# Wooden Polyhedron



## xcab02 (Jan 20, 2012)

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/...sp?productId=prod691031&categoryId=cat1701013


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## woodnthings (Jan 24, 2009)

Quote:
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.

You will need a rectangular/triangular section to keep the angles in registration against a fence. Round "dowels" will rotate and be impossible to hold in position end for end. 

http://www.woodworkingtalk.com/f27/angles-setting-miter-saw-9644/

http://www.woodworkingtalk.com/f27/jig-do-22-5-angle-ts-14333/
As far as what angles you need that's a whole 'nother ball game, and I don't play math that well. You will find that making angles less than 45 degrees on the miter saw will require an additional wedge against the fence for those acute angles. This appears to be a simple project, is in reality quite complex for a beginner. Thankfully all the sections are "modular" and once you get one, you just make multiples all the same.  bill


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## cabinetman (Jul 5, 2007)

woodnthings said:


> You will find that making angles less than 45 degrees on the miter saw will require an additional wedge against the fence for those acute angles.



The miter saws I have cut less than 45 degrees, requiring no wedges...or did you mean more than?

The figure in question looks to be of equilateral triangles (maybe not). Some spacing is spacing between triangles. Just for samples, assembling the triangles as they go might show the fitted angles to be cut.










 







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## woodnthings (Jan 24, 2009)

*acute angles on the miter saw*

We have had this discussion previously. I covered it with photos in this link: Angles and setting on the miter saw

If you can show how you would cut an acute angle on the end of a piece, measured with an angle gauge or protractor, say 22.5 degrees, on a miter saw, Jig to do 22.5 angle for TS * without using a wedge against the fence,* that would be useful. :yes: bill


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## cabinetman (Jul 5, 2007)

woodnthings said:


> If you can show how you would cut an acute angle on the end of a piece, measured with an angle gauge or protractor, say 22.5 degrees, on a miter saw, Jig to do 22.5 angle for TS without using a wedge against the fence, that would be useful. :yes: bill


There's no real secret. Place the subject piece on the table against the fence, then set the saw table to 22.5 degrees (it's marked...see below). Then cut.:yes:

















 







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## woodnthings (Jan 24, 2009)

*that's not 22.5 on the workpiece*

It's 67.5 on the workpiece. As stated say 22.5 degrees "on the end of the workpiece measured with a protractor" not a setting on the miter saw. :no:


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## cabinetman (Jul 5, 2007)

woodnthings said:


> It's 67.5 on the workpiece. As stated "on the end of the workpiece measured with a protractor" not a setting on the miter saw. :no:


Saw settings are indicators from 90 degrees. Of course if you want to you could start a movement to change all that.:laughing:







 







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## jonnyba (Jan 13, 2012)

You're looking at a "regular icosahedron": http://en.m.wikipedia.org/wiki/Icosahedron

The angle between the faces is the 'dihedral angle' on that page: about 138 deg. So you build 20 regular flat triangles with 60deg corners (30 deg miter), then the triangle edges need a 21 deg bevel to fit together.


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## woodnthings (Jan 24, 2009)

*so we agree?*



cabinetman said:


> Saw settings are indicators from 90 degrees. Of course if you want to you could start a movement to change all that.:laughing:
> 
> 
> 
> ...


Quote from link: Angles and setting on the miter saw








*Angles and settings on the miter saw* 
.... The settings on the miter saw are different than the angles cut on a piece held against the back fence...except at 45 degrees where they are the same. *The settings on the mitersaw must be subtracted from 90 (degrees) to obtain the actual included angle on the workpiece*. Example a 22 1/2degree setting on the mitersaw produces a cut or angle on the workpiece of 67 1/2 degrees. This might be a source of confusion :blink: for folks just starting out. ...*So "settings" do not equal "angles".* 


Quote from C-man:
Saw settings are indicators from 90 degrees. Of course if you want to you could *start a movement* *to change all that*.:laughing:

No, I don't want to start a movement, I'm way too busy having mindless discussions on WWT about how to measure angles less than 45 degrees on workpiece using a protractor and *why you need a wedge against the fence on the miter saw to accomplish *those cuts. Of course after 7 years at the University of Illinois as a student for a MFA, 2 years as an instructor, and 30 years at GM Design studio measuring clay surfaces to 1/2 mm or .01 " I could be wrong, and I really don't know how to measure anything...even a piece of wood. 
I donno? :laughing::laughing: bill

Like this:


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## cabinetman (Jul 5, 2007)

woodnthings said:


> Quote from C-man:
> Saw settings are indicators from 90 degrees. Of course if you want to you could *start a movement* *to change all that*.:laughing:
> 
> No, I don't want to start a movement, I'm way too busy having mindless discussions on WWT about how to measure angles less than 45 degrees on workpiece using a protractor and *why you need a wedge against the fence on the miter saw to accomplish *those cuts. Of course after 7 years at the University of Illinois as a student for a MFA, 2 years as an instructor, and 30 years at GM Design studio measuring clay surfaces to 1/2 mm or .01 " I could be wrong, and I really don't know how to measure anything...even a piece of wood.
> I donno? :laughing::laughing: bill


I get impressed every time you post your resume.:yes: I'm surprised you think it's a mindless discussion. Saw settings are for what you cut off, not what's left. Of course I could be wrong about that, as I don't have a long list of impressive credentials to list. Doesn't seem mindless to me. Seems pretty simple.










 







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## woodnthings (Jan 24, 2009)

*cut offs?*



cabinetman said:


> I get impressed every time you post your resume.:yes: I'm surprised you think it's a mindless discussion. *Saw settings are for what you cut off, *not what's left. Of course I could be wrong about that, as I don't have a long list of impressive credentials to list. Doesn't seem mindless to me. Seems pretty simple.
> 
> 
> 
> ...


Never heard that theory before. I always measure from the blade to the fence for the workpiece, and then the cut off is what ever it is.....
I always cut off what I don't want ...using a circular saw, RAS saw and Miter saw, otherwise you end up holding the "short end" Your method requires you allow for the kerf in the process ... too much measuring. That's why it's called "waste" but of course I could be wrong...again.:laughing::laughing::laughing:


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## aaronhl (Jun 2, 2011)

jonnyba said:


> You're looking at a "regular icosahedron": http://en.m.wikipedia.org/wiki/Icosahedron
> 
> The angle between the faces is the 'dihedral angle' on that page: about 138 deg. So you build 20 regular flat triangles with 60deg corners (30 deg miter), then the triangle edges need a 21 deg bevel to fit together.


Could you post a picture, not sure what a bevel is?


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## jonnyba (Jan 13, 2012)

aaronhl said:


> Could you post a picture, not sure what a bevel is?


Here is one leg - you'll need sixty of these total. The measurements of the legs don't really matter -- you just need the angle right, and all sixty to be exactly the same. 

top view (shows the 60deg miter). The part shaded in gray is looking down the bevel. 










side view (shows the 21deg angle to attach the triangles). Note that you're looking at the mitered edge here. 










sketchup file is attached.


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## xcab02 (Jan 20, 2012)

Thanks everbody for input. 

jonnyba - Thanks for the angles, I will try that and report back.


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## thegrgyle (Jan 11, 2011)

I would love to see this when you get it finished... .please post a pic.


Fabian


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