To determine the number of edges [tex]\( E \)[/tex] in a polyhedron with 6 faces ([tex]\( F \)[/tex]) and 8 vertices ([tex]\( V \)[/tex]), we can use Euler's formula for polyhedra. Euler's formula is given by:
[tex]\[ F + V = E + 2 \][/tex]
Here's a step-by-step solution:
1. Identify the given values:
- Number of faces ([tex]\( F \)[/tex]): 6
- Number of vertices ([tex]\( V \)[/tex]): 8
2. Substitute the known values into Euler's formula:
[tex]\[ 6 + 8 = E + 2 \][/tex]
3. Simplify the equation to solve for [tex]\( E \)[/tex]:
[tex]\[ 14 = E + 2 \][/tex]
4. Isolate [tex]\( E \)[/tex] by subtracting 2 from both sides of the equation:
[tex]\[ 14 - 2 = E \][/tex]
[tex]\[ 12 = E \][/tex]
Therefore, the polyhedron has [tex]\( 12 \)[/tex] edges.
So, a polyhedron with 6 faces and 8 vertices has [tex]\(\boxed{12}\)[/tex] edges.
