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A robotic platform for mobile manipulation needs to satisfy two contradicting requirements for many real-world applications: A compact base is required to navigate through cluttered indoor environments, while the support needs to be large enough to prevent tumbling or tip over, especially during fast manipulation operations with heavy payloads or forceful interaction with the environment. This paper proposes a novel robot design that fulfills both requirements through a versatile footprint. It can reconfigure its footprint to a narrow configuration when navigating through tight spaces and to a wide stance when manipulating heavy objects. Furthermore, its triangular configuration allows for high-precision tasks on uneven ground by preventing support switches. A model predictive control strategy is presented that unifies planning and control for simultaneous navigation, reconfiguration, and manipulation. It converts task-space goals into whole-body motion plans for the new robot. The proposed design has been tested extensively with a hardware prototype. The footprint reconfiguration allows to almost completely remove manipulation-induced vibrations. The control strategy proves effective in both lab experiment and during a real-world construction task.