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Structural DNA nanotechnology has enabled the design and construction of complex nanoscale structures with precise geometry and programmable dynamic and mechanical properties. Recent efforts have led to major advances in the capacity to actuate shape changes of DNA origami devices and incorporate DNA origami into larger assemblies, which open the prospect of using DNA to design shape-morphing assemblies as components of micro-scale reconfigurable or sensing materials. Indeed, a few studies have constructed higher order assemblies with reconfigurable devices; however, these demonstrations have utilized structures with relatively simple motion, primarily hinges that open and close. To advance the shape changing capabilities of DNA origami assemblies, we developed a multi-component DNA origami 6-bar mechanism that can be reconfigured into various shapes and can be incorporated into larger assemblies while maintaining capabilities for a variety of shape transformations. We demonstrate the folding of the 6-bar mechanism into four different shapes and demonstrate multiple transitions between these shapes. We also studied the shape preferences of the 6-bar mechanism in competitive folding reactions to gain insight into the relative free energies of the shapes. Furthermore, we polymerized the 6-bar mechanism into tubes with various cross-sections, defined by the shape of the individual mechanism, and we demonstrate the ability to change the shape of the tube cross-section. This expansion of current single-device reconfiguration to higher order scales provides a foundation for nano to micron scale DNA nanotechnology applications such as biosensing or materials with tunable properties.