His works include the Science fountain and Great Rivers statues at the Missouri State Capitol, the "Iron Mike" statue at Parris Island, South Carolina, several military sculptures at West Point, the Temple of Music and the Dewey Monument in San Francisco, California, and sculptural works for the Liberty Memorial in Kansas City, Missouri.
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Another pair of bronze flagpole bases by Menconi, showing an American eagle and representations of the four seasons, to designs of Egerton Swartwout, stand before the Missouri State Capitol.