The disclosed invertible structures rely on combinations of translational movements to effect inversion. An exemplary invertible structure includes a track operable to be slidably coupled to a connector element of a longitudinal structure. In an embodiment, the connector element may include at least two connectors at least partially disposed in a slot defined in the track, which may have a plurality of translational axes for translational movements of the connectors of the longitudinal structure that would effect the inversion of the longitudinal structure.