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

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#### Explanation

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#### Explanation:

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Alan P. Share
Jul 8, 2016

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
$\textcolor{w h i t e}{\text{XXX}} \Rightarrow 10$ faces

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
There are

• 8 edges around the top face
• 8 vertical edges
• 8 edges around the bottom face
$\textcolor{w h i t e}{\text{XXX}} \Rightarrow 24$ edges

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
There are

• 8 vertices where the top edges meet the vertical edges
• 8 vertices where the bottom edges meet the vertical edges
$\textcolor{w h i t e}{\text{XXX}} \Rightarrow 16$ vertices.

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

For verification purposes,
note that this satisfies Euler's formula:
$\textcolor{w h i t e}{\text{XXX}} V + F = E - 2$

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