Through a couple of classes here, I've been introduced to the work of Christian Bök, who is an amazing experimental poet. My favorite project of his is Eunoia (literally "beautiful thinking"), a book which, along with some other miscellany, has five chapters, each of which uses only one vowel. I just ordered it online and I'm pretty excited to read it. Bök prepared for it rigorously, and tried to use as many words that obeyed the one-vowel rule as he could find.
I'm probably partial to it because univocalic writing is something I've attempted before in prose, which you can find on my small site for constrained writing from my younger days, OtherWORDly. I only did it for E and O, my acumen not as quite as honed as Bök's (note dramatic understatement.) Also on that site are some abecedarian stories, where each word starts or ends with the next letter of the alphabet; some "counting stories," in which each word has an ever-increasing number of letters; a story without E; and a sort of prose riddle.
Texts which leave out letters are more generally called lipograms. One of the most famous of these is Gadsby by Ernest Vincent Wright.
Anyway, I can't let this go without giving you some trivia. Bök chose the title Eunoia at least in part because it's the shortest word he could find in English that contains all five vowels. So, the answers to all the trivia below are words that also contain all five vowels.
Can you name:
1. A word with all five vowels that rhymes with eunoia?
2. A country with all five vowels?
3. A nine-letter word with all five vowels in order?
4. A scientific term consisting only of the five vowels?