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

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Alan P. Share
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
    enter image source here

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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:
#color(white)("XXX")V+F=E-2#

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