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polyphyodont

n. Any animal whose tooth are continuously replaced.

Wikipedia
Polyphyodont

A polyphyodont is any animal whose teeth are continuously replaced. In contrast, diphyodonts are characterized by having only two successive sets of teeth.

Polyphyodonts include most toothed fishes, many reptiles such as crocodiles, geckos, and most other vertebrates, mammals being the main exception. New, permanent teeth grow in the jaws, usually under or just behind the old tooth, from stem cells in the dental lamina. Young animals typically have a full set of teeth when they hatch; there is no tooth change in the egg. Within days, tooth replacement begins, usually in the back of the jaw continuing forward like a wave. On average a tooth is replaced every few months.

Crocodilia are the only non-mammalian vertebrates with tooth sockets. Alligators grow a successional tooth (a small replacement tooth) under each mature functional tooth for replacement once a year, each tooth being replaced up to 50 times in the alligator's life. Crocodilia are researched for tooth regeneration in humans.