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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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