I have zero background in linguistics, so forgive me if this is trivial.
The Wikipedia article for relative clauses claims that, with regard to the positioning of the relative clause, “English, for example, is generally head-first”.
However, intuitively, it makes sense that a “reduced object passive relative clause” would be able to precede the head noun. Yet, I cannot find any example online where such a case serves as an example of the usage of a reduced relative clause.
In the 2009 University of Georgia Classic City Classic tournament, this sentence appears in one question:
Formed by reattaching the ends of a closed band after cutting the band and giving it a half-twist, name this structure named after a German mathematician, a one-sided, nonorientable surface.
Of interest is this:
Formed by reattaching the ends of a closed band after cutting the band and giving it a half-twist
Hence my question: can reduced relative clauses precede a head noun, or if not, what sort of grammatical structure is this?
Academic sources would be appreciated.
As far as I can tell, “Formed by reattaching the ends of a closed band after cutting the band and giving it a half-twist” is not a (complete) relative clause: there is no finite/tensed verb, and also no relative pronoun (that said, relative pronouns are not found in all relative clauses, so the absence of a finite verb is a more important criterion).
It is a “participle clause” (I’m not sure about the exact terminology). While these are sometimes analyzed as “reduced relative clauses” in certain sentences, I don’t see any reason to adopt that analysis in this sentence.
As has been mentioned in the comments, its position in this sentence is unconventional from the perspective of typical English usage: it follows the specialized conventions for tournament questions of this type.
It also doesn’t directly “precede the noun”, which is what is normally being discussed when talking about head-final vs. head-initial word orders.