It looks like a Mannheim Coolus (which doesn't date to this era) worn backwards with Attic or Montefortino cheekpieces, IMO, but I honestly have no clue.
A word of warning: the visor of the helmet is a restoration, and therefore need not be accurate (Heckler, 1912: 315). The cheek-straps do seem to be Montefortino style, although some caution is also necessary, as what we think the fastenings of Montefortino cheek straps look like comes from archaeologists studying this particular bust! Nonetheless, Sekunda 2006 suggests that it is Montefortino (ish), and may reflect Pyrrhus' adoption of some Italian equipment. Wish the helmet was better preserved!
Also important to note that the only reason that this portrait is identified with Pyrrhus is that it is a) martial in nature (i.e. helmeted), and b) wearing oak leaves, and therefore harkens to the oak tree at the sanctuary at Dodona. While the Pyrrhus identification is 100 years old, and largely unchallenged, it is important to note that it rests on relatively tenuous ground.
I would rather say the helmet belongs to the large and somewhat heterogenous group of the "Attischer Typ mit Stirnschirm" (Attic helmet with visor).
In the English terminology they are sometimes called "Thracian" .
Usually the known examples have also a "Stirngiebel" with volutes on the sides. On the Pyrrhus-helmet this might have been omitted because of the crest.
Some examples to compare:
I used this chin strap arrangement for my Montefortino as I always found trying to tie a lace around the studs on the end of the cheek guards unsatisfactory. I can vouch for the effectiveness of this arrangement.
Quote:"Stirngiebel" (what's the English word for it?)
I can't think of a single word in English but, then, the German is a combination of two words - stirn = brow, front; giebel = gable, pediment. So, combining these elements and bearing in mind the structure of the helmets, I would suggest, 'pediment-shaped brow ridge'.
Michael King Macdona
And do as adversaries do in law, -
Strive mightily, but eat and drink as friends.
(The Taming of the Shrew: Act 1, Scene 2)