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I would like to know the best technique to cut a wooden ball into four identical pieces that meet together in the middle. Obviously, cutting it along two perpendicular planes is a solution, but I want something that resembles this:

This is done on a tetrahedron, but the idea is the same for the ball: the pieces should meet together in the middle the same way they do on this tetrahedron. Here is an applet I found that allows for 3D manipulation of the tetrahedron, as well as offsetting the four pieces a bit.

I would like to know the cleanest way to do it, as later I'd like to carve little cylindrical holes on each piece to add magnets that hold the thing together, and allow for manipulation. Considering I can do the measurements (and that's easier said than done), how do do the actual cutting? How to know where the blade should stop without going too far in the middle?

Maybe a better solution would be to just double the amount of material and start with a half-ball, that I can then carve to the correct shape? But I can see two issues with that:

  • It double the costs on material, because of the waste that will be produced.
  • How to make sure that the pieces are fitting together nicely? Cutting one too much and you're left with something that's closer to an ostrich's egg than to an actual round ball...
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    Welcome to WSE. Looking at your pyramid example it appears to have 5 pieces. Any tool used to cut it (or a ball) would only work in one plane, so all cuts must meet at intersections or extend thru the object. In fact, I don't think you can cut the pyramid shown into the pieces shown from one solid object.
    – Ashlar
    Dec 1, 2021 at 23:30
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    @Ashlar it has 4 pieces. The base is a triangle (since it's a tetrahedron). Dec 2, 2021 at 5:58
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    @Caleb I woudn't be so harsh - he want's to make it from wood, so he asks here, that seems reasonable to me. You could argue you can make a lot of things from oher materials
    – Jan Spurny
    Dec 2, 2021 at 20:02
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    @Caleb - also, if he wanted to make it from metal, I would suggest getting one ball made from something which can be cut easily (wood, polystyrene, ...) cutting 1/4 perfectly, making a 2-piece mold and casting it, which is impossible for wood (or I would be very surprised if it was possible). If he wanted plastic, 3d printing would probably be best.
    – Jan Spurny
    Dec 2, 2021 at 20:05
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    I can assure you, there are many experienced amateurs and pros who would not be able to make this with assurance at first attempt; and some could not do it, period. And not just because of the geometry. After the absolutely mandatory accurate marking out (a mini challenge in itself!) you're then faced with two aspects of the same issue: how to workhold when 'cutting' and how to do those 'cuts'. Both require quite a bit of pondering, and for some workholding for the bulk of the careful fitting work (done by chiselling, scraping or sanding) may be an insurmountable problem.
    – Graphus
    Dec 3, 2021 at 8:55

2 Answers 2

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This is what I would do:

  • make those 4 equal parts separately as 4 little tetrahedrons - that way I'd be able to make sure the angles are correct
  • make inter-contact surfaces as good fit as I can (while completely ignoring the "outer" surfaces)
  • dry fit several times to make sure it fits together nicely
  • finish the inner contact surfaces with something really hard and durable - polyurethane, epoxy, etc.)
  • wait for the finish to fully cure (this could be a long time for poly)
  • temporarily glue all pieces together (blue tape and superglue, doublesided tape, etc..)
  • carefully turn out into a sphere on a lathe
  • break temporary glue and clean up
  • finish outer surface
  • drill small holes and glue/screw in the magnets
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    Excellent answer+1! Maybe preferable to leave inner surfaces bare, to use 'paper joint', traditional method for temporary hold of wooden parts
    – Volfram K
    Dec 2, 2021 at 6:21
  • Didn't think about turning, that's a nice idea!
    – Anthony
    Dec 2, 2021 at 8:56
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I would like to know the best technique to cut a wooden ball into four identical pieces that meet together in the middle.

Jan Spurny's solution is a good one, maybe the best way to go if you just want to end up with pieces that can be assembled into a sphere. However, it doesn't solve the problem if you actually want to start with a sphere and end up with a sphere. For that, you need a different approach.

You're really facing two practical problems:

  1. Commonly available woodworking tools can't make deep, stopped cuts.

  2. A saw blade removes material in its kerf, so as soon as you cut a sphere the pieces won't go together to form a real sphere.

You can solve the first problem by cutting all the way through the sphere rather than trying to only cut partway through. This will leave you with 12 pieces (I think) rather than the four sections you want: each one will have to be glued together from three smaller pieces, but that's really the only practical way to start with a sphere and end up with one.

To solve the second problem, you need to replace the wood that's lost to the saw kerf. If I were going to attempt this project, I'd definitely choose a band saw; of the various common tools, it takes the narrowest kerf by far, and it's well suited to cutting a thick, round object like a sphere. Band saw blades that cut a 0.048" kerf aren't hard to find, and adhesive-backed 0.020" veneer is available. If you can manage to cut your sphere in half cleanly, you can add a layer of veneer to each cut face. Between the veneer and the adhesive, you'll just about make up for the missing wood. (You could skip the veneer if you don't care about the final sphere being exactly a sphere, but I'd worry that errors caused by the kerfs might accumulate.)

Take your sphere and imagine that it's circumscribed about a tetrahedron. Mark the 4 vertices of that tetrahedron on the surface, and then connect each pair of vertices with a line, continuing the lines all the way around the sphere to form four great circles. Those are your cut lines. Before you start cutting, number all the triangles formed on the surface by the intersecting circles and take pictures of both sides of the sphere for later references. Cut the sphere in half along one of those lines; realistically, you're probably going to want to build some sort of jig for holding the sphere securely during each cut. Separate the hemispheres, add the veneer, and put them back together, securing them with some reliable tape around the cut line. Rotate and cut another line, add veneer, and so forth until you finish all four cuts.

Next, you'll need to identify the three parts that make up each section and glue them back together. You should end up with four sections that fit together to make a sphere.

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