The extent of the influence that molecular curvature plays on the self‐assembly of supramolecular polymers remains an open question in the field. We began addressing this fundamental question with the introduction of “carpyridines”, which are saddle‐shaped monomers that can associate with one another through π‐π interactions and in which the rotational and translational movements are restricted. The topography displayed by the monomers led, previously, to the assembly of highly ordered 2D materials even in the absence of strong directional interactions such as hydrogen bonding. Here, we introduce a simple strategy to gain control over the dimensionality of the formed structures yielding classical unidimensional polymers. These have been characterized using well‐established protocols allowing us to determine and confirm the self‐assembly mechanism of both fibers and sheets. The calculated interaction energies are significantly higher than expected for flexible self‐assembling units lacking classical “strong” non‐covalent interactions. The versatility of this supramolecular unit to assemble into either supramolecular fibers or 2D sheets with strong association energies highlights remarkably well the potential and importance of molecular shape for the design of supramolecular materials and the applications thereof.