Summary

This is a shape which, like a ball, always has the same width all the way around. Though it appears to be a strange shape, you could run a board over it as smooth as marbles.

Here's a gif of these things in action: https://i.imgur.com/YpW7Cej.gifv

Inspired by the book "How Round is Your Circle" by John Bryant & Chris Sangwin.

Instructions

This was actually quite difficult to design, it's deceptively simple looking. I modeled this in Solidworks this afternoon, struggled with it a bit. Had to export it as a STEP file at one point and reimport it just to get the geometry cuts to work.

The final filets gave me a bit of trouble too, but in the end it worked out beautifully.

The design used a large number of 1.5" radius revolve-cuts, dealing with all manner of intersections. This is the more advanced version of the object of constant width (OoCW), the actual tetrahedron design.

There's a much easier to design acorn-like design that also funtions as a OoCW). I'll upload that as well.

No sooner had I built it than I realized some might enjoy printing these out on a 3D printer. They would be fairly difficult to machine on a traditional lathe or mill, so a 3D printer is perfect.

Object of Constant Width - Tetrahedron