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... whereas one of the "bases" of prisms are vertices.
Prisms consist of two polygonal "bases" and rectangular faces joining them. Prisms are named after the polygonal bases.
No, Triangular prisms have two bases that are triangular but these need not be equilateral.
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Prisms have polygons as bases whereas cylinders have circles as bases. In a way, a cylinder is like a circular prism.