Reuleaux tetrahedron - Solid of "almost" constant width (OpenSCAD)

prusaprinters

<p>After watching Angus video, I got curious and decided to experiment with the concept of "solid of constant width". <a href="https://youtu.be/2eUWT9cI23o">https://youtu.be/2eUWT9cI23o</a></p> <p>I implemented it based on a tetrahedron.</p> <p>[Update 06/05/2017]: It turns out that this shape is called a Reuleaux tetrahedron, and it's NOT a shape of constant width. It has a slight extra width between 2 opposite edges. The popular solution to make it constant width is to implement the Meissner tetrahedra. The mathematician in me doesn't like that none-symmetrical shape. It looks like a patched shape. I'm pretty sure we can apply "half" the correction to all 6 edges to make a symmetrical shape. I will have to do more studies on the subject and understand the math before trying to implement it.</p> <p>According to this paper, the shape I'm trying to implement is called a Spheroform tetrahedron: <a href="http://www.xtalgrafix.com/Reuleaux/Spheroform%20Tetrahedron.pdf">http://www.xtalgrafix.com/Reuleaux/Spheroform%20Tetrahedron.pdf</a></p> <p>I found an OpenSCAD implementation on Thingiverse: <a href="https://www.thingiverse.com/thing:408157">http://www.thingiverse.com/thing:408157</a></p> <p>[Edit 2018-08-16] Angus made a 3D model of this shape with Fusion 360, and it is a lot easier to print. You can download his model for free. Have a look at his video (download link in video description): <a href="https://youtu.be/8wPu2Y4hk6A">https://youtu.be/8wPu2Y4hk6A</a></p> Category: Math Art