A polyhedron has 6 faces and 8 vertices. How many edges does it have?

Options

A. 14
B. 15
C. 10
D. 12

Answer

To find the number of edges (E) in a polyhedron with 6 faces (F) and 8 vertices (V), we can use Euler's formula for polyhedra, which states:

\[ F + V - E = 2 \]

### Step-by-Step Solution:

1. **Identify the given values:**
- Number of faces (F) = 6
- Number of vertices (V) = 8

2. **Substitute the values into Euler's formula:**
\[ F + V - E = 2 \]
Substituting the known values:
\[ 6 + 8 - E = 2 \]

3. **Simplify the equation:**
\[ 14 - E = 2 \]

4. **Rearrange to solve for E:**
\[ E = 14 - 2 \]

5. **Calculate the number of edges:**
\[ E = 12 \]

### Final Answer:
The polyhedron has **12 edges**.

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