  In this work, we propose a new methodology for obtaining 3D carbon allotrope
structures from 2D ones through topological mapping. The idea is to select a 3D
target structure and 'slice' it along different structural directions, creating
a series of 2D structures. As a proof of concept, we chose the Tubulane
structure 12-hexa(3,3) as a target. Tubulanes are 3D carbon allotropes based on
cross-linked carbon nanotubes. One of obtained 2D 'sliced' structures was
mapped into the biphenylene carbon (BPC). We showed that compressing BPC along
different directions can generate not only the target Tubulane 12-hexa(3,3) but
at least two other structures, bcc-C6 and an unreported member of the Tubulane
family, which we called Tubulane X. The methodology proposed here is completely
general, it can be used coupled with any quantum method. Considering that new
2D carbon allotropes, such as the biphenylene carbon network, which is closely
related to BPC, have been recently synthesized, the approach proposed here
opens new perspectives to obtain new 3D carbon allotropes from 2D structures.

Materials Science