Definitions

# Oloid

An oloid is an geometric object created by Paul Schatz (1898-1979).

An oloid is formed when two disks of same size and diameter are intersected at right angles within one another, and that the distance of two centers of disks is the same as their radius $R$, though its $3R$ long. Then you take their convex hull.

While rolling, the distance between center of gravity and floor has two minimums and maximums, though it rolls very swinging but smooth: it never falls over its edges. It is the only known object that develops its entire surface while rolling. Its Surface is $4 pi r^2$, same as the sphere. Its exact Volume is unknown.

The oloid (pronounced “oh-loh-weed”) was discovered by Paul Schatz. Schatz discovered in 1929 that the Platonic solids could be inverted, and one of the products of the inversion of the cube was the oloid. Based on two circles set perpendicular to each other, it rolls in a straight line such that its whole surface touches the plane on which it is rolled. Its gentle, rhythmic motion is extremely effective in mixing, aerating and purifying. The oloid is extremely evocative visually, resembling a Möbius strip. Schatz came to his geometric insights by studying the work of Rudolf Steiner, the founder of anthroposophy. Schatz obtained Swiss Patent no 500000 for his oloid mixer. Development has since continued, and the oloid is applied in ever more numerous ways.

Another object is defined, when the distance of the intersecting disks is √2 times their radius. This is often called "Two circle roller". It is not solid as the oloid, it consists just of the two disks. It is interesting, because its center of gravity has a constant distance to floor, thus it rolls smoothly but straightforward, not as swinging as the oloid, which it is sometimes confused with.

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