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Conventional datacenters, based on wired networks, entail high wiring costs, suffer from performance bottlenecks, and have low resilience to network failures. In this paper, we investigate a radically new methodology for building wire-free datacenters based on emerging 60-GHz radio frequency (RF) technology. We propose a novel rack design and a resulting network topology inspired by Cayley graphs that provide a dense interconnect. Our exploration of the resulting design space shows that wireless datacenters built with this methodology can potentially attain higher aggregate bandwidth, lower latency, and substantially higher fault tolerance than a conventional wired datacenter while improving ease of construction and maintenance.