During a Nazirite vow, what was never to touch the Nazirite's head?

Answer: A razor

Numbers 6:5: for the whole period of his vow no razor was to touch his head; he had to let the hair of his head grow long.

“For the entire period of his vow of separation, no razor shall touch his head. He must be holy until the time of his separation to the LORD is complete; he must let the hair of his head grow long.”— Numbers 6:5 (BSB)