Schwarzite—The holy grail of carbon allotropes

The discovery of different sp²-carbon allotropes such as fullerenes (0D), carbon nanotubes (1D), and graphene (2D) has tremendously impacted molecular materials research. Starting from simple but highly interesting non-planar hydrocarbon building blocks, the logical extension into three dimensions—curved structures called schwarzites—was theoretically predicted by Mackay and Terrones in 1991 but remains elusive, owing to the tremendous synthetic challenge these structures present. In this perspective, we discuss approaches toward schwarzite carbon materials and present our own vision of how atomically precise schwarzites might be synthesized. Key steps of this approach are the template-mediated preorganization of small molecular cutouts of schwarzites and the subsequent formation of the desired, three-dimensionally conjugated carbon allotrope under suitable conditions for C–C bond formation and reorganization.