This paper presents the design and synthesis of a fully metallic, low-profile flat lens that utilizes twist symmetry structures to control wave front, while minimizing the thickness. Higher-symmetry metasurfaces enable enhanced phase manipulation, broadband performance, fabrication robustness, and efficient energy transmission. However, multi-layered nature of their design often results in increased bulk, which this work addresses by optimizing the configuration. In this design to reduce the thickness, we avoid polarization transformation, considering it at the unit-cell stage design, to eliminate the additional layers required later in the lens design. Besides, the utilization of a constant order of high symmetry and sweeping the dimensional parameter, enables to span the required phase range smoothly while reducing the thickness, result in achieving a low-profile fully metallic flat lens suitable for advanced electromagnetic applications in the Ku-band.