Vertices refers to the angles (and is the plural form of vertex). If your "triangle-based prism" has triangles for every face including the base, then it would have three vertices at the base (the bottom triangle) and one at the top (where the three side triangles meet) for a total of four vertices.
By "triangle-based prism" you could also mean a pyramid shape with a square base consisting of four vertices at the base and one at the top where the four side triangles meet, in which case there would be five total vertices.
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Total rubbish! A prism is a prism and not a pyramid!
A triangle based prism is one with two congruent and parallel triangular faces, joined together by three rectangular faces (like a Toblerone box). It has 6 vertices.
A triangular prism has as much to do with a triangular pyramid as an icosahedron!
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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.