Some time ago my friend asked me an interesting question: what body (possessing internal volume) has three orthogonal projections being circles (of the same radii), but isn't a sphere. I could imagine a stationary view of such object, but couldn't really rotate it in my head. I guess, my rendering software needs some practice ;-). Sasha Parfenov (my friend) actually made it out of paper. At first I thought about making it out of Styrofoam using a cookie-cutter technique, but instead I decided to read AutoCAD manual a bit more. After ~1 hour of reading and tweaking the object was drawn and rendered from different angles:
Orthogonal projections:
It would be really cool to machine this body on lathe (from brass). Maybe in a very distant future it will happen. But for now here is the next best thing:
I couldn't find description of this body in any of my math books nor on the Internet. A hypothesis that it is a "cylindroid" wasn't correct. One definition of
cylindroid is:
cyl·in·droid n.1. A cylindrical surface or solid all of whose sections perpendicular to the elements are elliptical.
2. A mucous thread with pointed or split ends, observed microscopically in the urine, and resembling a urinary cast.
adj. Resembling a cylinder.
Cylindroid is also a different name for
Plücker's conoid. It would be interesting to find out the actual name of this body.
P.S. The object's name is a
tricylinder. The general name for a body formed by an intersection of cylinders is
Steinmetz Solid. Looking through some of the 3D objects on
WolframMathWorld, I finally found it after searching for "intersecting cylinders". The 3D applet they use is very cool and many shapes are pretty interesting 
