On 2/22/07, steve uurtamo <[EMAIL PROTECTED]> wrote:
> I'm not sure I agree with this. I hypothesize that 2d, 3d, 4d, torus,
> or any other shape is completely irrelevant with regard to game play.
> The only thing that matters is the graph topology.
it is true that the only thing that matters is graph topology. it is
also true that graph topology cannot be separated from the actual
topology of the surface. dimensionality of the embedding space is
irrelevant -- topology of the embedded surface is quite important.
you should be able to extract the topology of the graph from any
embedded surface upon which it can be drawn and vice-versa.
If I take a plane, I can draw a 9x9 board on it or a 19x19 board on
it. I can also draw the previously mentioned circular / cylindrical
board on it. Could you explain how you propose to extract the topology
of these, given only the fact that I have drawn them on a plane?
I don't see it
cheers
stuart
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