Answer: When the Rhinoceros´skin rubbed himself creating wrinkles and making the buttons came off.
Step-by-step explanation:
The climax is usually the penultimate element in the dramatic structure, near the end of a story, which brings back the conflict growing since the exposition (between the Rhinoceros and the Parsee) and right before the resolution (the Parsee going away and rhinoceroses having wrinkly skin and bad mood since then).