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A solid figure that has some of the same faces but some different faces, and has one more face than the other, is a prism and a pyramid. A prism has two identical bases and rectangular or square faces, while a pyramid has a polygonal base and triangular faces that meet at a single point, called the apex. The prism has one more face than the pyramid.
a pentagonal prism....
9 for prism, 6 for pyramid
There can be a quadrangular pyramid or a quadrangular prism or other quadrangular shapes. "Quadrangular" is an adjective, not a noun. You need to be more specific.