Solids of constant with are 3 dimensional forms that have a constant width regardless of their orientation. The simplest one is created from a equilateral triangle and is called a Reuleaux Triangle. Essentially, it is triangle with rounded sides.
For the students, this has been a fun, and brief, inquiry into how CAD software CAM technologies can be used to inquire into mathematical concepts.We've been experimenting with these in class, exploring how we could create solids with different numbers of faces, as well as the applications of this kind of shape in design. The most common example is a rolling system comprised of non-spherical forms (Solids of constant width).
Files for Downloading:
STL files of shapes
File on Autodesk A360 (you can download the Fusion 360 data files here)