. COMBINATION MOVEMENT OF THE BISHOP

The Bishop may move and capture by performing an orthogonal FIELD move with an orthogonal CUBE move. The only concern
is the state of the destination CELL, it must be either empty or enemy-occupied.  If the CELL is empty, the Bishop may
continue with another COMBINATION move in the same directions.

Example:


1a1 CUBE       2a1 CUBE       3a1 CUBE
Level 3
[ ][ ][ ]      [ ][ ][ ]      [ ][ ][ ]
[ ][ ][ ]      [ ][ ][ ]      [ ][ ][ ]
[ ][ ][ ]      [ ][ ][ ]      [x][ ][ ]

Level 2
[ ][ ][ ]      [ ][ ][ ]      [ ][ ][ ]
[ ][ ][ ]      [ ][ ][ ]      [ ][ ][ ]
[ ][ ][ ]      [x][ ][ ]      [ ][ ][ ]

Level 1
[ ][ ][ ]      [ ][ ][ ]      [x][ ][ ]
[ ][ ][ ]      [x][ ][ ]      [ ][ ][ ]
[o][ ][ ]      [ ][x][ ]      [ ][ ][x]

or

1a1 CUBE       2a1 CUBE       3a1 CUBE
Level 3
[ ][ ][o]      [ ][x][ ]      [x][ ][ ]
[ ][ ][ ]      [ ][ ][x]      [ ][ ][ ]
[ ][ ][ ]      [ ][ ][ ]      [ ][ ][x]

Level 2
[ ][ ][ ]      [ ][ ][x]      [ ][ ][ ]
[ ][ ][ ]      [ ][ ][ ]      [ ][ ][ ]
[ ][ ][ ]      [ ][ ][ ]      [ ][ ][ ]

Level 1
[ ][ ][ ]      [ ][ ][ ]      [ ][ ][x]
[ ][ ][ ]      [ ][ ][ ]      [ ][ ][ ]
[ ][ ][ ]      [ ][ ][ ]      [ ][ ][ ]


This COMBINATION move allows the Bishop access to all CUBES of the FIELD while maintaining its 'diagonal' form of movement
along with its colorbound state.

2.4. UNICORN

There are 4 Unicorns for each player.

White
(2a1,2a1)(2a1,2a2)
(2a1,2b1)(2a1,2b1)

Black
(2c3,2b2)(2c3,2b3)
(2c3,2c2)(2c3,2c3)

2.4.1 CUBIC MOVEMENT OF THE UNICORN

The Unicorn slides through one or two adjacent triagonal CELLS.

Example

[o][ ][ ]
[ ][ ][ ]  Level 3
[ ][ ][ ]

[ ][ ][ ]
[ ][x][ ]  Level 2
[ ][ ][ ]

[ ][ ][ ]
[ ][ ][ ]  Level 1
[ ][ ][x]

or

[ ][ ][o]
[ ][ ][ ]  Level 3
[ ][ ][ ]

[ ][ ][ ]
[ ][x][ ]  Level 2
[ ][ ][ ]

[ ][ ][ ]
[ ][ ][ ]  Level 1
[x][ ][ ]

or

[x][ ][x]
[ ][ ][ ]  Level 3
[x][ ][x]

[ ][ ][ ]
[ ][o][ ]  Level 2
[ ][ ][ ]

[x][ ][x]
[ ][ ][ ]  Level 1
[x][ ][x]

2.4.2. FIELD MOVEMENT OF THE UNICORN

There are no direct FIELD moves of the Unicorn.  The ability of the Unicorn to change CUBE will be addressed in its
COMBINATION move.

2.4.3. COMBINATION MOVEMENT OF THE UNICORN

The COMBINATION move of the Unicorn can take two forms.  An orthogonal FIELD move then a diagonal CUBE move, or a diagonal
FIELD move followed by an orthogonal CUBE move.  If the destination CELL is empty, the Unicorn may make another move, in the
same directions.

Examples:

Orthogonal FIELD and diagonal CUBE move

1a3 CUBE          2a3 CUBE       3a3 CUBE
[ ][ ][ ]         [ ][ ][ ]      [ ][ ][ ]
[ ][ ][ ] Level 3 [ ][ ][ ]      [ ][ ][x]
[ ][ ][ ]         [ ][ ][ ]      [ ][ ][ ]

[ ][ ][ ]         [ ][ ][ ]      [ ][ ][ ]
[ ][ ][ ] Level 2 [ ][x][ ]      [ ][ ][ ]
[ ][ ][ ]         [ ][ ][ ]      [ ][ ][ ]

[ ][ ][ ]         [ ][x][ ]      [ ][ ][ ]
[o][ ][ ] Level 1 [ ][ ][ ]      [ ][ ][ ]
[ ][ ][ ]         [ ][x][ ]      [ ][ ][ ]

 
Diagonal FIELD and orthogonal CUBE move

2a3 CUBE          3b3 CUBE
[ ][ ][ ]         [ ][ ][ ]
[ ][ ][ ] Level 3 [ ][x][ ]
[ ][ ][ ]         [ ][ ][ ]

[ ][ ][ ]         [ ][x][ ]
[ ][o][ ] Level 2 [x][ ][x]
[ ][ ][ ]         [ ][x][ ]

[ ][ ][ ]         [ ][ ][ ]
[ ][ ][ ] Level 1 [ ][x][ ]
[ ][ ][ ]         [ ][ ][ ]


2.5. FAVOURITE


There are 2 Favourites for each player.

Initial positions:

White
(1a1,1a2)(1a1,1b1)

Black
(3c3,3b3)(3c3,3c2)

2.5.1. CUBIC MOVEMENT OF THE FAVOURITE

The Favourite performs CUBIC moves either as a Bishop or Rook.

2.5.2. FIELD MOVEMENT OF THE FAVOURITE

The Favourite performs FIELD moves either as a Bishop or Rook.

2.5.3. COMBINATION MOVEMENT OF THE FAVOURITE

The Favourite performs COMBINATION moves as a Bishop.

2.6. ARCHBISHOP

There are 2 Archbishops for each player.

Initial positions:

White
(1a1,3a1)
(1a1,3b2)

Black
(3c3,1b2)
(3c3,1c3)

2.6.1. CUBIC MOVEMENT OF THE ARCHBISHOP

The Archbishop performs CUBIC moves either as a Bishop or Unicorn.

2.6.2. FIELD MOVEMENT OF THE ARCHBISHOP

The Archbishop performs FIELD moves as a Bishop.

2.6.3. COMBINATION MOVEMENT OF THE ARCHBISHOP

The Archbishop performs COMBINATION moves either as a Bishop or Unicorn.


2.7  DRAGON

There are 2 Dragons for each player.

Initial positions:

White
(1a1,1a2)
(1a1,1b1)

Black
(3c3,3b3)
(3c3,3c2)

2.7.1. CUBIC MOVEMENT OF THE DRAGON

The Dragon performs CUBIC moves either as a Rook or Unicorn.

2.7.2. FIELD MOVEMENT OF THE DRAGON

The Dragon performs FIELD moves as a Rook.

2.7.3. COMBINATION MOVEMENT OF THE DRAGON

The Dragon performs COMBINATION moves as a Unicorn.


2.8. QUEEN

There is 1 Queen for each player

Initial positions:

White
(1a1,2a1)

Black
(3c3,2c3)

2.8.1. CUBIC MOVEMENT OF THE QUEEN

The Queen performs CUBIC moves either as a Bishop, Rook or Unicorn.

2.8.2. FIELD MOVEMENT OF THE QUEEN

The Queen performs FIELD moves as either a Bishop or Rook.

2.8.3. COMBINATION MOVEMENT OF THE QUEEN

The Queen performs COMBINATION moves either as a Bishop or Unicorn.

2.9. KING

There is 1 King for each player.

Initial positions:

White
(1a1,1a1)

Black
(3c3,3c3)

2.9.1. CUBIC MOVEMENT OF THE KING

The King performs a single CUBIC move either as a Bishop, Rook or Unicorn.

2.9.2. FIELD MOVEMENT OF THE KING

The King performs a single FIELD move as either a Bishop or Rook.

2.9.3. COMBINATION MOVEMENT OF THE KING

The King performs a single COMBINATION move either as a Bishop or Unicorn.

2.10. KNIGHT

There are 2 Knights for each player.

Initial positions:

White
(1a2,2a1)(1b1,2a1)

Black
(3b3,2c3)(3c2,2c3)

2.10.1  CUBIC MOVEMENT OF THE KNIGHT

The Knight performs its CUBIC leap by moving through one orthogonal then one diagonal CELL, or through one diagonal then one
orthogonal.  Basically, this is a translation within a 3x2x1 area from one corner to its opposite.  This a direct translation 
regardless of the state of the intervening CELLS.

Example:


[o][ ][ ]
[ ][ ][x] Level 3
[ ][x][ ]

[ ][ ][x]
[ ][ ][ ] Level 2
[x][ ][ ]

[ ][x][ ]
[x][ ][ ] Level 1
[ ][ ][ ]

2.10.2 FIELD MOVEMENT OF THE KNIGHT

See section 2.10.3.

2.10.3 COMBINATION MOVEMENT OF THE KNIGHT

The Knight performs its COMBINATION move by translating to the same point of an adjacent orthogonal CUBE thus reducing its
3x2x1 area leap to either a 3x1x1 or 2x2x1 area leap, or by translating to an adjacent diagonal CUBE and reducing the
3x2x1 area leap to a simple 2x1x1 move.  This all means that the Knight arriving at its initial point within an orthogonal 
adjacent CUBE can either continue with a two-step orthogonal leap or one diagonal step, or when arriving at its initial
point within a diagonal adjacent CUBE the Knight continues with an orthogonal step.

Example:

Orthogonal CUBE

[ ][ ][ ]         [ ][ ][ ]
[ ][ ][ ] Level 3 [x][ ][ ]
[ ][ ][ ]         [ ][ ][ ]

[ ][ ][ ]         [x][ ][ ]
[ ][ ][ ] Level 2 [ ][ ][ ]
[ ][ ][ ]         [x][ ][ ]

[ ][ ][ ]         [ ][x][ ]
[o][ ][ ] Level 1 [ ][ ][x]
[ ][ ][ ]         [ ][x][ ]

or

[ ][ ][o]         [x][ ][ ]
[ ][ ][ ] Level 3 [ ][x][ ]
[ ][ ][ ]         [ ][ ][x]

[ ][ ][ ]         [ ][x][ ]
[ ][ ][ ] Level 2 [ ][ ][x]
[ ][ ][ ]         [ ][ ][ ]

[ ][ ][ ]         [ ][ ][x]
[ ][ ][ ] Level 1 [ ][ ][ ]
[ ][ ][ ]         [ ][ ][ ]


Diagonal CUBE

[ ][ ][ ]         [ ][ ][ ]
[ ][ ][ ] Level 3 [ ][x][ ]
[ ][ ][ ]         [ ][ ][ ]

[ ][ ][ ]         [ ][x][ ]
[ ][o][ ] Level 2 [x][ ][x]
[ ][ ][ ]         [ ][x][ ]

[ ][ ][ ]         [ ][ ][ ]
[ ][ ][ ] Level 1 [ ][x][ ]
[ ][ ][ ]         [ ][ ][ ]



2.11 HIPPOGRIFF

There are 2 Hippogriffs for each player.

White
(1a2,1a1)(1b1,1a1)

Black
(3b3,3c3)(3c2,3c3)

2.11.1 THE CUBIC MOVEMENT OF THE HIPPOGRIFF

The Hippogriff performs its CUBIC leap by moving through one orthogonal then one triagonal CELL, or through one
triagonal then one orthogonal.  Basically, this is a translation within a 3x2x2 area from one corner to its opposite.
This a direct translation regardless of the state of the intervening CELLS.

Example:


[o][ ][ ]
[ ][ ][ ] Level 3
[ ][ ][ ]

[ ][ ][ ]
[ ][ ][x] Level 2
[ ][x][ ]

[ ][ ][ ]
[ ][x][ ] Level 1
[ ][ ][ ]

2.11.2 THE FIELD MOVEMENT OF THE HIPPOGRIFF

See section 2.11.3.

2.11.3 COMBINATION MOVEMENT OF THE HIPPOGRIFF

The Hippogriff performs its COMBINATION move by translating to the same point of an adjacent orthogonal CUBE thus reducing 
its 3x2x2 area leap to either a 3x2x1 or 2x2x2 area leap, or by translating to the same point of an adjacent diagonal CUBE
thus reducing its leap to a 3x1x1 or 2x2x1 area.  This all means that the Hippogriff arriving at its initial point within 
an orthogonal adjacent CUBE can either continue with a Knight leap or one triagonal step, or when arriving at its initial
point within a diagonal adjacent CUBE the Hippogriff continues with a two-step orthogonal leap or a diagonal step .

Example:

Orthogonal CUBE

[ ][ ][ ]         [ ][ ][ ]
[ ][ ][ ] Level 3 [ ][x][ ]
[ ][ ][ ]         [ ][ ][ ]

[ ][ ][ ]         [ ][x][ ]
[ ][ ][ ] Level 2 [ ][ ][ ]
[ ][ ][ ]         [ ][x][ ]

[ ][ ][ ]         [ ][ ][x]
[o][ ][ ] Level 1 [ ][ ][ ]
[ ][ ][ ]         [ ][ ][x]

or

[ ][ ][o]         [ ][ ][ ]
[ ][ ][ ] Level 3 [x][ ][ ]
[ ][ ][ ]         [ ][x][ ]

[ ][ ][ ]         [x][ ][ ]
[ ][ ][ ] Level 2 [ ][x][ ]
[ ][ ][ ]         [ ][ ][x]

[ ][ ][ ]         [ ][x][ ]
[ ][ ][ ] Level 1 [ ][ ][x]
[ ][ ][ ]         [ ][ ][ ]

Diagonal CUBE

[ ][ ][ ]         [ ][ ][ ]
[ ][ ][ ] Level 3 [x][ ][ ]
[ ][ ][ ]         [ ][ ][ ]

[ ][ ][ ]         [x][ ][ ]
[ ][ ][ ] Level 2 [ ][ ][ ]
[ ][ ][ ]         [x][ ][ ]

[ ][ ][ ]         [ ][x][ ]
[o][ ][ ] Level 1 [ ][ ][x]
[ ][ ][ ]         [ ][x][ ]

or

[ ][ ][o]         [x][ ][ ]
[ ][ ][ ] Level 3 [ ][x][ ]
[ ][ ][ ]         [ ][ ][x]

[ ][ ][ ]         [ ][x][ ]
[ ][ ][ ] Level 2 [ ][ ][x]
[ ][ ][ ]         [ ][ ][ ]

[ ][ ][ ]         [ ][ ][x]
[ ][ ][ ] Level 1 [ ][ ][ ]
[ ][ ][ ]         [ ][ ][ ]




2.12 WYVERN

There are 2 Wyverns for each player.

Initial positions:

White
(1a2,3a1)(1b1,3a1)

Black
(3b3,1c3)(3c2,1c3)

2.12.1 THE CUBIC MOVEMENT OF THE WYVERN

The Wyvern performs its CUBIC leap by moving through one diagonal then one triagonal CELL, or through one triagonal
then one diagonal.  Basically, this is a translation within a 3x3x2  area from one corner to its opposite.  This a 
direct translation regardless of the state of the intervening CELLS.

Example:


[o][ ][ ]
[ ][ ][ ] Level 3
[ ][ ][ ]

[ ][ ][ ]
[ ][ ][ ] Level 2
[ ][ ][x]

[ ][ ][ ]
[ ][ ][x] Level 1
[ ][x][ ]

2.12.2 THE FIELD MOVEMENT OF THE WYVERN

See section 2.12.3.

2.12.3 THE COMBINATION MOVEMENT OF THE WYVERN

The Wyvern performs its COMBINATION move by translating to the same point of an adjacent orthogonal CUBE thus reducing 
its 3x3x2 area leap to either a 3x2x2 or 3x3x1 area leap, or by translating to the same point of an adjacent diagonal
CUBE thus reducing its leap to 3x2x1 or 2x2x2 area move.   This all means that the Wyvern arriving at its initial point 
within an orthogonal adjacent CUBE can either continue with a Hippogriff leap or a two-step diagonal leap, or when 
arriving at its initial point within a diagonal adjacent CUBE the Wyvern continues with a Knight leap or a triagonal step.


Example :

Orthogonal CUBE

[ ][ ][ ]         [ ][ ][ ]
[ ][ ][ ] Level 3 [ ][ ][x]
[ ][ ][ ]         [ ][ ][ ]

[ ][ ][ ]         [ ][ ][x]
[ ][ ][ ] Level 2 [ ][ ][ ]
[ ][ ][ ]         [ ][ ][x]

[ ][ ][ ]         [ ][ ][ ]
[o][ ][ ] Level 1 [ ][ ][ ]
[ ][ ][ ]         [ ][ ][ ]

or

[ ][ ][o]         [ ][ ][ ]
[ ][ ][ ] Level 3 [ ][ ][ ]
[ ][ ][ ]         [x][ ][ ]

[ ][ ][ ]         [ ][ ][ ]
[ ][ ][ ] Level 2 [x][ ][ ]
[ ][ ][ ]         [ ][x][ ]

[ ][ ][ ]         [x][ ][ ]
[ ][ ][ ] Level 1 [ ][x][ ]
[ ][ ][ ]         [ ][ ][x]

Diagonal CUBE

[ ][ ][ ]         [ ][ ][ ]
[ ][ ][ ] Level 3 [ ][x][ ]
[ ][ ][ ]         [ ][ ][ ]

[ ][ ][ ]         [ ][x][ ]
[ ][ ][ ] Level 2 [ ][ ][ ]
[ ][ ][ ]         [ ][x][ ]

[ ][ ][ ]         [ ][ ][x]
[o][ ][ ] Level 1 [ ][ ][ ]
[ ][ ][ ]         [ ][ ][x]

or

[ ][ ][o]         [ ][ ][ ]
[ ][ ][ ] Level 3 [x][ ][ ]
[ ][ ][ ]         [ ][x][ ]

[ ][ ][ ]         [x][ ][ ]
[ ][ ][ ] Level 2 [ ][x][ ]
[ ][ ][ ]         [ ][ ][x]

[ ][ ][ ]         [ ][x][ ]
[ ][ ][ ] Level 1 [ ][ ][x]
[ ][ ][ ]         [ ][ ][ ]


2.13 GARGOYLE

There are 2 Gargoyles for each player.

Initial positions:

White
(2a1,1a1)(2a1,3a1)

Black
(2c3,1c3)(2c3,3c3)

2.13.1. THE CUBIC MOVEMENT OF THE GARGOYLE

The Gargoyle performs its CUBIC move by leaping two triagonal, diagonal or triagonal CELLS.  Basically, this is a translation 
within a 3x3x3, 3x3x1 or 3x1x1 area.  This a direct translation regardless of the state of the intervening CELLS.

Example:


[o][ ][x]
[ ][ ][ ] Level 3
[x][ ][x]

[ ][ ][ ]
[ ][ ][ ] Level 2
[ ][ ][ ]

[ ][ ][x]
[ ][ ][ ] Level 1
[x][ ][x]

2.13.2. THE FIELD MOVEMENT OF THE GARGOYLE

See section 2.12.3.

2.13.3. THE COMBINATION MOVEMENT OF THE GARGOYLE

The Gargoyle performs its COMBINATION move by translating to the same point of an adjacent orthogonal CUBE thus reducing 
its 3x3x3, 3x3x1 or 3x1x1 area leap to a either a 3x3x2, 3x2x1 or 2x1x1 area leap, or by translating to the same point of 
an adjacent diagonal CUBE thus reducing its leap to 3x2x2 or 2x2x1 area move.   This all means that the Gargoyle arriving 
at its initial point within an orthogonal adjacent CUBE can continue with a Wyvern leap or a Knight leap or an orthogonal
step, or when arriving at its initial point within a diagonal adjacent CUBE the Gargoyle continues with a Hippogriff leap 
or a diagonal step.


Example :

Orthogonal CUBE

[ ][ ][ ]         [ ][x][ ]
[ ][ ][ ] Level 3 [x][ ][x]
[ ][ ][ ]         [ ][x][ ]

[ ][ ][ ]         [x][ ][x]
[ ][ ][ ] Level 2 [ ][ ][ ]
[ ][ ][ ]         [x][ ][x]

[ ][ ][ ]         [ ][x][ ]
[ ][ ][ ] Level 1 [x][ ][x]
[o][ ][ ]         [ ][x][ ]


Diagonal CUBE

[ ][ ][ ]         [ ][ ][ ]
[ ][ ][ ] Level 3 [ ][x][ ]
[ ][ ][ ]         [ ][ ][ ]

[ ][ ][ ]         [ ][x][ ]
[ ][ ][ ] Level 2 [x][ ][x]
[ ][ ][ ]         [ ][x][ ]

[ ][ ][ ]         [ ][ ][ ]
[ ][ ][ ] Level 1 [ ][x][ ]
[o][ ][ ]         [ ][ ][ ]



3. THE OBJECT OF TRANS-DIMENSIONAL CHESS

Checkmate the opponent King.

4. JUSTIFICATION OF TRANS-DIMENSIONAL CHESS

In 3D Chess, games suffer from playing fields which are either too small or large.  Too small, they offer little area for
development, strategy or the occupation by a substantial force.  Too large, development and strategy becomes unfathomable
with the necessity of a unwieldy amount of forces.

The answer was to utilize a large playing FIELD divided into uniform subsets.

4.1 JUSTIFICATION OF THE PLAYING FIELD

V.R. Parton proposed the concept of subsets with his introduction of Ecila Chess.  He utilized 2x2x2 CUBES arranged into a
2x2x2 playing FIELD to demonstrate the effectiveness of this style of 3D play.  He suggested both the 3x3x3 and the 4x4x4
patterns for increased complexity of play.

The 2x2x2 pattern, with an effective 4x4x4 playing FIELD, offered very little room for development.  In fact, Parton 
suggested alternating placement of the pieces at the start of play, without checking the opponent King, as a way of 
creating a form of development.  The 4x4x4 pattern, with its effective 16x16x16, began to push the limits of enjoyable
game play with the possibility of excessively long games.

This left the 3x3x3 pattern.  The 3x3x3 CUBES offered enough area for some form of game play but the overall 3x3x3 pattern
of CUBES reduced this potential by their proximity to each other.  There was the possibility, with any form of standard
set-up pattern that check could be achieved within only 2 turns, with first a FIELD move followed with a CUBE move.  This 
could have been dissuaded by placing all the CELLS of CUBES adjacent to the set-up patterns under attack, but this would
also have to include the limiting of ranging pieces across the overall playing FIELD.

By removing the central CUBE from each of the FIELD's planes, this forced pieces to move through short interconnected
'corridors' and effectively created a good 'distance' between CUBES on opposite points of the playing FIELD.  

This also reduced the number of CELLS in the overall playing FIELD from 729 to 540.  This was close to the 512 CELLS of
a simple 8x8x8 playing FIELD, but could be thoroughly occupied and defended by 48 pieces for each players rather than the
128 normally suggested for a FIELD of this size.

4.2  JUSTIFICATION OF PIECE MOVEMENT

It is to be expected that each piece would dominate the 3x3x3 CUBE according to specific patterns.  They would also 
move to and attack CELLS within neighboring CUBES according to specific patterns.  These pieces would include types
which use stepping, sliding or leaping moves.  Keeping these move types separate would aid in the quick evaluation 
of any piece and its position. Steps and slides would include moves along orthogonal, diagonal and triagonal lines.  
Leaps would involve those spaces one step away including those spaces not covered by the step or slide move.


Stepping and            Leaping
Sliding moves           moves

[U][ ][B][ ][U]         [ ][W][ ][W][ ]
[ ][ ][ ][ ][ ]         [W][H][N][H][W]
[B][ ][R][ ][B] Level 5 [ ][N][ ][N][ ]
[ ][ ][ ][ ][ ]         [W][H][N][H][W]
[U][ ][B][ ][U]         [ ][W][ ][W][ ]

[ ][ ][ ][ ][ ]         [W][H][N][H][W]
[ ][U][B][U][ ]         [H][ ][ ][ ][H]
[ ][B][R][B][ ] Level 4 [N][ ][ ][ ][N]
[ ][U][B][U][ ]         [H][ ][ ][ ][H]
[ ][ ][ ][ ][ ]         [W][H][N][H][W]

[B][ ][R][ ][B]         [ ][N][ ][N][ ]
[ ][B][R][B][ ]         [N][ ][ ][ ][N]
[R][R][o][R][R] Level 3 [ ][ ][o][ ][ ]
[ ][B][R][B][ ]         [N][ ][ ][ ][N]
[B][ ][R][ ][B]         [ ][N][ ][N][ ]

[ ][ ][ ][ ][ ]         [W][H][N][H][W]
[ ][U][B][U][ ]         [H][ ][ ][ ][H]
[ ][B][R][B][ ] Level 2 [N][ ][ ][ ][N]
[ ][U][B][U][ ]         [H][ ][ ][ ][H]
[ ][ ][ ][ ][ ]         [W][H][N][H][W]

[U][ ][B][ ][U]         [ ][W][ ][W][ ]
[ ][ ][ ][ ][ ]         [W][H][N][H][W]
[B][ ][R][ ][B] Level 1 [ ][N][ ][N][ ]
[ ][ ][ ][ ][ ]         [W][H][N][H][W]
[U][ ][B][ ][U]         [ ][W][ ][W][ ]

o=moving piece 
B=Bishop H=Hippogriff N=Knight R=Rook U=Unicorn W=Wyvern


Of course, this diagram represents a 5x5x5 playing FIELD.  In Trans-Dimensional Chess, the assumedly restrictive 3x3x3 
playing FIELD will be utilized.


4.2.1. JUSTIFICATION OF THE PAWN

This is the most move-restricted piece on the FIELD.  To keep with the 'spirit' of the Pawn, it is allowed to effectively
defend CELLS within its CUBE.  Its movement throughout the FIELD is very restrictive.  Whether it occupies a side CUBE or
a corner CUBE changes both its FIELD move and capture options.  The COMBINATION capture to an adjacent CUBE allows it to
maintain its familiar form of defense.

Example:


Initial           Orthogonal     Diagonal
[x][x][x]         [ ][x][ ]      [ ][ ][ ]
[x][o][x] Level 3 [x][x][x]      [ ][x][ ]
[x][x][x]         [ ][x][ ]      [ ][ ][ ]
 
[x][x][x]         [ ][x][ ]      [ ][ ][ ]
[x][o][x] Level 2 [x][x][x]      [ ][x][ ]
[x][x][x]         [ ][x][ ]      [ ][ ][ ]

[x][x][x]         [ ][x][ ]      [ ][ ][ ]
[x][o][x] Level 1 [x][x][x]      [ ][x][ ]
[x][x][x]         [ ][x][ ]      [ ][ ][ ]

With a row of Pawns occupying the b2 point of each level of a CUBE, they thoroughly attack the entire 3x3x3 area without
actually defending each other.  They also attack a large portion of the CELLS within the neighboring orthogonal CUBE.  
If the one on Level 2 was to perform a non-capturing FIELD move to the neighboring orthogonal CUBE, the other two Pawns 
would each then defend it.  But if one of the Pawns was to make a capture FIELD move to the diagonal CUBE, it would lose
its defenders.

A Pawn located in an edge CUBE can perform one orthogonal non-capturing FIELD move, up to two diagonal capturing FIELD
moves and up to six capturing COMBINATION moves. A Pawn located in a corner CUBE could perform up to two orthogonal 
non-capturing FIELD moves and up to twelve capturing COMBINATION moves.

The restrictive nature of the non-capturing move assures the desire for gradual Pawn development within the game.  While
the promise of promotion spurs the players overall strategy.

Pawn promotion was restricted to the recovery of captured pieces because of the overall variety of pieces within the
game and the prevention of the possible domination of the game by the first player to merely promote.

The name is a classical designation of this type of playing piece.  The term 'pawn' is derived form the term 'peon',
a foot soldier.

4.2.2. JUSTIFICATION OF THE ROOK

There has been no attempt to modify the move power of the Rook above that of the simple orthogonal slide.

Any of its shortcomings are adjusted with the introduction of the Favourite and the Dragon, both which also utilize the
orthogonal slide.

Therefore, the Rook is allowed to exist in its seemingly weakened condition upon the 3D playing FIELD.

The name is a classical designation of this type of playing piece.  Although this piece has come to be physically
represent by a tower, or rookery, it was derived from the words 'rukh', 'rukhkh' and 'roc', a mythical bird of enormous
size and strength.  

4.2.3. JUSTIFICATION OF THE BISHOP

With this piece is introduced the apparent backward slide with the COMBINATION move.  This comes about because the diagonal
move is basically a change along two axes.  In the COMBINATION move, the orthogonal FIELD move is considered one axis of the
diagonal and therefore the orthogonal CUBE move completes it.  The Bishop is allowed to take this orthogonal CUBE move in
any 'direction' within the CUBE with the only stipulation that if the Bishop continues with a COMBINATION move that it do
so by keeping to both 'directions' of the first.

This allows the Bishop to remain a colorbound piece and gives it access up to six CELLS in the first destination CUBE and
up to three in the next CUBE.

A Bishop located in an edge CUBE attacks six adjacent CUBES, the two adjacent corner CUBES and their four connecting edge
CUBES.

A Bishop located in a corner CUBE attacks the three connecting edge CUBES. 

The name is a classical designation of this type of playing piece.  Although the term 'bishop' has become a religious
title, its original meaning was that of 'overseer'.

4.2.4. JUSTIFICATION OF THE UNICORN

With the Unicorn, we are introduced to the first move which is unique to 3D.  The triagonal is a move which performs a
change along three axes.  The Unicorn is able to utilize this particular move within any CUBE.  But since there are no
triagonally adjacent CUBES in this FIELD, the Unicorn is unable to perform a simple FIELD move and must rely on the
COMBINATION move in order to change CUBE.

With the orthogonal move being a change on one axis and the diagonal a change on two, we arrive at the following
potential COMBINATION moves for the Unicorn:

a. One orthogonal FIELD move + two orthogonal CUBE moves 
b. Two orthogonal FIELD moves + one orthogonal CUBE move 
c. One orthogonal FIELD move + one diagonal CUBE move
d. One diagonal FIELD move + one orthogonal CUBE move

Move 'b' is automatically rejected because it violates the concept that sequential FIELD moves should change the same
'directions' on each consecutive step.  Move 'a' is rejected because it violates the concept that sliding and leaping
moves should not be utilized by the same piece and this move would involve the Unicorn translating to a CELL which is
separate from the point in the destination CUBE which corresponds to the point in its starting CUBE.

This leaves both moves 'c' and 'd' which each allow the Unicorn to perform a single translation to a neighboring CUBE to
a CELL which is adjacent to its initial point.  Move 'c' also allows for a sequential FIELD move which obeys the concept
of the continuation of the same changes of 'directions'. 

The name is the classical designation of this type of playing piece.  Most are familiar with the mythical 'one-horn
horse', but a 'Unicorn', capitalized, designates 'one of the Scottish pursuivants, a state messenger with power to
execute warrants'.  This is also a common heraldic symbol

4.2.5. JUSTIFICATION OF THE FAVOURITE

----------------------------------------------------------------------------------------------------------------------
|GENERAL NOTE ON COMPOSITE SLIDERS                                                                                   |
|The primary purpose of the composite sliders to offer the player an effective variety of power pieces which are     |
|necessary to the 3D playing FIELD.  In 2D, the King can be easily checkmated by two Rooks on an open playing FIELD. |
|In 3D, there is the necessity of six Rooks to checkmate the King on an open playing FIELD. With both the Favourite  |
|and the Dragon having the orthogonal slide, this requirement is satisfied.  Finishing out the possible combinations |
|offers the player a well-rounded and comprehensible force to operate with throughout the game.                      |
----------------------------------------------------------------------------------------------------------------------

The Favourite represents one of the four composite sliders.  It utilizes both the orthogonal and diagonal slide.

The name is a classical designation of this type of playing piece.  A 'favourite' was an individual given special
ranks and privileges by a monarch.

4.2.6. JUSTIFICATION OF THE ARCHBISHOP

See section 4.2.5. for GENERAL NOTE ON COMPOSITE SLIDERS

The Archbishop represents one of the four composite sliders.  It utilizes both the diagonal and triagonal slide.

The name is a classical designation of this type of playing piece.  The term 'archbishop' designated someone who
had authority over other bishops.  With additional power of the triagonal move, this 'bishop' piece is no longer
colorbound and therefore is superior to the ordinary 'bishop'.

4.2.7. JUSTIFICATION OF THE DRAGON

See section 4.2.5. for GENERAL NOTE ON COMPOSITE SLIDERS

The Dragon represents one of the four composite sliders.  It utilizes both the orthogonal and triagonal slide.

This is a new name for this comtemporary piece.  This is to continue the heraldic titles assigned new 3D chess pieces.
A 'Dragon' was a mounted infantryman of the 16th and 17th century who carried a short musket of the same name.

4.2.8. JUSTIFICATION OF THE QUEEN

See section 4.2.5. for GENERAL NOTE ON COMPOSITE SLIDERS

The Queen represents the last of the four composite sliders.  It utilizes the orthogonal, diagonal and triagonal slide.

At first glance, this piece may appear too powerful.  It can complete dominate the 3x3x3 area of a CUBE.  But the overall
pattern of the FIELD prevents it from assaulting no more than six other CUBES.  If all 27 CUBES were available in the
FIELD, the Queen would effective assault 15 of them thus reducing good game play.

The name is a classical designation of this type of playing piece.  The term 'queen' denotes a female monarch.

4.2.9.  JUSTIFICATION OF THE KING

The King is basically the only piece which fully utilizes the single step move.  And being the prize, it needed to have full
range of such movement.  In other 3D Chess games, this freedom allowed the King to evade most capture. But with the playing
FIELD of Trans-Dimensional Chess, this freedom does not interfere with the possible pin and capture of this piece.

The name is a classical designation of this type of playing piece.  A term 'king' denotes a male monarch

4.2.10. JUSTIFICATION OF THE KNIGHT

----------------------------------------------------------------------------------------------------------------------
|GENERAL NOTE ON LEAPING PIECES                                                                                      |
|                                                                                                                    |
|Within the 3x3x3 CUBE, leaps are confined and scattered adding to the need for strategic placement within the game. |
|It was also determined that only a single FIELD move would be allowed any leaping piece.  This was based upon the   |
|restriction to sliding pieces that multiple FIELD and COMBINATION moves should be of equal 'distances'.  Also this  |
|allows the sliding pieces a proper 'range' beyond that of the leaping pieces.                                       |
|                                                                                                                    |
|The primary purpose of the leaping piece is to create opportunities for forks, the simultaneous attack of several   |
|opposing pieces.  By dividing the leaps into four specific types, this offers the player opportunity for strategic  |
|utilization and possible defensive stances against particular forking patterns.                                     |
----------------------------------------------------------------------------------------------------------------------

As the first of the game's leaping pieces, the Knight sets the tone.

The player may be familiar with and able to visualize the 'L' leap of the Knight within its 3x3x3 CUBE.  The orthogonal
and diagonal COMBINATION move will also become familiar and easy to visualize. Think of the starting CUBE as the first
'space' of the leap, then the destination CUBE as the continuation.

Remember that the Knight performs the 'L' leap with its CUBE, a two-step orthogonal leap or a diagonal step in the 
adjacent orthogonal CUBE and a simple orthogonal step in the adjacent diagonal CUBE.  All from the same point within each
3x3x3 area.

If a Knight was to only remain in its CUBE, its move pattern would appear to cover the following CELLS:


[x][x][x]
[x][x][x]  Level 3
[x][x][x]

[x][x][x]
[x][ ][x]  Level 2
[x][x][x]

[x][x][x]
[x][x][x]  Level 1
[x][x][x]

To attack the 2b2 point of this CUBE, the Knight could translate to an edge point of an adjacent orthogonal CUBE then
return using the COMBINATION move with the diagonal step, or translate to the face point of an adjacent diagonal CUBE
then returning.

>From the 2b2 point of any CUBE, the Knight has no CUBE move and must perform a COMBINATION move to change locations.

The name is a classical designation of this type of playing piece.  The 'knight' was a term given feudal times to
one of honorable military rank, often the veteran of a campaign and well versed in arms.

4.2.11. JUSTIFICATION OF THE HIPPOGRIFF

See section 4.2.10. for GENERAL NOTE ON LEAPING PIECES

As the second of the game's leaping pieces, the Hippogriff adds an interesting factor within the COMBINATION moves of the
leaping pieces.  With the COMBINATION move to an adjacent orthogonal CUBE, there appears the familiar 'L' pattern of the 
Knight's leap or the simple triagonal step. With the COMBINATION move to an adjacent diagonal CUBE, there appears the simple
diagonal step.

With its 3x2x2 leap within the 3x3x3, the Hippogriff seems confined.  If the piece was to remain in the 3x3x3 are of a
particular CUBE, its move pattern would appear to cover the following CELLS:

[x][x][x]
[x][x][x]  Level 3
[x][x][x]

[x][x][x]
[x][ ][x]  Level 2
[x][x][x]

[x][x][x]
[x][x][x]  Level 1
[x][x][x]

Like the Knight, the 2b2 point of the CUBE can only be attack by translating to a neighboring CUBE then returning.  This
can be done by translating to the corner point of an adjacent orthogonal CUBE then returning using the COMBINATION move 
with the triagonal step.  Or by translating to an edge point of an adjacent diagonal CUBE the returning using the 
COMBINATION move with the diagonal step.

>From the 2b2 point of any CUBE, the Hippogriff has no CUBE move and must perform a COMBINATION move to change locations.

The name is a classical designation of this type of playing piece.  The 'hippogriff' is a mythical creature which
resembles a griffin (a creature with the head and wings of an eagle and the body of a lion) but having the body and
the hind parts of a horse.  It is also a heraldic symbol.

4.2.12. JUSTIFICATION OF THE WYVERN

See section 4.2.10. for GENERAL NOTE ON LEAPING PIECES

As the third of the game's leaping pieces, the Wyvern continues the interesting factor which was found in the COMBINATION
moves of the Hippogriff.  With the COMBINATION move to an adjacent orthogonal CUBE, there appears the pattern of the 
Hippogriff's CUBE leap or the two-step diagonal leap. With the COMBINATION move to an adjacent diagonal CUBE, once again 
the familiar 'L' pattern of the Knight's leap or the simple triagonal step.

With its 3x3x2 leap within the 3x3x3, the Wyvern appears to be the most restricted of the leaping pieces.  If the piece 
was to remain in the 3x3x3 are of a particular CUBE, its move pattern would appear to cover the following CELLS:

[x][x][x]
[x][ ][x]  Level 3
[x][x][x]

[x][ ][x]
[ ][ ][ ]  Level 2
[x][ ][x]

[x][x][x]
[x][ ][x]  Level 1
[x][x][x]

[Hmmmmmm. That pattern looks very familiar. ;-)]

With the Wyvern, we are faced with a large number of CELLS which can only be accessed from an adjacent CUBE.  Translating
to an adjacent orthogonal CUBE, the Wyvern can access all eight of the face CELLS with the return COMBINATION move of the
Hippogriff leap.  From an adjacent diagonal CUBE, the Wyvern can access any face CELL using the COMBINATION move with the
Knight's leap,  both the face CELLS and the center 2b2 CELL with the COMBINATION move with the triagonal step.

>From the 2b2 point of any CUBE, the Wyvern has no CUBE move and must perform a COMBINATION move to change locations.

The Wyvern is not able to access the 2b2 CELL of the eight corner CUBES.  This knowledge can be used for strategic value.

The name is a classical designation of this type of playing piece.  The 'wyvern' is a two-legged winged dragon having
the hinder part of a serpent with a barbed tail.  It is also a heraldic symbol.

4.2.13. JUSTIFICATION OF THE GARGOYLE

See section 4.2.10. for GENERAL NOTE ON LEAPING PIECES

As the last of the game's leaping pieces, the Gargoyle is a composite of all the two-step direct leaps.  In the COMBINATION
moves are represented all the other leaping pieces.

With the COMBINATION move to an adjacent orthogonal CUBE, there appears the pattern of the Wyvern's CUBE leap along with 
the Knight's leap and the orthogonal step. With the COMBINATION move to an adjacent diagonal CUBE, there is the Hippogriff's 
leap or the diagonal step.  Some may jump to an assumption that the Gargoyle could make a direct diagonal COMBINATION move
by a modified 3x1x1 CUBE leap but this is not correct.  There is no possible diagonal move with the 3x1x1 CUBE leap, 
therefore no diagonal COMBINATION move using the 3x1x1 leap.

Within in its CUBE, the Gargoyle's moves are quite easy to visualize.  In a corner CELL it is able to move to all the other
corner CELLS of that CUBE.  In an edge CELL, it is only able to move to the four edge CELLS of that particular plane.  In
a face CELL, it is only able to move to the opposite face CELL.

Although the Gargoyle appears to only reach a limited number of CELLS initially, the following diagrams should relate
how after several turns with COMBINATION moves it can reach every CELL in a CUBE.


Initial(A)         Orthogonal(B) Diagonal(C)
[x][ ][x]          [ ][x][ ]     [x][ ][x]
[ ][ ][ ]  Level 3 [x][ ][x]     [ ][x][ ]
[x][ ][x]          [ ][x][ ]     [x][ ][x]

[ ][ ][ ]          [x][ ][x]     [ ][x][ ]
[ ][ ][ ]  Level 2 [ ][ ][ ]     [x][ ][x]
[ ][ ][ ]          [x][ ][x]     [ ][x][ ]

[x][ ][x]          [ ][x][ ]     [x][ ][x]
[ ][ ][ ]  Level 1 [x][ ][x]     [ ][x][ ]
[x][ ][x]          [ ][x][ ]     [x][ ][x]

or
    
Initial(B)         Orthogonal(D) 
[ ][x][ ]          [x][x][x] 
[x][ ][x]  Level 3 [x][x][x]
[ ][x][ ]          [x][x][x]

[x][ ][x]          [ ][x][ ]
[ ][ ][ ]  Level 2 [x][ ][x]
[x][ ][x]          [ ][x][ ]

[ ][x][ ]          [x][x][x]
[x][ ][x]  Level 1 [x][x][x]
[ ][x][ ]          [x][x][x]

or

Initial(C)         Orthogonal(E) Diagonal(C)
[x][ ][x]          [x][x][x]     [x][ ][x]
[ ][x][ ]  Level 3 [x][ ][x]     [ ][x][ ]
[x][ ][x]          [x][x][x]     [x][ ][x]

[ ][x][ ]          [x][ ][x]     [ ][x][ ]
[x][ ][x]  Level 2 [ ][x][ ]     [x][ ][x]
[ ][x][ ]          [x][ ][x]     [ ][x][ ]

[x][ ][x]          [x][x][x]     [x][ ][x]
[ ][x][ ]  Level 1 [x][ ][x]     [ ][x][ ]
[x][ ][x]          [x][x][x]     [x][ ][x]

or

Initial(E)         Orthogonal(F)
[x][x][x]          [x][x][x]
[x][ ][x]  Level 3 [x][x][x]
[x][x][x]          [x][x][x]

[x][ ][x]          [x][x][x]
[ ][x][ ]  Level 2 [x][ ][x]
[x][ ][x]          [x][x][x]

[x][x][x]          [x][x][x]
[x][ ][x]  Level 1 [x][x][x]
[x][x][x]          [x][x][x]

or

Initial(F)         Orthogonal(G) Diagonal(G)
[x][x][x]          [x][x][x]     [x][x][x]
[x][x][x]  Level 3 [x][x][x]     [x][x][x]
[x][x][x]          [x][x][x]     [x][x][x]

[x][x][x]          [x][x][x]     [x][x][x]
[x][ ][x]  Level 2 [x][x][x]     [x][x][x]
[x][x][x]          [x][x][x]     [x][x][x]

[x][x][x]          [x][x][x]     [x][x][x]
[x][x][x]  Level 1 [x][x][x]     [x][x][x]
[x][x][x]          [x][x][x]     [x][x][x]


Initial(G)         Orthogonal(G) Diagonal(G)
[x][x][x]          [x][x][x]     [x][x][x]
[x][x][x]  Level 3 [x][x][x]     [x][x][x]
[x][x][x]          [x][x][x]     [x][x][x]

[x][x][x]          [x][x][x]     [x][x][x]
[x][x][x]  Level 2 [x][x][x]     [x][x][x]
[x][x][x]          [x][x][x]     [x][x][x]

[x][x][x]          [x][x][x]     [x][x][x]
[x][x][x]  Level 1 [x][x][x]     [x][x][x]
[x][x][x]          [x][x][x]     [x][x][x]



-------------
| B E | A C |
|  G  |  D  |
|     | F G |
------------
| A C |
|  D  |
| F G |
-------


This is a new piece to 3D Chess.  Its Gothic name was to reflect both its nature and potential presence. In the 3D Cubic
playing FIELD, it would be necessary for the use of 8 Gargoyles in order to cover every CELL.  The Gargoyle would
stand upon its particular CELL ready to pounce.  But, with care, a player could easily avoid it.  Mainly by staying
off of its potential CELLS.  In the 3D Cubic playing FIELD, it would be considered a weak piece.  But on the
Trans-Dimensional FIELD, its potential has increase exponentially.  Its name was also to compliment the Rook, another
piece often given an architectural appearance, which has become classic.

4.3. JUSTIFICATION OF THE INITIAL SET-UP

The first consideration of the initial set-up is the number of pieces allotted each player. Once an agreeable amount
of force has been decided upon, the initial placement on the playing FIELD would then be determined.

4.3.1. JUSTIFICATION OF THE NUMBER OF PIECES

In 2D Chess, each player utilizes 16 pieces.  If, for example, one was to extrapolate this value into the 8x8x8 playing 
FIELD with 512 CELLS that number would jump to 128.  This could be used to justify 135 pieces for the playing FIELD of
Trans-Dimensional Chess.  These are neither an easily comprehended nor enjoyable amounts.

Looking at 2D Chess, we can arrive at certain values which will help in arriving at a manageable force.

First, each player should have one King.  This is necessary for the object of the game.  Any additional units of this
piece would defeat the basic intent of the game.

Next, each player should have one Queen.  As the most powerful sliding piece in the FIELD, its capture must be cause for
regret and its recovery by promotion cause for aggressive behaviour between the players.

In 2D Chess, the remaining power pieces are represented in pairs.  This has an effect on the behaviour of the game, as a
player who has lost one of a pair will sometimes favor or risk the other.  So all the other power pieces in the game would
be represented by pairs, with one exception the Unicorn.

Like the Bishop, the Unicorn is restricted to particular CELLS within the playing FIELD.  As there must be two Bishops
to fully cover the FIELD, there needs to be a minimum of four Unicorns to fully cover the same playing FIELD.

So far, we have:

1 King
1 Queen
2 Favourites
2 Dragons
2 Archbishops
2 Rooks
2 Bishops
4 Unicorns
2 Knights
2 Hippogriffs
2 Wyverns
2 Gargoyles

For a total of 24 power pieces.

Although a greater number than the 8 of the 2D game, it is a far cry from the potential of more than 77.

The last consideration would be the number of Pawns.  The first value to leap to mind would be '24', the same as
the number of power pieces.  This number will be both logical and practical.  

The Pawn in its 2D set-up position acts as a 'wall' requiring the player to develop in order to introduce non-leaping 
pieces into the game.  This simple and logical function will be maintained.  



4.3.2. JUSTIFICATION OF THE PLACEMENT OF PIECES


Symmetry and distance are to be used as the primary values.  There must be a match of forces between the two players, this 
will eliminate any unfair advantages of non-symmetrical placement.

There are only edge and corner CUBES in the FIELD available for set-up.  In an edge CUBE, the player would need to maintain
the defense of four separate 'corridors'.  In a corner CUBE, the player need defend only three 'corridors'.  So set-up
will begin in triagonally opposing corner CUBE, in order to give each player the best defendable position with the most
'distance' for the opponent.  These were designated CUBE 1a1 for White and CUBE 3c3 for Black.  

The Kings being the prize of the game should be placed as far from the other on the FIELD.  So, the 1a1 CELL of CUBE 1a1
and the 3c3 CELL of CUBE 3c3 was assigned to the respective Kings.

The Queen should stand next to its King, offering its obvious protection.  Looking at CUBE 1a1, we have the 1a2, 1b1
and 2a1 as the closest orthogonal CELLS.  CELL 2a1 was selected as it offered the easiest to mirror with CELL 2c3 of
CUBE 3c3.

Next began the placement of the pairs of power pieces begin with the sliders.  

The piece which needed specific conditions for its placement was the Bishop.  Being colorbound, it was necessary that each 
piece occupy the appropriate CELLS.  In maintaining symmetry, the simplest method would be to place one above the other 
with the CUBE.  It was decided that these two pieces would occupy the two CELLS diagonal from both the King and Queen, 
CELL 1b2 and 2b2 of CUBE 1a1 and CELL 2b2 and 3b2 of CUBE 3c3.

The Favourites were then placed on either side of the King.  CELLS 1a2 and 1b1 of CUBE 1a1, CELLS 3b3 and 3c2 of CUBE 3c3.

The Rooks were then placed on either side of the Queen.  CELLS 2a2 and 2b1 of CUBE 1a1, CELLS 2b3 and 2c2 of CUBE 3c3.

With the Dragons, it was decided that they be placed in the same columns as the other orthogonal sliders.  CELLS 3a2 and
3b1 of CUBE 1a1, CELLS 1b3 and 1c2 of CUBE 3c3.

This left the Archbishop to fill CELLS 3a1 and 3b2 of CUBE 1a1, CELLS 1b3 and 1c2 of CUBE 3c3.

We now have a 2x2x3 column of pieces, a total of 12 pieces.

The remaining 36 pieces will be placed in such a manner as to block the FIELD moves of the sliders, thus encouraging
opening development.

With the leapers, we have a piece with which it is considered in normal play that they have quick access to the open FIELD.
These will be placed in the adjacent CUBES in the CELLS corresponding to the column occupied by their King and Queen.

It is necessary, because of their large leaps, for the Hippogriff, the Wyvern and the Gargoyle to occupy corner CELLS,
that they may have a good number of opening opportunities.  They were given all six of the corner CELLS of the three 
columns in the adjacent CUBE.  

The Knights occupy the 2a1 CELLS of CUBE 1a2 and CUBE 1b1, the 2c3 CELLS of CUBE 3b3 and CUBE 3c2.

The Unicorns needing to placed in such a manner that they are able to move to any CELL within a particular CUBE and were
placed on the CELLS 2a1, 2a2, 2b1 and 2b2 of CUBE 2a1, the CELLS 2b2, 2b3, 2c2 and 2c3 of CUBE 2c3.

The remaining CELLS within the 2x2x3 columns in these three adjacent CUBES were filled with the 24 Pawns.

We now have a set-up pattern that both highly defended and encourages development.

This is the set-up pattern for each players' forces.

White
CUBE 1a1          CUBE 1a2 & 1b1     CUBE 2a1   
[ ][ ][ ]         [ ][ ][ ]          [ ][ ][ ]
[D][A][ ] Level 3 [P][P][ ]          [P][P][ ]
[A][D][ ]         [W][P][ ]          [G][P][ ]

[ ][ ][ ]         [ ][ ][ ]          [ ][ ][ ]
[R][B][ ] Level 2 [P][P][ ]          [U][U][ ]
[Q][R][ ]         [N][P][ ]          [U][U][ ]

[ ][ ][ ]         [ ][ ][ ]          [ ][ ][ ]
[F][B][ ] Level 1 [P][P][ ]          [P][P][ ]
[K][F][ ]         [H][P][ ]          [G][P][ ]

Black
CUBE 3c3          CUBE 3b3 & 3c2     CUBE 2c3   
[ ][F][K]         [ ][P][H]          [ ][P][G]
[ ][B][F] Level 3 [ ][P][P]          [ ][P][P]
[ ][ ][ ]         [ ][ ][ ]          [ ][ ][ ]

[ ][R][Q]         [ ][P][N]          [ ][U][U]
[ ][B][R] Level 2 [ ][P][P]          [ ][U][U]
[ ][ ][ ]         [ ][ ][ ]          [ ][ ][ ]

[ ][D][A]         [ ][P][W]          [ ][P][G]
[ ][A][D] Level 1 [ ][P][P]          [ ][P][P]
[ ][ ][ ]         [ ][ ][ ]          [ ][ ][ ]


A=Archbishop  B=Bishop      D=Dragon   F=Favourite  
G=Gargoyle    H=Hippogriff  K=King     P=Pawn  
Q=Queen       R=Rook        U=Unicorn  W=Wyvern



5.  SUMMARY

So, you've read through all the instructions to Trans-Dimensional Chess and hopefully there were no typographical
errors and erroneous data to add confusion.

I hope that the reader has found this information complete and comprehensible.  If not, feel free to send me any
constructive criticism.  For my e-mail address click on the link below.

A developer can use standard FIDE pieces for 3D Chess.  I outlined a way to easily differentiate them in the 
following message posted at the 3D Chess Group at Yahoo!
http://groups.yahoo.com/group/3-d-chess/message/1526