Question

**URGENT - WILLING TO PAY HIGH POINTS!** A soccer ball is constructed using 32 regular polygons with equal side lengths. Twelve of the polygons are pentagons, and the rest are hexagons. A seam is sewn wherever two edges meet. What is the number of seams in the soccer ball. Please show how you solved, thank you!

Answer 1

A pentagon has 5 sides, 12 pentagons have 60 sides.

A hexagon has 6 sides, 20 hexagons have 120 sides.

In total, there are 120 + 60 = 180 sides.

However, if you look (or imagine) at any ball, you can see that each side is touching two faces. This means that every 2 sides in those 180 sides join together to form one seam.

So, there are 180/2 = 90 seams.

Just for fun, a soccer ball is a truncated icosahedron. You can easily verify online that it has 90 edges.

Answer 2

A pentagon has 5 sides 12 pentagons have 60 sides. A hexagon has six sides 20 hexagons has 120 sides In total there are 120+60=180sides
however if you imagine a ball you will see that 2 sides are touching the floor so there are 180/2 =90 it is said that it has 90° edges