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This paper presents the exchanged hypercube, a new interconnection network obtained by systematically removing links from a binary hypercube. It maintains several desirable properties of the binary hypercube yet with reduced interconnection complexity. We also introduce the extended binomial tree, a spanning tree of the exchanged hypercube that preserves many desirable properties of the original binomial tree. A fault-tolerant routing strategy is also proposed for the exchanged hypercube.