Polyhedra and polytopes29 of 113
Geodesic dome and Goldberg polyhedra
Bauersfeld 1926, Fuller 1954; C₆₀ 1985
Divide each face of an icosahedron into small triangles and push every point out to the sphere: a geodesic dome. Its dual is a ball of hexagons, and however fine it gets it always needs exactly twelve pentagons, the same count as a football or the carbon molecule C₆₀.
V − E + F = 2 ⟹ 12 pentagons
On mathcurve.com as Géode et fullerène
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1Work the library cites and does not hold: in copyright, never released as a file, or not a file at all. The cited shelf
- 1967
United States Pavilion, Expo 67 (the Biosphère)
A geodesic sphere of steel tubes 76 metres across, the best known of Fuller’s domes.
Not yet checkedSuggested by an AI model, 2026-10-08
An AI reviewer had doubts, 2026-10-09: The 76 metre width and the Fuller geodesic design are supported, but the page says Disney "expanded on Biosphere's three-quarter-sphere to create a full sphere", so the Biosphere is not a whole geodesic sphere. The texts also describe a steel truss frame with acrylic cells, not steel tubes, and nothing in them calls it the best known of Fuller's domes.