Twofold-, threefold-, and fivefold-symmetry elements are observed in the ne
ar-surface region of the quasicrystal Al70Pd20Mn10 using a real-space imagi
ng technique based on secondary-electron emission. The observed icosahedral
point-group symmetry implies the presence of atomic clusters within the an
alyzed region of the solid. The same surface produces perfect low-energy el
ectron diffraction patterns typical for well-defined crystallographic plane
s. We present a model which reconciles this dual structural nature of quasi
crystals. Our model is constructed from an icosahedral seed followed by con
centric symmetry-preserving "growth" to form the macroscopic solid.