Dunham was elected prosecuting attorney of Washington County, Indiana in 1845 and then served as a member of the Indiana State House of Representatives for one term from 1846 to 1847.
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Cyrus Livingston Dunham then successfully ran for Congress, being elected to the Thirty-first, Thirty-second, and Thirty-third Congresses (March 4, 1849 – March 3, 1855) as a Democrat.
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He served on the board of the Memorial Hermann Healthcare System in Houston, the board of visitors of M.D. Anderson Cancer Center, the board of Trustees of the Houston Symphony, the George Bush Presidential Library, and the Smithsonian Institution.
The building, the second-tallest in the city at the time, incorporated a subway stop into its basement levels.
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Cyrus Eidlitz was the nephew of the noted builder Marc Eidlitz of Marc Eidlitz & Son Builders N.Y.C. and the grandson of the architect Cyrus Warner (who was the father of architects Samuel A. Warner and Benjamin Warner).
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He was the son of Lazelle Warner and influential New York architect Leopold Eidlitz, one of the founders of the American Institute of Architects.
Their eldest son, Cyrus Lazelle Warner Eidlitz (1853–1921), named after his maternal grandfather, also became an architect.
His brother Leopold Eidlitz was a well-known architect, as was Leopold's son, Cyrus L. W. Eidlitz.
Dunham erected a monument at Jefferson Barracks National Cemetery in honor of those who served with the 3rd Infantry Division.
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When Dunham was presented with the Medal of Honor, General Alexander Patch said as he placed the award around Dunham's neck that his actions in single-handedly destroying the machine gun nests saved the lives of 120 U.S. soldiers who had been pinned down.