The torus topology produced the fastest computers in the world for the better part of a decade.

IBM Blue Gene /L (2004, LLNL): 3D torus, 65,536 compute cards, each with 2 PowerPC 440 cores, 16 GB/s torus bandwidth. First machine to reach 100 TFLOPS sustained. The network was the differentiator -- the processors were modest.

IBM Blue Gene /P (2007): 3D torus, up to 884,736 cores. Same principle, more nodes.

IBM Blue Gene /Q (2011, Argonne/LLNL): 5D torus, each node connecting to 10 neighbours (2 per dimension). 1,638,400 cores in the largest deployments.

Cray XT3 -> XT5 -> XE6 (2004-2012): 3D torus built from SeaStar / Gemini interconnect chips. Cray's later XC series (Aries interconnect, 2012) evolved toward dragonfly.

Fujitsu K computer (2011): 6D Tofu torus, 88,128 nodes, 10 petaflops peak. Each node had 10 torus links (2 per dimension). Tofu's full name is 6-dimensional mesh/torus.

The pattern is consistent: dimension count climbed as vendors tried to reduce average hop count while maintaining locality for scientific codes. More dimensions mean more links per node -- higher cost, higher bandwidth, shorter paths.