3D shape with orthogonal projections that form circles of the same radius.

Question

Let's say you have a 3D shape. The side view, front view, and top view of the shape are all circles of the same radius. Does the shape have to be a sphere, or is it possible that it could be another shape?

Answer 1

Take 3 very thin circular disks of the same radius; a red one, a green one, and a blue one. Then put them together so that the side view, the front view, and the top view be like this:

Answer 2

One variation of Steinmetz solid is the intersection of three mutually-perpendicular cylinders.

(Image credit: Weisstein, Eric W. "Steinmetz Solid." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SteinmetzSolid.html)