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