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