To determine the number of edges (E) in a polyhedron with 7 faces (F) and 7 vertices (V), we can use Euler's formula for polyhedra. Euler's formula states:
[tex]\[ F + V = E + 2 \][/tex]
Here's the step-by-step solution:
1. Identify the values given in the problem:
- Number of faces, [tex]\( F = 7 \)[/tex]
- Number of vertices, [tex]\( V = 7 \)[/tex]
2. Plug these values into Euler's formula:
[tex]\[ 7 + 7 = E + 2 \][/tex]
3. Simplify the equation:
[tex]\[ 14 = E + 2 \][/tex]
4. Solve for [tex]\( E \)[/tex] by isolating it on one side of the equation:
[tex]\[ E = 14 - 2 \][/tex]
[tex]\[ E = 12 \][/tex]
Therefore, a polyhedron with 7 faces and 7 vertices has 12 edges.
