3D Model

Meissner Tetrahedron

After some late night viewing of Numberphile's video on Shapes and Solids of constant width I became interested in how hard it would be to model a Meissner Tetrahedron. Two things come up:

  1. Yes, watching Numberphile videos late at night is something that goes on at Artifex; it keeps the engineering chops sharp.
  2. It turns out it takes a fair bit of work to model a Meissner Tetrahedron.

What is a Meissner Tetrahedron? Well it's a shape of constant width that looks like this

Even better, you can play around with our actual model below!


To refresh you (or teach you in the first place) on the details of what a Meissner Tetrahedron is you can watch the video or read below.

The Meissner Tetrahedron is a tetrahedron of constant width.  For reference a pyramid is a tetrahedron or a 4 sided object made up of equilateral triangles.  What is special about the Meissner tetrahedron is the constant width property.  Essentially, if you slice the object in half through its center of rotation and touch the corresponding sectioned shape with two parallel planes, no matter the orientation of the section, the parallel planes will always be the same distance apart. The most trivial object that you can do this to is a sphere. 

The  Rouleaux triangle  which is the (almost) constant width section of a Meissner Tetrahedron

The Rouleaux triangle which is the (almost) constant width section of a Meissner Tetrahedron

We're going to try and see if we can get some of these made for anyone who wants them and also explore some other constant width shapes.  Stay tuned.