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Wikipedia tells us, that "...the first dome that could be called "geodesic" in every respect was designed after World War I by Walther Bauersfeld, chief engineer of the Carl Zeiss optical company, for a planetarium to house his planetarium projector."
Bauersfeld first built a small, temporary dome on the roof of one of the Zeiss factory buildings in 1924. After the success of that display, other planetariums were built in the German towns Wuppertal, Leipzig and Düsseldorf. On July 18, 1926 the large Zeiss Planetarium, also called the Wonder of Jena opened.
The dome was later covered with rectangular concrete tiles, disguising its geodesic origin, but the internal structure - as shown in the historic picture of its construction - is indeed a geodesic dome derived from the icosahedron. Since the three earlier planetariums were all destroyed in World War II, the dome of the Zeiss Planetarium in Jena is today the oldest geodesic dome still standing.
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