Reuleaux tetrahedron - Solid of "almost" constant width (OpenSCAD)
thingiverse
After watching Angus' video, I felt compelled to investigate the concept of "solid of constant width". I decided to experiment with this idea based on a tetrahedron. [Update 06/05/2017]: Further research revealed that this shape is actually called a Reuleaux tetrahedron, but it's not a solid of constant width. It has a slight extra width between two opposite edges. The solution to make it constant width is often the Meissner tetrahedra. However, I'm not satisfied with its non-symmetrical design. It looks like a patched shape. I believe we can apply half the correction to all six edges to create a symmetrical shape. According to this paper, the shape I'm trying to implement is called a Spheroform tetrahedron: http://www.xtalgrafix.com/Reuleaux/Spheroform%20Tetrahedron.pdf I discovered an OpenSCAD implementation on Thingiverse: http://www.thingiverse.com/thing:408157. [Edit 2018-08-16] Angus created a 3D model of this shape using Fusion 360, and it's much easier to print. You can download his model for free by following the link in his video description: https://youtu.be/8wPu2Y4hk6A
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