In the present work we have studied the electronic and magnetic properties of the new one- and two-dimensional pi-conjugated materials containing biphenylene (Bp)-monomer on the basis of DFT calculations including the periodic boundary condition for the infinite structures. Thus, we have predicted a new planar and stable graphene allotrope composed of a combination of the four-, six- and eight-membered rings of the (4, 6, 6, 8) topology, which resembles the classical graphene. These novel materials are predicted to demonstrate the promising hole/electron mobility values which are typical for the ambipolar organic semiconductors. Furthermore, the growth of pi-conjugated Bp-based 2D sheets leads to the material with the band-gap being significantly smaller than that for the 1D polymer ribbons containing the same number of the Bp-units. The Bp-based nanotubes are also designed and are predicted to be promising candidates for miniaturizing electronics. (C) 2014 Elsevier B.V. All rights reserved.