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I'm trying to make a platonic solid out of solid wood.

I've computed that each edge should deviate 31.77 degrees from the vertical.

I'm confident that I can produce a set of identical pentagons with the edges at 90 degrees.

Now how can I cut the remaining material ? How does a deviation from the theoretical angle affect the final product. I am also going to add some kind of helpers to help align the edges during the assembly.

dodecahedron

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    Your question does not discuss how you will use a router to make these edges. It strikes me that a table saw would be a much better tool for these complex 3D shapes.
    – Ashlar
    Jan 30 at 1:06
  • some kind of tilting mechanism for the router, a really straight axle to extend the chuck of the router so that I can measure the angle, and maybe some kind of sled that can set the angle right and allows me to push the work piece in a straight line, as the opposing feature is a vertex, not a parallel edge.. The trick is .. if I include those pieces of information in the question, they're going to end up in the answers. I'm just looking for fresh ideas.
    – alecail
    Jan 31 at 14:47
  • I would suggest you add the info to the question and point out that you are looking for other approaches than what you have.
    – Ashlar
    Jan 31 at 15:00

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I'm confident that I can produce a set of identical pentagons with the edges at 90 degrees.

If this is using a table saw then perhaps a very simple modification to the method would be able to achieve what you want. I am presuming however that you didn't mean a table saw, or that you do but yours doesn't have a tilt feature.

If it is the latter then a tilting jig could be built to achieve the angled edges..... remembering the adage: if you can't make it perfect, make it adjustable :-)

Now how can I cut the remaining material ?

Based on the tags you used, obviously you're thinking router/router table, maybe a straight-cutting bit and a jig of some sort.

While I'm sure this is possible I think the way to go is actually using a hand plane.

For a start you could set to work immediately practising the planing if you have a plane, using any scrap wood or MDF you have to hand. Only additional things required are a bevel gauge to check progress and a protractor (or something else to set the angle precisely). Plus a good way to hold the workpiece at a comfortable height obviously.

To get the pieces to come together properly you might think that the bevel angle has to be dead on, but to give you some literal and metaphorical wiggle room you could aim to slightly overshoot, at least at the back of each edge. This will leave some gaps in the back of course, but the right glue (epoxy + filler) can easily compensate for that, and the helpers you already plan to make will ensure everything stays aligned.

Alternatively, chisel. This does sound crazy until you see the method demonstrated at the end of a video from Taylor Toolworks on super-fast chisel resurrection. Link to the relevant section.


Much as I hate to say it, this project does scream CNC.....

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