“…It is well known that the geometric symmetries are one of the critical factors in determining the fundamental physical, chemical and material properties. The condensed-matter sys-tems, which are purely made up of carbon atoms, include the significant sp 3 [73,74,75,76], sp 2 [73,75,76], and sp chemical bondings [73,77], being, respectively, revealed as the 3D bulk, 2D surface, and 1D line structures, such as, diamond, graphene and carbon chain. Apparently, the diversified orbital hybridizations in C-C bonds originate from the four half occupied orbitals of [2s, 2p x , 2p y , 2p z ].…”