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I am a computer geek, and thinking about connecting systems together for a supercomputer.

In the most simple case we have a flat grid of computers. At a certain point, the amount of time to transit across the plane might take longer than it is 'worth'.

*BTW - yes, it seems that connecting the 'edges' together doesn't help you (cannot speed up the amount of time it takes to physically get there, because physics) - but in the real world each 'hop' across takes time - so a 'direct' connection of the edges crosses the same amount of distance, but with only one 'hop' it will be faster. For the purposes of this question, I'm not looking for computer science but topology. But the threats/suggestions at the beginning told me to be detailed, so I'm trying here.

Now, you could connect the edges to one another across the, hmmm - let's call it the X axis, making a cylinder. And again with the Y axis, and I have a torus.

Well, modern systems are stacked in racks, so I have (say) 40 nodes stacked on top of one another. Well, how am I to represent the following to determine how long it takes to 'get anywhere'? A stack of tori doesn't seem quite right to me, as the connection (hmmmm - 'diagonally'???) between a node in row 1, rack 1 1st level, and a node in row 2, rack 2, 2nd level goes through the 'hole' in the torus - as opposed to going around it to get there (assuming I have a point to point connection between anything).

Also - if it is determined that the transit time between the 'top' and the 'bottom' is too 'far' and we connect the top of the cube to the bottom - what is that called? Is there a way to visualize that? I'm getting myself confused due to my lack of education in such things, and lack of practice in thinking along these lines.

Any help is appreciated.

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    It seems that you might be describing a solid torus, but it's hard to tell what is connecting to what. It would be simpler if you describe your nodes as a grid of size $40\times 40\times 40$ and use coordinates of boundary nodes to identify what is connected to what. – 2017-02-25
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    There are computer science books about this kind of thing. – 2017-02-25
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    OK - the start is a cube of 40X40X40 This would be 40 computers (nodes) in a rack, 40 racks per row, and 40 rows Each node is connected to the one above, below, either side, and front and back - with the exceptions being the 'edges'. What am I looking at if I connect the 'Sides'? What am I looking at if I connect the 'Top and bottom' as well? – 2017-02-25

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