Cyber graphics as an emerging technology has been playing key roles as human interfaces of cyber worlds. With the ever increasing roles of cyber worlds in the real world, as seen in e-financial trading that deals GDP-equivalent in a day, understanding of cyber graphics is becoming essential. To this end, scientific research has been conducted to grasp the foundation as invariants. Cellular modeling has been found to be of key importance. The adjunction spaces and cell attaching functions of cyber graphics are investigated through varieties of examples to find out the invariants successfully.