3709 Polypoites is a Jupiter Trojan asteroid that orbits in the L4 Lagrangian point of the Sun-Jupiter system in the Greek Camp of Trojan asteroids. It was named after the Greek hero Polypoites who fought during the Trojan War. It was discovered by Carolyn S. Shoemaker on October 14 1985 in Palomar California at the Palomar Observatory.
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