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    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##

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