How can we use Euler’s formula to determine the number of faces in a polyhedron with 15 vertices and 24 edges?

by

Using Euler’s Formula to Find the Number of Faces

Euler’s formula is a fundamental relation in geometry that connects the number of vertices (V), edges (E), and faces (F) of a convex polyhedron. The formula is expressed as:

            V - E + F = 2

In this case, we are given:

  • Number of vertices (V) = 15
  • Number of edges (E) = 24

We want to find the number of faces (F) using Euler’s formula. Let’s plug in the known values into the formula:

            15 - 24 + F = 2

Now, simplify the equation:

            -9 + F = 2

Next, we add 9 to both sides of the equation to isolate F:

            F = 2 + 9

Therefore:

            F = 11

Thus, a polyhedron with 15 vertices and 24 edges has 11 faces.

Leave a Comment