Making a lamp
Relationship to 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.