An icosahedron has got 12 edges. You can connect them creating 3 rectangles. [br]These rectangles are so called golden rectangles. The ratio [math]\frac{width}{length}[/math] equals [math]\varphi[/math].[br]At first sight this looks strange, for the side surfaces aren't regular pentagons but equilateral triangles.[br]The icosahedron is one of the 5 Platonic bodies, and this is the key to understand why [math]\varphi[/math] occurs in an icosahedron. You can read more about it in the next activity.[br]