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

##### 1 Answer

Jul 8, 2016

#### Answer:

An octagonal prism has

- 10 faces
- 24 edges
- 16 vertices

#### Explanation:

(See image below of an octagonal prism).

If placed on one of its ends, an octagonal prism has

- 8 vertical faces (thus the "oct..." part of its name)
- plus a top and bottom face

#color(white)("XXX")rArr 10# faces

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

There are

- 8 edges around the top face
- 8 vertical edges
- 8 edges around the bottom face

#color(white)("XXX")rArr 24# edges

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

There are

- 8 vertices where the top edges meet the vertical edges
- 8 vertices where the bottom edges meet the vertical edges

#color(white)("XXX")rArr 16# vertices.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

For verification purposes,

note that this satisfies Euler's formula: