The purpose of this paper is to develop the Islamic geometric patterns from planar coordinates to three dimensions with aperiodic symmetry. We are proposing techniques that cover four families of girih: acute, median, obtuse, and two-point tessellation by using the historical method, polygons in contact (PIC), in our pattern production. What’s more, we employ Penrose P2 and P3 prototiles as our main template. This study effectively answers the question regarding the gap between planar design from medieval Islamic architecture and contemporary demands in modern art and design.