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What's a 5 dimensional torus? I know a 3D is Circle x Circle, is a 5-d torus a Circle x Circle x Circle x Circle?

If so, that could be interpreted as simply a 4D square grid which wraps around the edges, right? (just as a 3D torus is a 2D grid which wraps)

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Think of it as loops in 5 dimensions (x,y,z,a,b). I believe each node connects to 10 different neighboring nodes (2 in each of 5 dimensions), although I could be mistaken on that. You can actually tune which direction you prefer the nodes to communicate over by passing certain flags when you submit a job.

Also here's an image... which I admit is not terribly useful, but its what the national lab people put out. https://computing.llnl.gov/tutorials/bgq/images/5Dtorus.400p...

Oh so it's actually a 5D grid that wraps around. Confusingly that would make the standard torus a 2D torus, they're referring to the surface dimension instead of the euclidean space it can be embedded into.

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