The surface area of an oloid is given by:

At each point during this rolling motion, the oloid touches the plane in a line segment.

The convex hull of these two circles forms a shape called an oloid.

Since this difference is fairly small, the oloid's rolling motion is relatively smooth.

Where r is the oloid's circular arcs radius.

It resembles the oloid in shape and, like it, is a developable surface that can be developed by rolling.

An oloid is a three-dimensional curved geometric object that was discovered by Paul Schatz in 1929.

The oloid and the sphericon are members of a special family of solids that develop their entire surface when rolling down a flat plane.

However, its equator is a square with four sharp corners, unlike the oloid which does not have sharp corners.

The surface of the oloid is a developable surface, meaning that patches of the surface can be flattened into a plane.

In each rolling cycle, the distance between the oloid's center of mass and the rolling surface has two minima and two maxima.

Unlike the oloid its center of gravity stays at a constant distance from the floor, so it rolls more smoothly than the oloid.

Oloid mesh Polygon mesh of the oloid, and code to generate it.

Rolling oloid, filmed at Swiss Science Center Technorama, Winterthur, Switzerland.

It can either be formed (like the oloid) as the convex hull of the circles, or by using only the two disks bounded by the two circles.

Another object called the two circle roller is defined from two perpendicular circles for which the distance between their centers is 2 times their radius, farther apart than the oloid.

While rolling, it develops its entire surface: every point of the surface of the oloid touches the plane on which it is rolling, at some point during the rolling movement.

Paul Schatz (22 December 1898, Konstanz - 7 March 1979) was a German-born sculptor, inventor and mathematician who patented the oloid, discovered the inversions of the platonic solids including the "invertible cube" which is often sold as an eponymous puzzle, the Schatz cube.