A non-example of a pyramid would be a sphere. Pyramids have a polygonal base and triangular sides that meet at a single point, while a sphere is a three-dimensional geometric shape with all points equidistant from its center. In contrast to the flat faces and sharp edges of a pyramid, a sphere has a curved surface with no edges or vertices.
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A pyramid.
I don't really understand your question, but one example of a rectangular based pyramid is the Great Pyramid in Giza.
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Your roof is a square based pyramid.
A square based pyramid can be found in house by looking in little kids room, But the answer is: SQUARE BASED PYRAMID BUILDING BLOCK!!