The oloid is a geometric body discovered in 1929 by the sculptor and mechanical engineer Paul Schatz (1898-1979). It is defined as the convex hull of two circles of equal size that intersect perpendicularly. The rounded edge of each circle goes through the center of the other circle. The centers are therefore at a distance from one another that is the same as the radius R of the circles.
An oloid has no vertices, two edges and one surface. The two edges each consist of 2/3 of a circle’s circumference, i.e. have an edge length of 4/3πR. Its surface area is the same as that of a sphere with the same radius, namely 4πR2. The volume of the oloid is about 3 R3, which is slightly smaller than the comparable volume of a sphere of the same radius, viz 4/3πR3 ≈ 4·R3 .
The Oloid can be rolled across a flat surface, making wobbling jerky motions. At any instant of unrolling, the oloid touches the underlying surface only with a straight line of its surface of length √3·R. The oloid has the rare property that after a full revolution the entire surface of the oloid has touched the underlying surface once.
The sculpture was carved from a limestone block in Gabor Hrusovszky’s stone studio. The cuboid enveloping the figure had the mass 3Rx2Rx2R = 33x22x22 cm (LxWxH) with a volume of 12·R3.
In order to get from the cuboid to the oloid, ¾ of the volume had to be removed.