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As the number of cores per die increases, be they processors, memory blocks, or custom accelerators, the on-chip interconnect the cores use to communicate gains importance. We begin this study with an area-performance analysis of the interconnect design space. We find that there is no single network design that yields optimal performance across a range of traffic patterns. This indicates that there is an opportunity to gain performance by customizing the interconnect to a particular application or workload. We propose polymorphic on-chip networks to enable per-application network customization. This network can be configured prior to application runtime, to have the topology and buffering of arbitrary network designs. This paper proposes one such polymorphic network architecture. We demonstrate its modes of configurability, and evaluate the polymorphic network architecture design space, producing polymorphic fabrics that minimize the network area overhead. Finally, we expand the network on chip design space to include a polymorphic network design, showing that a single polymorphic network is capable of implementing all of the Pareto optimal fixed-network designs.