Growth and structural characterization of InSb nanostructures formed on GaAs is presented. Saturated InSb nanostructure have a truncated pyramidal shape with rectangular base. In addition, some InSb nanostructures have twin truncated pyramidal configurations. The twin truncated pyramids align in parallel with each other and along [110] direction. We attribute the formation of rectangular base to the growth of highly mismatched InSb/GaAs system while the formation of twin configuration due to the nucleation of InSb islands on top of two-dimensional InSb plateau. The latter is suggested by an observation on the initial state of InSb nanostructure formation.