DFT B3LYP/6-31G(d) calculations were performed to examine the feasibility of graphene-like C42H18 and starbenzene C6(BeH)6 (SBz) polymers as ligands of 3D-extensible sandwich compounds (3D-ESCs) with uninterrupted sandwich arrays. The results revealed that sandwich compounds with three or more C42H18 ligands were not feasible. The possible reason may be the localization of π electrons on certain C6 hexagons due to π-metal interactions, which makes the whole ligand lose its electronic structure basis (higher degree of π electron delocalization) to maintain the planar structure. For comparison, with the aid of benzene (Bz) molecules, the SBz polymers can be feasible ligands for designing 3D-ESCs because the C-Be interactions in individual SBz are largely ionic, which will deter the π electrons on one C6 ring from connecting to those on neighbouring C6 rings. This means that high degree of π electron delocalization is not necessary for maintaining the planarity of SBz polymers. Such a locally delocalized π electron structure is desirable for the ligands of 3D-ESCs. Remarkably, the formation of a sandwich compound with SBz is thermodynamically more favourable than that found for bis(Bz)chromium. The assembly of 3D-ESCs is largely exothermic, which will facilitate future experimental synthesis. The different variation trends on the HOMO-LUMO gaps in different directions (relative to the sandwich axes) suggest that they can be developed to form directional conductors or semiconductors, which may be useful in the production of electronic devices.