Two kinds of planimetric diagrams, which consist of the boat form F6 and F5, the storm petrel form F6 and F5, respectively, were proposed to express the geometric structure of fullerene cage in this study. There are two chief advantages using the diagrams: (ⅰ) the spatial symmetrical characteristic of fullerene cage is not destroyed; (ⅱ) the coordination forms of F5 and F6 in the structure can be clearly expressed. This work has laid the foundation for studying the structural geometry of fullerene cage and its quantum chemistry and property.