1. Base is a square
2. The apex is usually directly above the centre of the square (ie if you drop a perpendicular from the base of the square passing through the apex, it hits the square in the middle)
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A square pyramid.
A square based pyramid has 5 corners - 4 for the square and 1 for the top of the pyramid.
A square based pyramid.
You cannot have a 2d pyramid - whether or not it is square based. The 2d cross section will depend on the plane of the cross section.
A square based pyramid has 12 angles