Icosahedral quasicrystals ( i-QCs) are long-range ordered solids that show non-crystallographic symmetries such as five-fold rotations. Their detailed atomic structures are still far from completely understood, because most stable i-QCs formas ternary alloys suffering from chemical disorder. Here, we present the first detailed structure solution of i-YbCd5.7, one of the very few stable binary i-QCs, by means of X-ray structure determination. Three building units with unique atomic decorations arrange quasiperiodically and fill the space. These also serve as building units in the periodic approximant crystals. The structure is not only chemically feasible, but also provides a seamless structural understanding of the i-YbCd5.7 phase and its series of related i-QCs and approximant crystals, revealing hierarchic features that are of considerable physical interest.