To determine the number of edges a polyhedron has using Euler's formula, we follow these steps:
1. Identify the known values:
- Number of faces, [tex]\( F = 6 \)[/tex]
- Number of vertices, [tex]\( V = 8 \)[/tex]
2. State Euler’s formula:
[tex]\[
F + V = E + 2
\][/tex]
This formula relates the number of faces ([tex]\( F \)[/tex]), vertices ([tex]\( V \)[/tex]), and edges ([tex]\( E \)[/tex]) of a polyhedron.
3. Substitute the known values into Euler’s formula:
[tex]\[
6 + 8 = E + 2
\][/tex]
4. Solve for [tex]\( E \)[/tex] (the number of edges):
[tex]\[
14 = E + 2
\][/tex]
5. Isolate [tex]\( E \)[/tex] by subtracting 2 from both sides of the equation:
[tex]\[
14 - 2 = E
\][/tex]
6. Simplify the equation:
[tex]\[
E = 12
\][/tex]
Therefore, a polyhedron with 6 faces and 8 vertices has [tex]\( 12 \)[/tex] edges.
