Electronic and geometric isomers of boron 13 clusters have been calculated in the local density approximation. Simulated annealing was used to identify the lowest energy atomic configuration. The filled icosahedral structure is unstable and evolves with continuously decreasing energy to a locally stable structure based on a capped hexagon. While locally stable, heating and slow cooling leads to a considerably more stable structure (0.68 eV) with high symmetry (C3v) and relatively high coordination which is also based on capped hexagons. The remarkable stability of this isomer may explain the measured high survival of B-13+ clusters on collision and its relatively low reactivity.