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is a city in and the county seat of Clay County, in the southeastern corner of the U.S. state of South Dakota, and the tenth largest city in the state. Vermillion lies atop a bluff on the Missouri River.
French fur traders first visited in the late 1700s, and Vermillion was founded in 1859 and incorporated in 1873. The name refers to the Lakota name: ''wa sa wak pa'la'' (red stream). Home to the University of South Dakota, Vermillion has a mixed academic and rural character: The University is a major academic institution for the state, boasting the state's only law and medical school, the state's only AACSB accredited business school, and several well-regarded academic departments. Major farm products include corn, soybeans, and alfalfa. The population was 9,765 at the 2000 census.
According to the United States Census Bureau, the city has a total area of 3.8 square miles (9.9 km²), all of it land.