Faces : The flat surface of any solid is called face.
Edges : Line segments where two faces meet is called an edge.
Vertices : Corners of the solid are its vertices.
Find the number of edges and vertices respectively of octahedron.

Options

A. 12, 6
B. 6, 12
C. 8, 12
D. 12, 8

Answer

To find the number of edges and vertices of an octahedron, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **Faces**: The flat surfaces of a solid.
- **Edges**: The line segments where two faces meet.
- **Vertices**: The corners of the solid.

2. **Identify the Type of Solid**:
- An octahedron is a type of polyhedron. The prefix "octa" indicates that it has 8 faces.

3. **Count the Faces**:
- An octahedron has 8 triangular faces.

4. **Count the Edges**:
- To find the edges, we can visualize or draw the octahedron.
- Each triangular face has 3 edges, but each edge is shared between two faces.
- Therefore, the total number of edges can be calculated as follows:
\[ \text{Total edges} = \frac{8 \text{ faces} \times 3 \text{ edges per face}}{2} = 12 \text{ edges} \]

5. **Count the Vertices**:
- An octahedron has 6 vertices.
- You can visualize this by noting that it consists of two pyramids with a square base joined at the base.

6. **Summarize the Findings**:
- The octahedron has 8 faces, 12 edges, and 6 vertices.

### Final Answer:
- The number of edges is **12** and the number of vertices is **6**.