The hexagonal ZrNiAl-type (space group: P ! 6 2m) and the tetragonal Mo 2 FeB 2 -type (space group: P4/mbm) structures, which are frequently formed in the same Yb-based alloys and exhibit physical properties related to valence-fluctuation, can be regarded as approximants of a hypothetical dodecagonal quasicrystal. Using Pd-Sn-Yb system as an example, a model of quasicrystal structure has been constructed, of which 5-dimensional crystal (space group: P12/mmm, a DD =5.66 Å and c=3.72 Å) consists of four types of acceptance regions located at the following crystallographic sites; Yb [00000], Pd[1/3 0 1/3 0 1/2], Pd[1/3 1/3 1/3 1/3 0]and Sn[1/2 00 1/2 1/2]. In the 3-dimensional space, the quasicrystal is composed of three types of columns, of which c-projections correspond to a square, an equilateral triangle and a 3-fold hexagon. They are fragments of two known crystals, the hexagonal α-YbPdSn and the tetragonal Yb 2 Pd 2 Sn structures. The model of the hypothetical quasicrystal may be applicable as a platform to treat in a unified manner the heavy fermion properties in the two types of Yb-based crystals. ! 6 2m) and the other tetragonal Mo 2 FeB 2 -type (space group: P4/mbm) structures. Such Yb-based crystals have been studied intensively for the last decade from the viewpoint of valence-fluctuation, and competition between the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida interaction. The former, Kondo effect, favors a nonmagnetic ground state, and the latter magnetic ordered state. Competition of the two effects gives rise to intriguing phenomena such as heavy fermions, non-fermi liquid and quantum criticality. In the alloy system of Yb-Pd-Sn, both types of structures are formed [8,9]. The hexagonal α-YbPdSn belonging to ZrNiAl-type is formed as a low-temperature phase