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Douglas Harper's Etymology Dictionary
vomitorium

1754, "passage or opening in an ancient amphitheater, leading to or from the seats," from Latin (Macrobius, Sat., VI.iv), from vomitare (see vomit (n.)) + -orium (see -ory). Meaning "place where ancient Romans (allegedly) deliberately vomited during feasts" is attested by 1876.

Wiktionary
vomitorium

n. 1 A passage located behind a tier of seats in an amphitheatre used as an exit for the crowds 2 (''see #Usage notes'') An area in which vomiting takes place, in particular a chamber ''supposedly'' used by ancient Romans to vomit during a feast so they could continue eating.

Wikipedia
Vomitorium

A vomitorium is a passage situated below or behind a tier of seats in an amphitheatre or a stadium, through which big crowds can exit rapidly at the end of a performance. They can also be pathways for actors to enter and leave stage. The Latin word vomitorium, plural vomitoria, derives from the verb vomō, vomere, "to spew forth". In ancient Roman architecture, vomitoria were designed to provide rapid egress for large crowds at amphitheatres and stadiums, as they do in modern sports stadiums and large theatres.

Usage examples of "vomitorium".

Plucking his cloak from the astonished slave in charge of the cloakroom, he headed for the privacy of the vomitorium to take the call.

Listening to the voice on the other end, Astoroth was momentarily distracted by the sight of a portly tribune who staggered into the vomitorium and, oblivious to the demons presence, leant over a hole in the floor and emptied his stomach of all contents.

Franz had remained for nearly a quarter of an hour perfectly hidden by the shadow of the vast column at whose base he had found a resting-place, and from whence his eyes followed the motions of Albert and his guides, who, holding torches in their hands, had emerged from a vomitorium at the opposite extremity of the Colosseum, and then again disappeared down the steps conducting to the seats reserved for the Vestal virgins, resembling, as they glided along, some restless shades following the flickering glare of so many ignes-fatui.

Key West, because who in his right mind would bother exploiting an end-of-the-world rat hole and college-student vomitorium the size of a New York City park, with a speed limit of thirty, way more bicycles than cars, and only one road in or out?

How about I tell her how you need your own Roman vomitorium, you fucking bulimic.

When in Rome, to paraphrase St Ambrose, use the vomitorium as the Romans do.

He who was so acutely inconvenienced by the absence of a vomitorium in the wool-shed.

Coupons for fitness centers on my desk, links for vomitoriums in my mail.

Phillium, a world-renowned architect of vomitoriums, was given the fateful book by his niece, as a present on the occasion of the third anniversary of his successful buttocks-reduction surgery.

At once the vomitoria were thrown open, and all who could hastened to the portico outside where the restaurateurs had their quarters.