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The present contribution deals with one of the possible structure types of nongraphitic carbon adsorbents. The proposed structure consists of infinite strips of condensed aromatic rings arranged into a hexagonal honeycomb-like structure with the edge formed only by sp2 carbon atoms. Quantum chemical calculations were performed at the UHF/STO-3G level using the CRYSTAL95 program package for periodical approach. The extremely high adsorption ability of some low-density paramagnetic carbon forms can be elucidated by the presence of the sp2 honeycomb carbon structure and the specific properties of its electronic structure.