By "corners", do you mean vertices or edges?
9: the eight vertices of the octagon plus the vertex at the apex of the pyramid.
well in a triangular pyramid it depends on the structure and how you look at it. In my very correct opinion you should see it has three not including the tip, but if you want to you can and it will...
All true pyramids are triangular and they all have 4 points/corners.
5 4 in the square (base) and 1 at the top . /\\ / \ \ / \ \ / . \ \. /.________\./