The main types of punches are: 1. Straight punch/Reverse punch (what was used to demonstrate the previous steps) 2. Jab (quick punch off the lead hand) 3. Cross (Back hand punch to the head) 4. Hook punch (Coming in from the side, usually to the jaw) 5. Uppercut (upward strike to the chin, sending the head backward) 6. Twist punch (taught in many martial arts schools)
Again, all of these use the first two knuckles to strike with.