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Discussion Starter · #1 ·
Hi, I would like to make some polyhedra out of plywood. I can reliably cut all the shapes accurately and repeatedly. My problem is that I do not know how to work out the angle to bevel the side so the pieces will fit neatly together into a solid.

A dodecahedron would be a good start. Does anyone have any experience with this? If so I would appreciate any information on how to do this.

Thanks and regards,

willt
 

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Do you mean you can't figure out what the angle should be, or you need help setting up the saw to make the cut?
 
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I have a nice little textbook: Platonic & Archimedean Solids, by Daud Sutton 2002.
ISBN 0-8027-1386-6
Should you care to build, say, a Great Rhombicosidodecahedron, there's a data table.
 

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Discussion Starter · #5 ·
follow up

Thanks for the replies,

Chris, I just need to know how to calculate the angle, given the thickness of the material. I can set up the saw. It would seem that if I have the pieces all cut to shape and precisely the same size then cutting a bevel on each edge at the correct angle is what is necessary. Does that not seem right?

Robson Valley: I have looked in books, and online, where I find all sorts of ways to make polyhedra out of paper, plastic straws, playing cards, you name it and it is out there, except how to calculate the angle to cut an X thick piece of plywood or whatever material if I actually want to make one of these things that can be held in my hands.

Regards,

willt
 

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Discussion Starter · #6 ·
Just ordered the Daud Sutton book. Looks like it might be just the thing. Thanks for the tip.

Also, I sat down and worked it out I think. Took a while to visualize it properly but it seems that if I take the radius of a sphere that would encompass the dodecahedron touching all vertices, and construct an isosceles triangle with that radius number for two sides and the length of any edge of the dedecahedron as the third side, then the angle between the third side and one of the radius sides would be the correct angle to cut the edge keeping in mind that each edge is shared by two hexagons so the actual cutting angle would be the above mentioned angle divided by two and for the angle where vertices meet divide by three.

Does that sound right?
 

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Sorry but the math escapes me altogether!

Wood Carving Illustrated magazine is published by Fox Chapel Publications. I'm not a subscriber.
But, I do belong to the Carving Forums in their website. Somebody used a recent issue to carve
a couple of polyhedra. I've seen them on line but can't find them again (some weird thread title).
Without knowing, there might be some treatment of the geometry in that article.

Daud Sutton goes to some length to explain how to expand from the Platonic solids into other shapes.

Found it: WCI magazine #61 and the Complete Beginner's Guide to Whittling for 2013.
 

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How many sides are you using on each panel? Divide 360 by that number and that is the angle for the back cut. It is equal to half the angle of the facets. So, on a six sided panel you would cut it to 60 degrees and a pentagon would be 72. Unless you are producing some crazy wacked out star or something.
 

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That's the advantage of Daud Sutton's book: the data tables give you all the angles for all the sides and all the corners, the vertices, even if there are 60 pieces to cut for a ". . . crazy wacked out star. . . "
Those I would like to see.
 
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