Oloid


Paul Schatz in 1968 with one of his polyhgedra, the ``Durchlauf Turbula" Image: Paul Schatz foundation. 		Hiro, one of the students in this class, mentioned the Oloid, beautiful structure popular in the 3D printing community. The object is the convex hull of the two circles r(t) = [cos(t),sin(t),0] and s(t) = [cos(t)+1/2,0,sin(t)]. As a convex hull of two curves, it is a so called ruled surface.

The object has been described first by the German sculptor and Mathematician Paul Schatz in 1932. Schatz (1998-1979) lived from 1927 to 1979 in Arlesheim Switzerland. The german Wikipedia page on Schatz is more informative than the English version. There is a Paul Schatz foundation. He also found the Invertible cube (Schatz cube) (I mention a related puzzle in the last few minutes of This youtube video on Rubik type puzzles.
One can buy his oloids in various shapes like in wood:
Here are some video links (thanks to Hiro for the links): Here is an article of Hans Dirnboeck and Hellmuth Stachel about the Oloid from 1997. It shows for example that the surface is area is the same than the one of the sphere.
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Acryl glass sculpture by Paul Schatz: Durchdringungen von Koerpern