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
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There are
8 edges around the top face
8 vertical edges
8 edges around the bottom face
##color(white)(“XXX”)rArr 24## edges
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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.
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For verification purposes,
note that this satisfies Euler’s formula:
##color(white)(“XXX”)V+F=E-2##