To find the number of faces of a polyhedron using Euler’s formula, we can apply the formula itself, which is:
V – E + F = 2
Here, V is the number of vertices, E is the number of edges, and F is the number of faces.
In our case:
- V (vertices) = 15
- E (edges) = 24
- F (faces) = ?
We can rearrange the formula to solve for F:
F = E – V + 2
Now, let’s substitute the values of V and E into the equation:
F = 24 – 15 + 2
F = 24 – 15 + 2 = 11
Thus, the number of faces F is 11.
In summary, using Euler’s formula, with 15 vertices and 24 edges, we find that the polyhedron has 11 faces.