### 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.

### Reference

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