We have analyzed the measured S-parameters as a function of positron incident energy for the icosahedral quasicrystal (QC) Al71.5Pd20.3Mn8.2 and Al70.7Pd21.34Re7.96 within the framework of the structural model of approximant crystal. Highly resistive icosahedral QC Al72Pd21Re7 was investigated by the slow positron beam technique. The result indicated that icosahedral QC Al72Pd21Re7 contains a dense distribution of structural vacancy-type sites like another icosahedral QCs. Considerably high structural vacancy densities (on the order. of 10(20) cm(-3)) Were determined. (C) 2002 Elsevier Science B.V. All rights reserved.