Wooden Polyhedron

[xcab02]

Anyone ever make one of these?

I have been trying to duplicate this since I saw it in the Restoration Hardware catalog. Because why pay over $200 when I can make it for under $20, right? I cannot seem to figure out the proper angles to cut so that they all line up correctly.

I figured out the triangle cuts being 60deg, then noticed that the middle two section create a pentagon. So I found out an angle of 22.5deg to make a pentagon. I just cannot figure how to make a double angle cut so that the triangle create the pentagon and triangle and at the same time angle towards themselves as they share points.

Any help would be greatly appreciated as this I believe might drive me crazy if I don't figure it out just for a mere accomplishment of creating one on my own.

I am using a compound miter saw and 1/2" or 3/4" square dowels. I did notice in the picture it looks as they used some kinda molding, so not sure if they will make a difference or not.

Here is the link if anyone wants to get a better look. Thanks again for any input.
http://www.restorationhardware.com/c...yId=cat1701013Polyhedron.jpg

[petzl]

Hi, I think the issue you might be dealing with is what angle to cut into each dowel.
(I'm coming at this from math not woodworking, btw, so forgive me if i get the terms wrong.)

What you might be having trouble in is the "dihedral angles" that join one triangle to another. The proper angle is 138.2°. So to get two sections to fit together you need to remove a 20.9° degree cut on any edge where triangle meets triangle. 90° - (138.2° / 2).

http://en.wikipedia.org/wiki/Icosahedron

[AndyD]

Sorry I don't have any suggestions for building this (looks complicated!). -- but you've found one of my favorite sources for design inspiration: Restorationhardware! Interesting stuff, isn't it?

[Dethpickle]

A few years ago I made some flowerpots like that.

It was all leftover cedar fence panels that I chopped up with a cheap Ryobi compound miter. Initially I started with the tapered square ones.
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They were fun and didn't turn out horribly so I moved on to the septagon tapered one.


Then on to the 12 sided and then the truncated icosohedron and on.


A big "Yay, MATH!" to this site for help with the angles. Look at the bottom of the referenced page for the polyhedra. Just half the dihedral angles and subtract from 90 to get the join angles. I'll assume you all can figure out the perimeter angles of each shape.

Here is a link to an album of them all.
http://s1195.photobucket.com/albums/...le/FlowerPots/

Incidentally... build-wise. I started out actually hammering nails into these things. But as the angles got more complicated and oblique, I had to borrow a friends pin-nailer to stand a chance putting these together. Getting the angles right was almost impossible. I approximated them by drawing accurate lines on a computer and then printing them out. I'd then put the printout on the miter saw and move the blade so it cut the line. Thats NOT accurate enough, but close. If you inspect the work in the close-ups, it's absolutely horrid. But from a few feet away, they look pretty good.

The goo you see is liquid-nails. That really firmed a couple of those up.

It's been about 4 years and they're still holding up well. Because they started life as fresh cedar fence slats at Home Depot, they really shrunk a bit. But since they're so small it didn't entirely wreck them. I'd like to try the project again, but maybe with a custom chamfer bit. What would it cost to get a custom 20.9 degree chamfer bit?

Dethpickle...

[Shop Dude]

This design is really neat. It perked my interest so thought i would revive this thread and try to help solve it.
I googled Polyhedron Puzzles and came across the following site. It has wooden puzzles based on polyhedrons and some jigs for cutting the pieces. Lots of info.Might be useful to someone for future reference.

http://www.johnrausch.com/PuzzlingWorld/chap23.htm