A prism is a generic term. It describes a solid shape bounded by two congruent polygons (with n sides each), and n rectangles joining them together. The prism is names after the shape of the two polygons.
A prism with an n-sided polygon as base has 2n vertices.
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An octagonal prism has 16 vertices
Not sure how many a rectagular prism douse have but a rectangular prism does have 8 vertices.
A prism with 9 faces is a heptagonal prism. That has 14 vertices.
A rectangular prism has 8 vertices/corners.
You count the number of vertices in the polygon that forms the base. The prism has twice as many vertices.