But a 3D lattice is actually quite bad in the sense of having a very high graph diameter for the same degree (6) as the number of nodes goes to infinity, compared to other designs, though probably not so bad for low n. Still far better than a square lattice, of course. Wiring of processors in clusters and supercomputers is one of the main uses of graphs with low degree and high diameter (see [1]). I also know that twisted hypercubes were used for connection graph of nodes in supercomputers, because they have a number of nodes which is a power of 2, fairly simple and uniform routing rules (in general other graphs don't), large bisection bandwidth, low diameter, high (maximal?) fault tolerance, and more.
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But a 3D lattice is actually quite bad in the sense of having a very high graph diameter for the same degree (6) as the number of nodes goes to infinity, compared to other designs, though probably not so bad for low n. Still far better than a square lattice, of course. Wiring of processors in clusters and supercomputers is one of the main uses of graphs with low degree and high diameter (see [1]). I also know that twisted hypercubes were used for connection graph of nodes in supercomputers, because they have a number of nodes which is a power of 2, fairly simple and uniform routing rules (in general other graphs don't), large bisection bandwidth, low diameter, high (maximal?) fault tolerance, and more.
[1] https://en.wikipedia.org/wiki/Table_of_the_largest_known_gra...