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3D Chess

Musings on 3D Chess
Introduction
Chessboards
Piece Movement
Game Variations
Conclusion

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Jeffrey M. Thompson

Musings on 3D Chess

Table of Contents

  1. Introduction

  2. Chessboards

  3. Piece Movement

  4. Game Variations
    5. 4.1.  Artemis - upright, varying, 4x4x4
    4.2.  Cant - cant, constant, 7x4x4
    4.3.  Selene - slant, constant, 4x7x4
    4.4.  Helios - skew, varying, 7x7x4
    4.5.  Zeus - upright, varying, 8x8x8
    4.6.  Tridimensional - slant (custom), constant, 6x10x7
  5. Conclusion
last modified: 03.07.26

4.  Game Variations

Premise 11: Restrict the board to 64 usable squares.

This premise really restricts the possibilities. If we look at the factors of 64:

28 or 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

for three dimensions gives these possiblities:

2 x 2 x 16
2 x 16 x 2
16 x 2 x 2		 2 x 4 x 8
2 x 8 x 4
4 x 2 x 8
4 x 8 x 2
8 x 2 x 4
8 x 4 x 2 		4 x 4 x 4

The simplest, most regular arrangement would be 4x4x4, or four boards of sixteen squares each. The classic Tridimensional Chess variation uses three boards of sixteen squares each plus four attack boards of four squares each, or (4x4x3) + (2x2x4).

I vote Premise 11 as the one most likely to be violated.

4.1.  Artemis - upright, varying, 4x4x4

This board is 4x4x4 with boards not offset and varying cell markings. All 64 cells in the chessboard volume are usable. More details are here.

4.2.  Cant - cant, constant, 7x4x4

This board is 7x4x4 with X offset boards and constant cell markings. 64 cells of 112 in the chessboard volume are usable.

4.3.  Selene - slant, constant, 4x7x4

This board is 4x7x4 with Y offset boards and constant cell markings. 64 cells of 112 in the chessboard volume are usable. More details are here.

4.4.  Helios - skew, varying, 7x7x4

This board is 7x7x4 with XY offset boards and varying cell markings. 64 cells of 196 in the chessboard volume are usable. More details are here.

4.5.  Zeus - upright, varying, 8x8x8

This board is 8x8x8 with boards not offset and varying cell markings. All 512 cells in the chessboard volume are usable. (This variation violates Premise 11!) More details are here.

4.6.  Tridimensional Chess - slant (custom), constant, 6x10x7

This board is 6x10x7 with Y offset boards and constant cell markings. 64 cells of 420 in the chessboard volume are usable, with 16 of these moveable during the game. More details are here.
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Copyright © 2003 Jeffrey M. Thompson 1