To determine the number of vertices for the given solid, we can use Euler's formula for polyhedra. Euler's formula states:
[tex]\[ V - E + F = 2 \][/tex]
where:
- [tex]\( V \)[/tex] represents the number of vertices,
- [tex]\( E \)[/tex] represents the number of edges,
- [tex]\( F \)[/tex] represents the number of faces.
Given:
- [tex]\( F = 8 \)[/tex] (the solid has 8 faces),
- [tex]\( E = 12 \)[/tex] (the solid has 12 edges).
We need to find [tex]\( V \)[/tex]. Using Euler's formula, we rearrange it to solve for [tex]\( V \)[/tex]:
[tex]\[ V = E - F + 2 \][/tex]
Now, substitute the given values into the equation:
[tex]\[ V = 12 - 8 + 2 \][/tex]
Perform the arithmetic:
[tex]\[ V = 4 + 2 \][/tex]
[tex]\[ V = 6 \][/tex]
Thus, the solid has 6 vertices. Therefore, the correct answer is:
B. 6
