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This paper promotes convertible data center network architectures, which can dynamically change the network topology to combine the benefits of multiple architectures. We propose the flat-tree prototype architecture as the first step to realize this concept. Flat-tree can be implemented as a Clos network and later be converted to approximate random graphs of different sizes, thus achieving both Clos-like implementation simplicity and random-graph-like transmission performance. We present the detailed design for the network architecture and the control system. Simulations using real data center traffic traces show that flat-tree is able to optimize various workloads with different topology options. We implement an example flat-tree network on a 20-switch 24-server testbed. The traffic reaches the maximal throughput in 2.5s after a topology change, proving the feasibility of converting topology at run time. The network core bandwidth is increased by 27.6% just by converting the topology from Clos to approximaterandom graph. This improvement can be translated into acceleration of applications as we observe reduced communication time in Spark and Hadoop jobs.