Additional data to report: https://doi.org/10.1021/jacs.5c22358 Key feature of the – so far only theoretically described – family of sp2 carbon allotropes called schwarzites is the negatively curved topology, which is introduced by the incorporation of heptagonal (or octagonal) rings in a graphene type lattice. We have constructed a cut-out of this material with a unique pattern of four heptagonal rings arranged in a row by Pd-catalyzed [4+3] and [5+2] annulation and characterized it thoroughly. The pronounced flexibility of the π-system, which was investigated by temperature-dependent NMR as well as theoretical calculations, promises to be advantageous for a template-mediated synthesis approach toward the parent schwarzite P216, as it allows to maximize shape complementarity with rigid templates like fullerenes, and orientational flexibility for subsequent C-C bond formations. We were able to prove and investigate the presence of supramolecular complexes with C60 and C70 in solution by concentration-dependent NMR titration experiments as well as in the solid state by single crystal X-ray and electron diffraction.