Gravity is Optional
Reuleaux shapes

A circle is a collection of points equidistant from the center. As a result, all cords from any point on the bounding circle, thru the center, and to the opposite side will have the same length. This is known as the diameter.

However, there are an infinite number of 2-dimensional objects which have a constant distance between two parallel surfaces. Drawings and a video. The Reuleaux triangle is the simplest of these.

The Wankel engine is based on shape similar to the Reuleaux triangle .. but with the edges slightly flattened.

It is also possible to produce non-spherical 3-dimensional objects that will maintain a constant distance between two parallel surfaces. Solids of constant width provides photos and a video (or two).

The cross section of the Reuleaux tetrahedra (the volume created by the intersection of 4 spheres) does not have a constant thickness because the face to edge distance is slightly larger than the point to face difference. (About 2% larger.) However, if some of the edges are rounded a bit, the Reuleaux tetrahedra can be converted into a non-spherical solid of constant thickness.


How round is your circle? Amazon
Weird 2D and 3D, non-circular and non-spherical, shapes that roll with a constant diameter .. and other weird stuff.

Author: Robert Clemenzi
URL: http:// / Reuleaux.html