In 1912 Walther Bauersfeld, chief engineer at the Carl Zeiss (manufacturers of optical equipment) started work on a building to house a planetarium at the suggestion of the German astronomer Max Wolf. Construction was suspended during the first World War and completed in 1923. That was the first structure to be considered geodesic.
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The geodesic dome was invented in the late 1940's
A geodesic dome is a spherical or partial - spherical shell structure or lattice shell based on a network of great circles on the surface of a sphere.
The 'big ball' at Epcot in Orlando Florida, is a Geodesic sphere. The old dome-like playground equipment is based on the same structure as a geodesic dome. I've posted a couple of links about geodesic domes with some pictures.
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The geometric shape that starts with the letter "G" is a "geodesic dome." A geodesic dome is a spherical structure composed of a network of geometric shapes called geodesic polyhedra. These polyhedra are typically triangles or other polygons that are arranged to form a dome-like structure. Geodesic domes are known for their strength and efficiency in distributing stress across the structure.