A square based pyramid is the best name. It is a pentahedron, but that could also refer to a pyramid on any quadrilateral base and so the name is far less informative.
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A square based pyramid is called a square pyramid
There are 8 edges in a Square Based Pyramid!
A square based pyramid has 5 verticies.
There's no such thing as a square pyramid, it's not possible. * * * * * A square pyramid refers to a square based pyramid. And that has 8 edges.
It is just called a square pyramid, but its not square. Its only square on the bottom, so they call it a square pyramid, or you can simply just call it a pyramid because a pyramid is a pyramid.