The icosahedron – the golden mean shows up again

Here's the lamp in a rough, partially finished state. You can see the three golden rectangles outlined in maple, mahogany, and walnut. (Scale: a side of a triangle = 10".)

A visual hint of its relationship to the dodecahedron. The icosahedron has 20 faces, each of which is a regular or equilateral triangle (equal sides and equal interior angles). Each set of five triangles that touch at a tip (vertex) form the outline of a pentagon, so you can also see 12 overlapping pentagons in the icosahedron. This is a visual hint of its relationship to its dual, the dodecahedron.

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