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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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Q: How many vertices are in a triangle-based prism?
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