The structures and stabilities of B13N13 polyhedrons with alternant B and N atoms formed by squares, hexagons and octagons are studied with DFT method. It is found that the isomers with octagon(s) also satisfy the square adjacency penalty rule, and their relative energies markedly increase with the number of octagons generally. However, an isomer with one octagon in C-1 symmetry is thermodynamically more stable than other isomers and it has approximate sphericity and fewest B-44 bonds. These findings suggest that the isomers with octagon(s) should be considered during the search for the lowest energy isomer of (BN)(n) polyhedrons. (C) 2009 Elsevier B. V. All rights reserved.