Imagine a solid cube of brass.
Imagine taking this cube of brass and putting it on a lathe and cutting it to a square cylinder, that is, a cylinder whose height is identical to the diameter.
When you look at this solid, from the top, you see a circle. We can call this the Z axis. When you look at it from the side, at any angle, you see a square. Let's define two axes, X and Y, which are perpendicular to each other and to the Z axis. Viewing the solid from any angle that is 90 degrees to Z will let you see a square, right?
So now we put it back in the lathe (tricky, but) such that the Z axis is facing towards us as we stand beside the lathe. We've mounted it so the X axis is along the line of the lathe.
We turn it again, to form another cylindrical-like object, which if you view it from the Z axis, looks like a circle, and from the X axis looks like a circle, but from the Y axis, looks like a square again.
Predictably, we then mount it so the Y axis is in line with the lathe (even trickier) and turn it a third time.
Now, in any one of the three axes, the side-profile looks like a circle. What does the whole item look like?
One interesting thing to note is that in a sphere, at any point on the surface, there is a compound curve, ie a curve which exists in two dimensions and can only be formed of arcs. On any point of a solid of three rotations, however, there is never a compound curve, and it can always be modelled by use of short line segments.
This was modelled using Bryce 2, a very groovy program.
this page created on 1.30.98