Question

How many pentagons are there in the 3-dimensional structure shown below?

Hint:

In a truncated icosahedron, the number of pentagonal faces is always 12.

Answer 1

Step 1: Understanding the structure.
The given 3-dimensional structure is a truncated icosahedron, which is a well-known polyhedron often referred to as the "soccer ball" shape. It consists of 12 black pentagonal faces and 20 hexagonal faces.
Step 2: Identifying the pentagons.
From the properties of the truncated icosahedron, we know that there are exactly 12 pentagonal faces.
Step 3: Conclusion.
Therefore, the total number of pentagons in the structure is 12.
\[ \boxed{12} \]