A disk top type closure is one where pressing on one side of the top of the cap will raise the other side slightly. You have seen these in many places. They are far more useful and beautiful than a flip-top cap.
Photo Note: These closures are shown on 8 oz Frosted Bullet HDPE Bottles Size 24 (101-6970). The closures are from left to right: white, frosted, and black.
