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The Egyptians built the great pyramid.
Yes, the Great Pyramid of Giza is a square pyramid. From a birds eye view, you could see that the bottom is in the shape of a square. See: http://www.mathsisfun.com/geometry/pyramids.html
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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The four corners of the great pyramid face the four compass directions of the world. The directions are North, West, South, and East.