1. Pertaining to or resembling an adamant, a legendary stone thought to be impenetrable: The ring that Joe bought his wife had an adamantine luster, like a diamond.

When Grace was at her dentist's office, he used some dental enamel when repairing her teeth and it had a very adamantine quality of being extremely hard and unbreakable.
2. Characterized as unyielding, inflexible; resolute: Jim's teacher was quite insistent and required, with adamantine discipline, that her students perform to their best ability in class and do their homework regularly.