Golden Lines in an Equilateral Triangle

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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



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.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.