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

An octagonal prism has

• 10 faces
• 24 edges
• 16 vertices

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