Summary: We propose a symmetrical scheme, by drawing results from group theory, and use it to build a new class of data center network models. The results are superior to current network models with respect to a number of performance criteria. Greater symmetry in networks is important, as it leads to simpler structure and more efficient communication algorithms. It also tends to produce better scalability and greater fault tolerance. Our models are general and are expected to find many applications, but they are particularly suitable for large-scale data-center networks.