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a piece of a very thick cake would be in the shape of a triangular prism so if you take a thick cake and cut it into regular sized pieces, the shapes of the pieces would be triangular prism
That sounds like a triangular prism.
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A triangular prism has 6 verticies
A triangular pyramid has 4 vertices, while a triangular prism has 6. Therefore, a triangular prism has 2 more vertices than a triangular pyramid.