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A square based pyramid is a 3-d object. It does not have a 2-d name!
Just the one square flat face.
A flat (2D) shape triangle has 3 straight edges. A triangular pyramid has 6 straight edges. A square pyramid has 8 straight edges. (Note, some vertical edges have already been counted as you move from one face to the next.)
3D = Pyramid 2D = Triangle
Yes. Just like a square is 2D.