Talk:Game Board Topology

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Revision as of 18:41, 18 August 2008 by JonPrud (Talk) (Edge adjacency)

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I've thought about this a lot, but never classified the types of boards. How do these descriptions sound?

Linear: This is often used in race games. Think Monopoly or Pachisi.

Rectangular: This is the standard board that most people probably think of as a game board. A square board is a subset of this. These are used in games such as: Chess, Volcano, etc. Non-square rectangular boards are used in games such as Scrabble, Go and Shogi. In these games you can play on either the points or the squares. (Which is why my volcano board is not raised.

Hexagonal: This is a natural "next step" from rectangular boards. They can be simulated by slightly offsetting squares from row to row or by putting a bunch of poker chips next to each other. (See Hexano for an example.) The hexagonal board can take different forms. Hex/Hex boards are used in many chess variants, hexano, and seige stones.

   0 0 0 
  0 0 0 0 
 0 0 0 0 0
  0 0 0 0
   0 0 0 

Rhomboid/Hex boards are used in Hex.

0 0 0 0
 0 0 0 0
  0 0 0 0
   0 0 0 0

Offset square/Hex boards are used in some chess variants.

0 0 0 0 
 0 0 0 0
0 0 0 0 
 0 0 0 0

Octagonal boards have been used in several "lesser known" games. Generally these have octogons touching each other leaving small squares in the four "corners".

Abstract as in considering the board as a matrix of possible piece placements. I find the easiest to create would be a three by three by three cube board then by adding three of these cubes in a row there is the fourth dimension interpolated. To draw this on a two by two screen would require 9 tic-tac-toe boards in a nine by nine grid. With the interrelatedness of the board being where the square that the piece is in is next to the other squares

1 x x||x x x||4 x 2

x x 3||x x 3||x x 3

x x x||x x x||x x x

x x x||1 4 x||x x x

x x x||x 2 x||x x x

x x x||x x x||x x x

x x 4||x x x||1 x x

x x x||x x x||x x x

2 x x||x x x||x x x

1, 2, 3, 4 would be possible movements in line across the boards such that 1=>1=>1 ...2,3,4 This can be written up much more clearly and I could use some editing help here to make a 9 by 9 grid... this as is seen reduces to the basic nine by nine board but there are intricate/abstract relationships between the actual locations on the board... Does this make sense to anyone?Xoet 23:00, 22 August 2007 (EDT)

There are many, many "odd" boards out there. For example, GRYB wouldn't fall into any of these categories. -JEEP 01:32, 30 Apr 2005 (GMT)

Following on the theme of "odd" boards, consider Eeyore's Martian Chess board segments shaped for three, five, and six-player games. What's the topology classification for this? What about for the three, five, and six-player assembled boards? --FreeTrav 13:32, 23 August 2007 (EDT)

Category Assignment

In response to Rootbeers comment on my talk page.

It's possible to have articles and other categories in the category. Game_Board_Topology is an article more or less about equipment, which is why I added it. It wouldn't hurt my feelings if others disagree and choose to remove it from the category. It's the only one I did like that, just to see how it worked out. --Tuxhedoh 02:36, 27 May 2005 (GMT)

IMHO if this were an article about game boards (as opposed to game board topology, an abstract concept), it would fit in the Equipment category. But since this article is really about the abstract concept of topology as opposed to a physical piece of equipmnent, it really doesn't fit in the category. -- Jeremiah 14:31, 27 May 2005 (GMT)
I see your point and I agree. The topolgy page should not be included in equipment.--Tuxhedoh 16:36, 27 May 2005 (GMT)

Edge adjacency

Aside from how the individual cells of a board is layed out, topology should include discussion as to how the edges of the board behave.

Does one pair of edges wrap around to each other, but no other pairs? This could be imagined as being played on the surface of a hollow tube.

On a board with two distinct pairs of edges, do both pairs wrap around to eachother? This could be imaged as being played on the surface of a torus.

On boards that wrap around, do you enter the 'other side' on the same row/column? If not, this could be described as twisted tubes/tori or Mobius strip and Klein bottles, depending on if they connect in the same order or not.

I am sure the mathematicians of topology have many more interesting descriptions as to how odd surfaces can be projected upon a planar board.

--JonPrud 01:37, 19 August 2008 (UTC)