Q:

How many vertices does an octagon have?

A:

An octagon has eight vertices. An octagon is a shape with eight sides, which makes eight angles and, therefore, eight vertices.

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Credit: Gareth Williams CC-BY 2.0

All octagons have eight sides made of straight lines, but only regular octagons have sides that are all equal, like a stop sign. Irregular octagons can even be concave, with some angles pointing inward. However, no side can cross another side in an octagon or in any type of polygon. An octagon is a type of polygon, as a polygon is an enclosed shape with straight lines for sides. Triangles, squares and rectangles are also polygons, as are hexagons. Circles, however, are not polygons.

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An octagon has eight interior angles. Octagons have eight interior angles because they have eight sides. Each side must create an angle with an adjacent side to create a closed figure.

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There are a total of 1,080 degrees in the interior of an octagon. The angles can be evenly divided into eight angles of 135 degrees, as in a regular octagon, or any random combination in an irregular octagon.

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A pentagonal prism has 10 vertices because there are two five-sided shapes at both ends of a prism. A pentagonal prism has 15 edges and seven faces. Five faces are between the pentagons on each end.