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A pyramid and a prism are two different kinds of polyhedra. There cannot be a pyramid prism just as there cannot be a square triangle!
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A cube has 6 faces and a triangular pyramid has 5 faces. So a cube has 1 more face than a triangular prism. But a triangular pyramid has four faces. You make the call. That is correct: A triangular prism has five faces, and a cube has six faces, but a triangular pyramid has four faces.
five A triangular based prism has 5 A triangular based pyramid has 4 and there is no such thing as a triangular based prism pyramid - unless you mean a truncated pyramid (or a frustum) which is essentially a prism.
4
A hexagonal prism has 2 hexagon faces and a hexagonal pyramid has 1 hexagonal face.
a triangular prism, square based pyramid, rectangular prism and much more