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I am trying (right now failing) to construct a 3D reuleaux solid in blender. For those of you who don't know a reuleaux solid basically is a fancy word for solids of constant width. If you are a math nerd like me then you should go check them out as they are quite fascinating! (Here is a link to a informative Wikipedia page: Reuleaux Tetrahedron Wikipedia

Right now I have the 2D version of it and it looks like this: My sad 2D mesh that wishes to one day become a 3D mesh

If anyone is wondering how I constructed this I accomplished it like this: Its basically the same way you would construct an equilateral triangle in geometry class. Construction

My question is how can I take this 2D mesh object and create a 3D mesh object such as this Reuleaux tetrahedron:

Perspective of a reuleaux solid

I tried using the screw modifier but the blender gods laughed in my face. I think that there must be some way of rotating the figure around itself to accomplish this but I have yet to come upon that solution.

Thanks for the help!

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The wikipedia article says

Four balls intersect to form a Reuleaux tetrahedron.

Which is easy to implement with boolean operations (and balls).

  1. Start with a pyramid. To create it, activate the Extra Objects Addon.
    enter image description here
  2. In the 3D View, add (⇧ ShiftA) a Geodesic Dome.
    enter image description here
  3. Add a subdivided cube cast into a sphere and snap it to the vertices of the pyramid.
    snap spheres to pyramid points
  4. Select one of the cubes and add three boolean modifiers. Choose the other three cubes as inputs.
    enter image description here
  5. The distance of the centers of the spheres is the length of an edge of the pyramid. The radius of the spheres should equal this value. (The dimensions (diameters in this case) will naturally be twice the value.) In my case the pyramid has an edge length of 1.633, hence the spheres have to be rescaled to match a dimension of 1.633 * 2.
    scale the spheres
  6. Hide all the objects, except the one with the boolean modifiers. Add an edge split modifier to clean up the seams. I used a high subdivision value (4).
    enter image description here

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  • $\begingroup$ Amazing! I tried that but I was so far from getting the result you got! Thanks again for the detailed answer! $\endgroup$ – a2mky Sep 4 '19 at 19:42
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Align your 2D reuleaux with a uv sphere and knife project it onto the sphere. Separate the selection with P and delete the sphere. Duplicate and rotate what remains and , to sum up , close it at the bottom with another duplicate. Finally, make everything one object. And make sure you've got the maths right.

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  • $\begingroup$ could you please illustrate? I think creating a tetrahedron, then subdivide, then spherize with shift alt S, works, even if you have to adjust to get the exact shape and the topology is not the one of the picture $\endgroup$ – moonboots Apr 9 '19 at 9:21
  • $\begingroup$ Forget it, I forgot i.a. the horizontal cuts need scaling to make them arcs. $\endgroup$ – Lukasz-40sth Apr 9 '19 at 10:29

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