That style of helmet is called Italo-Corinthian or Apulo-Corinthian. It imitates the look of a Corinthian helmet when it was pushed back on the head as one often sees on greek vase paintings. The Italo- or Apulo-Corinthian helmet was definitely never intended to pulled down to cover the face: the eye holes are much too small and I doubt it would sit properly on the head even if you tried to do so.
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