Nanocarbons, such as fullerenes, carbon nanotubes, and graphenes, have long inspired the scientific community. In order to synthesize nanocarbon molecules in an atomically precise fashion, many synthetic reactions have been developed. The ultimate challenge for synthetic chemists in nanocarbon science is the creation of periodic three-dimensional (3D) carbon crystals. In 1991, Mackay and Terrones proposed periodic 3D carbon crystals with negative Gaussian curvatures that consist of six- and eight-membered rings (the so-called Mackay-Terrones crystals). The existence of the eight-membered rings causes a warped nanocarbon structure. The Mackay-Terrones crystals are considered a "dream material", and have been predicted to exhibit extraordinary mechanical, magnetic, and optoelectronic properties (harder than diamond, for example). To turn the dream of having this wonder material into reality, the development of methods enabling the creation of octagon-embedding polycyclic structures (or nanographenes) is of fundamental and practical importance. This review describes the most vibrant synthetic achievements that the scientific community has performed to obtain curved polycyclic nanocarbons with eight-membered rings, building blocks that could potentially give access as templates to larger nanographenes, and eventually to Mackay-Terrones crystals, by structural expansion strategies.
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