Teumessian fox

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In Greek mythology, the Teumessian fox (Greek: Alopekos Teumesios) was a gigantic fox that was destined never to be caught. The fox was one of the children of Echidna. It was said that it had been sent by the gods (perhaps Dionysus) to prey upon the children of Thebes as a punishment for some national crime.

Creon, the then Regent of Thebes, set Amphitryon the impossible task of destroying this beast. He discovered a perfect solution to the problem by fetching the magical dog Laelaps, who was destined to catch everything it chased. Zeus, faced with an inevitable contradiction in fate (an uncatchable fox being pursued by an unavoidable dog) turned the pair of beasts into stone.