Probably not. On that scale, the end is too blunt to be considered a point.
A point is an idealization. On the scale of a building, the end of a spike is small enough to be considered an exact location, a point. But on the scale of your desk, its end is too blunt to exactly define one location. At the scale of a desk, the spike would have to taper to a pin point. Then, perhaps, you could consider its end to define a point.
But if you put that pin point under a microscope, then for that scale it is again too blunt. It would have to taper further, perhaps to the thickness of a bacterium, before the end could define a point. But now, on the scale of bacteria, the end of the spike is again too thick to exactly define a location.
So, points in 3D space are an idealization. For a computer model of a building, the sharp end of a spike is exact enough to be a point. The edges, planes, and other shapes that make up the building do not need to be specified to any greater accuracy.
Where, in space, is the end of the more distant spike? (Look at the picture again and envision the relationship between the two points.)