Golden Lines in an Equilateral Triangle

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Define a golden line in an equilateral triangle as the line that connects a vertex of the triangle to the point on the opposite edge that divides the edge in the golden ratio 1:. Each of the three golden lines is divided by its intersections into three parts of sizes 1, , and . The points of intersection coincide with the vertices of the regular icosahedron, octahedron, and tetrahedron. Dragging the "erect structure" slider folds the four triangles into a tetrahedron.

Contributed by: Sándor Kabai (June 2016)
Open content licensed under CC BY-NC-SA


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This Demonstration shows a possible conceptual design for a geometrical sculpture. Only one of the two possible golden lines starting from a vertex is shown. Showing both lines gives the vertices of a compound of two icosahedra.



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