This paper is a study on Development of polyhedral surfaces Quasicrystal System. Quasicrystal is the quasi-crystalline material, which is the intermediate material of the crystalline material and non-crystalline material. Quasicrystal is a structures that is ordered but not periodic, the basic form is a rhombus. These studies in the field of chemistry will proceed actively studied, in the field of construction a situation that still insufficient research. Therefore, in this paper, we presents the analysis of Quasicrystal system, and the research on the applicability of as dome structures. This paper described some examples of polyhedron form, and method of applying Quasicrystal system.