Mix hexagons and pentagons and you get a soccer ball
Look closely at a real soccer ball and you will see black pentagons joined to white hexagons. In mathematics, this shape is called a truncated icosahedron — it is formed by cutting off all 20 vertices of an icosahedron. Rotate it yourself.
Why are pentagons needed? Hexagons alone can only tile a flat surface (like a honeycomb). To curve into a ball, pentagons create a slight "angle deficit" — and mathematics determines that exactly 12 pentagons are needed.
Vertices (V)
60
Edges (E)
90
Faces (F)
32
Euler's formula: V − E + F = 60 − 90 + 32 = 2 ✅
💡 20 hexagons + 12 pentagons = 32 faces. This combination is not only found in soccer balls; it is also the actual structure of a molecule called fullerene (C60), made of 60 carbon atoms — the chemists who discovered this structure received a Nobel Prize.