The Three Punches (三捶) is better understood as the one of the core principles of the Six Harmonies branch of the Mantis school of martial arts, instead of one single move set.
The idea behind is not simply throwing three punches together, but to use the movements to maintain body composure and control, create tension, and draw power in a very short distance. This is essentially the same as the “one inch punch” made famous by Bruce Lee, but that is, in fact, a faulty translation, as the move is about how power can be generated in that distance without pulling the arms back, not about punching at all. The better translation would be Inch Explosion (寸勁).
Calling it an “explosion” is still figuratively inaccurate, as “explosion” can only describe how the energy is generated in such short amount of time and distance, but not how it feels when it lands: being hammered to the ground by a tank.
The hammering power is drawn from the whole body and the tension the opponent has given you, then release in a a tight and controlled burst, while maintaining tension and contact with the opponent, in a twisting motion and in a downward angle.
Because tension and contact are maintained, you can keep pressure and maintain control, thereby giving you faster reaction time and allowing you to open up your opponent in a safe manner. Therefore, it isn’t necessary to completely perform all three punches; the three punches help to understand the motion and tension better as a practice exercise.
Suppose the opponent counterattacks, you can parry that attack by turning one arm towards yourself and making it vertical in the process, then proceed with your own counter punch with the other arm. This is then called the Cruciform Punch (十字捶, lit. “figure ten” in Chinese character).