Question

How many faces, edges, and vertices are in an octagonal prism?

Answer 1

Step 1: Features of an Octagonal Prism

1. The octagonal prism is formed by square sides and two regular octagon caps.
2. A prism composed of octagonal faces is called an octagonal prism.
3. The two faces at either end are octagons and the rest of the faces are rectangular.

Step 2: Number of faces, edges, and vertices

1. An octagonal prism has $10$ number of faces.
2. There are $8$ vertical faces, one at top and one at the bottom.
3. Therefore, an octagonal prism has $24$ number of edges.
4. There are $8$ edges around the top face, $8$ vertical edges, and $8$ edges around the bottom face.
5. Therefore, an octagonal prism has $16$ number of vertices.
6. $8$ vertices where the top edges meet the vertical edges and $8$ vertices where the bottom edges meet the vertical edges.

Hence, an octagonal prism has $10$ faces, $24$ vertices and $16$ vertices.