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In this work, we propose a new methodology for obtaining 3D carbon allotropestructures from 2D ones through topological mapping. The idea is to select a 3Dtarget structure and 'slice' it along different structural directions, creatinga series of 2D structures. As a proof of concept, we chose the Tubulanestructure 12-hexa(3,3) as a target. Tubulanes are 3D carbon allotropes based oncross-linked carbon nanotubes. One of obtained 2D 'sliced' structures wasmapped into the biphenylene carbon (BPC). We showed that compressing BPC alongdifferent directions can generate not only the target Tubulane 12-hexa(3,3) butat least two other structures, bcc-C6 and an unreported member of the Tubulanefamily, which we called Tubulane X. The methodology proposed here is completelygeneral, it can be used coupled with any quantum method. Considering that new2D carbon allotropes, such as the biphenylene carbon network, which is closelyrelated to BPC, have been recently synthesized, the approach proposed hereopens new perspectives to obtain new 3D carbon allotropes from 2D structures.

Transforming 2D carbon allotropes into 3D ones through topological mapping: The case of biphenylene carbon (graphenylene)