Icosahedron has 3 intersecting golden angle rectangles inside. In fact, you can construct the icosahedron by 3 intersecting rectangles (try it by cutting out paper rectangles and fitting them together). The ratio of the long end to the short end of each golden rectangle is the golden ratio (φ) = 1.618... Hide rectangles or labels by setting their sliders to 0. The golden ratio φ is fundamental to distances between the 12 points (vertices) of the icosahedron.
The 12 corners of 3 the intersecting rectangles are exactly the 12 vertices of the icosahedron. Labels show original x y z coordinates of the vertices (before rotating). The distance of each x y z vertex (point, or corner) from the center (0 0 0) is an x y z of φ or 0 or 1 (or -φ and -1). So φ (golden ratio) is fundamental to the icosahedron. One way to see this quickly is to examine 3 golden ratio rectangles, one parallel to each of the x, y, and z planes.
