Is there an equivalent to a 'quarter' for twelfths?

Solution 1:

The word dodecafid means 1/12 or twelfth i.e. divisible into twelve parts or regions.

Reference link 1: allhotelscalifornia.com

Reference link 2: Wordnik.com

Citation from the book: Three Toed Sloths and Seven League Boots: A Dictionary of Numerical Expressions

Solution 2:

Most of the "sector" terms you refer to are derived from Latin. The equivalent for a twelfth would be something like duodectant, from the Latin duodecimus (twelfth).

But I'd not expect many English speakers to understand what you meant. A few might work it out from knowledge of Latin (not common), and a few more might connect it with some other 12-related word like dodecahedron (which is from Greek rather than Latin, so not an exact root match).

So you'd mostly be making up a new word, and needing to explain its meaning to anyone you spoke it to. In some contexts, coining neologisms is fine, and as long as you explain yourself the first time you use the word, you could then go on to use it repeatedly, and perhaps achieve more clarity than if you kept needing to say "a twelfth of a circle." But if you're only going to mention it once, or if you're speaking or writing in a context where linguistic creativity is frowned upon, you might just annoy the people you're communicating with.