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Communication networks are dimensioned for peak loads, but load fluctuates and networks are often underutilised. Energy consumption of routers and communication links is largely load independent, i.e. lightly loaded network have similar power consumptions than highly loaded networks. In light of the global focus on energy efficiency and greenhouse gas emissions, ideally, networks exhibit load proportional energy profiles. At the same time it is imperative that communication networks are resilient to link failure. This paper introduces the concept of resilient dynamic topologies where networks have the ability to reduce the number of active nodes and links during lightly loaded periods while maintaining resilience to link failures. Mathematical programming models are presented that result in reduced optimal network configurations. Using a sample network, energy consumption of networks with dynamic topologies and resilient dynamic topologies are compared. It is concluded that reduced resilient topologies with smaller energy footprints are feasible.