We use scanning tunneling microscopy (STM) to investigate the atomic structure of the icosahedral (i-) Al-Cu-Fe fivefold surface in ultra high vacuum (UHV). Studies show that large, atomically flat terraces feature many ten-petal “flowers” with internal structure. The observed flower patterns can be associated with features on Al rich dense atomic planes generated from two-dimensional cuts of bulk models based on x-ray and neutron diffraction experiments. The results confirm that the fivefold surface of i-Al-Cu-Fe corresponds to a bulk-terminated plane.