Final answer:
An icosahedron with 20 vertices and 30 edges has 12 faces.
Step-by-step explanation:
An icosahedron is a solid figure with 20 faces, each of which is an equilateral triangle. It also has 12 vertices, where the faces meet. In this case, the figure has 20 vertices and 30 edges.
Now, let's use Euler's formula to find the number of faces. Euler's formula states that the number of faces (F), edges (E), and vertices (V) of a polyhedron satisfy the equation: F + V - E = 2.
Substituting the given values, we have: F + 20 - 30 = 2. Simplifying this equation, we get: F - 10 = 2. Adding 10 to both sides, we find that the number of faces is 12. Therefore, the figure has 12 faces.