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rodger.

New project with crazy angles

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So I need to build a dodecahedron light fixture (12 pentagons joined together). I am still working through how to cut all these angles. I decided to make a prototype of a pentagon, and that went well.

Each cut was 36 degrees on the miter saw.

pentagon.jpg.1027cf04c99d8554ed2998f06b52c7b9.jpg

 

I will need 12 of these in total for the completed fixture. The problem I am having is the "dihedral" angle. Mathematically, it should be 116.57 degrees. So if I want to rip each edge on the table saw, is that 116.57 - 90 = 26.57 degrees? Or, is it (116.57 - 90)/2 = 13.285 degrees? Or, should i set my wixey on the blade, let it register 90, and then just adjust to 116.57?

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If I remember my solid geometry (iffy), the dihedral angle is the angle formed by the intersection of the side of one of your pentagons with the side of an adjacent pentagon.  So I think the bevel you want to cut on the sides is 116.57/2 = 58.285 degrees. 

If you were making a cube, the dihedral angle would be 90 degrees, and you'd cut 45-degree bevels, right?

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8 minutes ago, G Ragatz said:

If I remember my solid geometry (iffy), the dihedral angle is the angle formed by the intersection of the side of one of your pentagons with the side of an adjacent pentagon.  So I think the bevel you want to cut on the sides is 116.57/2 = 58.285 degrees. 

If you were making a cube, the dihedral angle would be 90 degrees, and you'd cut 45-degree bevels, right?

This sound reasonable. However, the blade sits at 90 degrees, so would that affect my blade settings?

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On 12/9/2018 at 7:22 PM, Just Bob said:

Here is a previous discussion.  

 

I looked through that earlier, but didn't find it overly helpful. Thanks for the suggestion though.

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1 hour ago, rodger. said:

This sound reasonable. However, the blade sits at 90 degrees, so would that affect my blade settings?

Okay, I see what you're asking.  On my TS, the bevel gauge runs from 0 degrees (a 90-degree cut) to 45 degrees.  To cut the bevel you need, I'd set my gauge to 90-58.285 = 31.715 degrees.  I'm guessing there would be quite a bit of trial-and-error to get there :unsure:

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I helped build a geodesic dome when I was a teen but can't remember squat about the angles. I would practice with scrap and see if it seems even close before cutting up any good wood. This could be a perfect use of MDF, it's cheap & cuts like butter.

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I remember we cut the angled long edges & rabbet before we cut the angles on the ends. You built that tripod legged base so we have faith that this is something that you can do !

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1 hour ago, wdwerker said:

I remember we cut the angled long edges & rabbet before we cut the angles on the ends. You built that tripod legged base so we have faith that this is something that you can do !

haha! I'm impressed that you remembered that build! I did enjoy the challenge of it, so I'm looking forward to this one too. Besides the angle madness, the glue up will be a challenge too.

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38 minutes ago, Isaac said:

does this approach help you at all?

I watched this a while back, but I should probably re-watch it to see if it holds any information I missed.

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That looks like it will work to me. I remember the angles weren't difficult on my cheap Craftsman direct drive saw that only lasted a few years. 

Dap makes a superglue for wood that lets you position parts for a few minutes it's called Rapid Fuse. 

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1 hour ago, rodger. said:

Are you asking a question, or making a suggestion?

I meant no offense; I just don't understand the use of the question mark in your response - it makes your response unclear (I also cannot see any of your photos - they come up broken links - I may need to revert to chrome).

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6 hours ago, I B said:

58.3 ?

 

 

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I reverted to chrome and looked at your illustrations - how in the world did you model it so fast? It took me hours to get about half as far as you did!

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26 minutes ago, wdwerker said:

That looks like it will work to me. I remember the angles weren't difficult on my cheap Craftsman direct drive saw that only lasted a few years. 

Dap makes a superglue for wood that lets you position parts for a few minutes it's called Rapid Fuse. 

Thanks, I'll look into the glue. I was thinking about maybe standard wood glue and some 23 gauge pin nails.

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22 hours ago, Isaac said:

does this approach help you at all?

Okay, I watched this again and it does look like a simpler way then the way I have been planning. The issue is that I don't have a good way to join the ends. The author uses  hot glue, but I will need something much stronger that than that. Do you think epoxy would work well here? Maybe a reinforcement on the inside where the joints meet.

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2 hours ago, rodger. said:

Okay, I watched this again and it does look like a simpler way then the way I have been planning. The issue is that I don't have a good way to join the ends. The author uses  hot glue, but I will need something much stronger that than that. Do you think epoxy would work well here? Maybe a reinforcement on the inside where the joints meet.

Others might have better ideas, but for this sort of situation, how about combining two glues? A dab of CA or hot glue, surrounded by epoxy or regular wood glue, which take longer to cure?

reinforcement would be nice, though could be as challenging to make as the side pieces!

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