High-level ab initio molecular-orbital methods have been employed to determine the relative stability among four neutral and anionic B 20 isomers, particularly the double-ring tubular isomer versus three low-lying planar isomers. Calculations with the fourth-order Møller-Plessset perturbation theory ͓MP4͑SDQ͔͒ and Dunning's correlation consistent polarized valence triple zeta basis set as well as with the coupled-cluster method including single, double, and noniteratively perturbative triple excitations and the 6-311G͑d͒ basis set show that the double-ring tubular isomer is appreciably lower in energy than the three planar isomers and is thus likely the global minimum of neutral B 20 cluster. In contrast, calculations with the MP4͑SDQ͒ level of theory and 6-311 +G͑d͒ basis set show that the double-ring anion isomer is appreciably higher in energy than two of the three planar isomers. In addition, the temperature effects on the relative stability of both 10 B 20 − and 11 B 20 − anion isomers are examined using the density-functional theory. It is found that the three planar anion isomers become increasingly more stable than the double-ring isomer with increasing the temperature. These results are consistent with the previous conclusion based on a joint experimental/simulated anion photoelectron spectroscopy study ͓B. Kiran et al., Proc. Natl. Acad. Sci. U.S.A. 102, 961 ͑2005͔͒, that is, the double-ring anion isomer is notably absent from the experimental spectra. The high stability of the double-ring neutral isomer of B 20 can be attributed in part to the strong aromaticity as charaterized by its large negative nucleus-independent chemical shift. The high-level ab initio calculations suggest that the planar-to-tubular structural transition starts at B 20 for neutral clusters but should occur beyond the size of B 20 − for the anion clusters.