> It's more like a preposition that exceptionally comes after the noun phrase instead of before it. (Is there another thing like that in English? I can't think of one, though there's one in German: entlang)

There are some similar constructions:

- Three days hence. (archaic)

- Three days later.

- Three days beforehand.

- Three days afterwards.

I failed to think of one that didn't have to do with time.

You could think of "three days later" as being supposed to have a complement supplied to later, as in "three days later [than that]", but interestingly enough this isn't possible for "beforehand" or "afterwards".

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postscript: I think this can be conflated with a general syntactic possibility in English. I can describe an establishment as being "one floor up" from some other contextually-determined establishment, or, as with later, I can make that relationship explicit by saying "one floor up from [wherever]". This is also similar to the bog-standard measurement construction that gets you phrases like "three feet tall".