Starting from the Zn17Sc3 cubic approximant, new quasicrystal alloys were sought by replacement of Zn with transition elements T. In the cases when T = Mn, Fe, Co and Ni, new icosahedral quasicrystals are formed in as-cast alloys as major phases at alloy compositions of Zn75T10Sc15. All these quasicrystals belong to a primitive type and have six-dimensional lattice parameters a(6D) ranging from 7.044 to 7.107 Angstrom. They have valence electron concentrations e/a ranging from 2.01 to 2.14, and almost the same ratios between the edge length a(R) of the Penrose tile and the averaged atomic diameter (d) over bar :a(R)/d approximate to 1.76. Moreover other Zn- and Cd-based quasicrystals, including the same type of atomic Tsai-type cluster, have the same values of e/a approximate to 2.1 and a(R)/(d) over bar approximate to 1.75 The equality in e/a indicates that the Hume-Rothery mechanism plays an important role for the formation of these quasicrystals.