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Douglas Harper's Etymology Dictionary
tonsillolith

1894, from tonsillo-, comb. form of tonsil + -lith "stone."

Wiktionary
tonsillolith

n. (context dentistry English) A calculus that forms in the rear of the mouth, in the crevasses of the palatine tonsils.

Wikipedia
Tonsillolith

Tonsilloliths, also known as tonsil stones, are clusters of calcified material that form in the crevices of the tonsils ( tonsillar crypts). While they occur most commonly in the palatine tonsils, they may also occur in the lingual tonsils. Tonsilloliths have been recorded weighing from 0.3g to 42g . They are composed mostly of calcium, but may contain other minerals such as phosphorus and magnesium, as well as ammonia and carbonate.

Protruding tonsilloliths may feel like foreign objects lodged in the tonsil crypt. They may be a nuisance and difficult to remove, but are usually not harmful. They are one of the causes of halitosis (bad breath) and always give off a putrid smell.

While true tonsillar stones are rare, small areas of calcification or concretions are relatively common.