Well, here are a couple, at least, to get folks started!
1) The base is a square.
2) The other four faces are triangles.
3) There are the same number of faces as there are vertices (five).
4) It is a self-dual polyhedron.
5) The volume of the pyramid is 1/3 * d2 * h, where "d" is the length of one side of the square base and "h" is the perpendicular height of the pyramid.
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Pyrimids of Giza in Egypt The Egyptian pyramids are fine examples of square based pyramids.
Yes. You can stack square pyramids.
One real world example of a square pyramids is the pyramids built in Egypt, like the Pyramid of Giza. Another example is the roof of many houses. Children's building blocks often include square pyramids as well.
they are different because there bases are different
This sounds like you are talking about a pyramid. Pyramids in Geometry are not restricted to the square pyramids you may be used to seeing in pictures of from Egypt. Pyramids are named after the type of polygon that make up their base. In Egypt, since the bases of those pyramids are squares, they are known as square pyramids. If you had a pyramid with a pentagon for a base, then it would be a pentagonal pyramid. Pyramids always have triangles for sides that meet at a common point at the top which is known as the apex.