Is there a prefix or adjective that means "one and a half", as "tri-" or "triple" is for "three"?
The exact usage I have is to describe "18" in terms of a dozen. Where I live they've started making 18-egg cartons, and the local grocer was wondering what name to give them in his computerised cash register, hoping for a single word.
Even slang, informal or invented term would do if there isn't such a term already.
Sesqui-.
However, it certainly isn't informal, and is also pretty obscure. About the only use of it is sesquicentennial and sesquipedalian which is at a few removes (it literally means 18inches long but it's originally figurative meaning of using long words is the only English meaning).
It certainly wouldn't go with dozen; one would just say "one and a half dozen", "dozen and a half" or "eighteen".
Edit:
If you really want a word meaning 18 of something, you've got octodecuple, which has been used in mathematics at least as far back as 1816 and probably earlier. But really, don't; unless you're talking about properties of mathematical tuples where octodecuples are interesting in some particular way, it would just be horrible.
One does occasionally hear the term three-halves.
An on-line search for three-halves yields many results, including
The expression three-ha'-pence was in common usage in the UK until 1971 as a common way of expressing 1½d (one-and-a-half pence) in the pre-decimal currency system (1½d = 1/160th of a pound sterling £).
An English three-halfpence silver coin was minted around 1561-1582 during the reign of Elizabeth I. 8
British three-halfpence silver coins were produced for use in certain British colonies at various times during the reign of Queen Victoria (1819 - 1901)9, as illustrated 11:
P.S. In answer to the original question, I would not suggest using the expression three half-dozens unless you want to test your readers / listeners!
The prefix that means "times one and a half" is sesqui-, as in sesquicentennial for the 150th anniversary of something.
The OED includes the following terms that begin with sesqui-:
sesquialter, sesquialtera, sesquialteral, sesquialterate, sesquialterous, sesquibasic, sesquicentenary, sesquicentennial, sesquicompound, sesquiduple, sesquiduplicate, sesquinonal, sesquiocellus, sesquioctaval, sesquioxidation, sesquioxide, sesquioxidic, sesquioxidized, sesquipedal, sesquipedalian, sesquipedalianism, sesquipedality, sesquiplane, sesquiplicate, sesquiquadrate, sesquiquarta, sesquiquartal, sesquiquintile, sesquiseptimal, sesqui-square, sesquiterpene, sesquitertia, sesquitertial, sesquitertian, sesquitertious.
So it is hardly informal or slang; anything but, actually: it's rather a bit fancy.
Another, rather archaic ordinal description is "half again as." That has the connotation of "half more" over one.
Hendecasyllabic is derived from Greek for an 11 syllable word litterally meaning 11 sounds. The greek prefix for 18 would be octodeca- I wouldn't know how to form a noun from it. But here is a great resource on greek and latin numerical prefixes
sesqui-duodenary
This is my suggested neologism.
Both component words directly originate from their Latin counterparts:
Where I come from, 18 is called "chai" from the two Hebrew letters that make up the word. Giving in multiples of 18 is considered good fortune as it's symbolic of giving life. I doubt, though, that you could refer to a dozen and a half eggs as a chai of eggs in a grocery without some perplexed looks, unless of course there are customers familiar with the term.
