BEVEL HELP for a tetrahedron - Woodworking Talk - Woodworkers Forum
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post #1 of 32 Old 03-07-2018, 12:08 PM Thread Starter
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Question BEVEL HELP for a tetrahedron

Hello, I am a sculptor and not particularly well versed on the intricacies of bevel angles and tables saws. I need to make a tetrahedron out of wood, which is essentially an object composed of 4 identical equilateral triangles that all join together with bevels to make a pyramid with 3 sides and a base. Can anyone who regularly works with angles help me with this? I mainly just need to determine the bevel angle I need to cut on the edges of the triangles and how to cut them the most effectively. Any help would be greatly appreciated! Thank you
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post #2 of 32 Old 03-07-2018, 12:13 PM
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Welcome to the forum! When you get a minute go ahead and complete your profile with first name and location. This helps us to help you. You can add your name to your signature line so it shows in each post.

Someone should be along shortly who can answer your question.

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post #3 of 32 Old 03-07-2018, 12:32 PM
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I think the bevel angle would be 30 degrees as the internal angles of an equilateral triangle are 60 degrees.

Measure twice, Cut once, Then force it to fit with a big hammer.

Last edited by AltcarBob; 03-07-2018 at 12:35 PM.
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post #4 of 32 Old 03-07-2018, 01:43 PM
where's my table saw?
 
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Not so ...

The faces are angled in towards the apex of the pyramid, not vertical. This site gives an example of finding the face angle or "bevel" . It turns out to be around 70.3 degrees:
http://www.nabla.hr/GE-AppTrigonomA2.htm

It will be very difficult to saw one from a piece of solid wood. It would be easier to make 4 separate identical length triangular faces and join them together... and much safer!

The answer to your question will only be as detailed and specific as the question is detailed and specific. Good questions also include a sketch or a photo that illustrates your issue. (:< D)
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post #5 of 32 Old 03-07-2018, 02:05 PM Thread Starter
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Not from solid (using 4 pieces)

I am trying to make this from 4 pieces of wood and join them together, with a hollow space inside. As opposed to creating the shape from one solid piece of wood. So in that case would 30degrees be the proper angle for the bevel on all of the triangles? Also, what would the best tool for this bevel cutting be? Thanks again!
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post #6 of 32 Old 03-07-2018, 04:39 PM
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How large is this when finished? That's going to have some bearing on which tool is best for cutting.

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post #7 of 32 Old 03-07-2018, 04:46 PM Thread Starter
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Various sizes

I will make them in various sizes but most likely not over 12in. I think a table saw may be best?
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post #8 of 32 Old 03-07-2018, 05:10 PM
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Quote:
Originally Posted by woodnthings View Post
The faces are angled in towards the apex of the pyramid, not vertical. This site gives an example of finding the face angle or "bevel" . It turns out to be around 70.3 degrees:
http://www.nabla.hr/GE-AppTrigonomA2.htm

It will be very difficult to saw one from a piece of solid wood. It would be easier to make 4 separate identical length triangular faces and join them together... and much safer!
It cant be 70.3 degrees its an Equilateral triangle all angles must add up to 180 degrees and must be divisible by 3. I think............ its been a long time since I did Trigonometry

Measure twice, Cut once, Then force it to fit with a big hammer.
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post #9 of 32 Old 03-07-2018, 05:19 PM
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You might be right ...

Quote:
Originally Posted by AltcarBob View Post
I think the bevel angle would be 30 degrees as the internal angles of an equilateral triangle are 60 degrees.
Quote:
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It cant be 70.3 degrees its an Equilateral triangle all angles must add up to 180 degrees and must be divisible by 3. I think............ its been a long time since I did Trigonometry
The angles between the sides are 30 degrees. The 70 degree angle is the angle of one face to the other face IF I'm understanding this math example. The proof will be in build, so we'll wait and see if it works with a 30 degree bevel.

The answer to your question will only be as detailed and specific as the question is detailed and specific. Good questions also include a sketch or a photo that illustrates your issue. (:< D)
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post #10 of 32 Old 03-07-2018, 05:26 PM
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Quote:
Originally Posted by PACHY View Post
I will make them in various sizes but most likely not over 12in. I think a table saw may be best?
Whatever you use think about safety when your cutting, doing compound bevels can be dangerous because you are cutting in 3 dimensions and a 12 inch piece can leave your fingers perilously close to the teeth. No good making a perfect pyramid if you end up only able to count to 9.
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Measure twice, Cut once, Then force it to fit with a big hammer.
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post #11 of 32 Old 03-07-2018, 05:45 PM
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Quote:
Originally Posted by woodnthings View Post
The angles between the sides are 30 degrees. The 70 degree angle is the angle of one face to the other face IF I'm understanding this math example. The proof will be in build, so we'll wait and see if it works with a 30 degree bevel.
The Dihedral angle is something about 70 degrees if I remember it right from 45 years ago. Or was it the Bisector angle.

Measure twice, Cut once, Then force it to fit with a big hammer.

Last edited by AltcarBob; 03-07-2018 at 05:50 PM.
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post #12 of 32 Old 03-07-2018, 05:56 PM
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Hi Pachy,

I work with angles regularly in several areas of my occupation(s). I have seen done what you have described, so correct me if I am not seeing part of your challenge clearly...

This will (or can) take more than just finding the "set angles" of a standard tetrahedron, but further...asking what angles you wish to achieve (or use) to create the intersection of the facet planes. Those angles could be very different depending on how you intend to join these.
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post #13 of 32 Old 03-07-2018, 06:24 PM
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Hi Pachy,

I occasionally (and in the past) teach Geometry and Trig, as well as, work with angles regularly when designing and building timber frames. Please correct me if you think I have not understood your request, but I believe there is more here than just finding the "set angles" of a standard tetrahedron...???

I will take it that you want to cut set even angles in something like 1" board stock...or something like that... to create the facets for your sculpture? Then you will take those 4 facet segments and join them in some fashion...like gluing them?

I can create the specific trigonometric steps should you wish if necessary that it would take to arrive at what is illustrated below.

Tetrahedron with 60° corner


Blow UP of Tetrahedron



Single Facet of Tetrahedron...


Last edited by 35015; 03-07-2018 at 07:18 PM.
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post #14 of 32 Old 03-07-2018, 06:52 PM
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Hi Patchy...

Just like me to get long winded...LOL...and not really give you the simple answer you wanted...Which I think is in the picture below?

Good luck,

j

Cut angle...

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post #15 of 32 Old 03-07-2018, 07:32 PM
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The math is also on the link I posted

This link has the trig involved and the angle arrived at of 54' 44" is the same as Jay C's.
http://www.nabla.hr/GE-AppTrigonomA2.htm

The answer to your question will only be as detailed and specific as the question is detailed and specific. Good questions also include a sketch or a photo that illustrates your issue. (:< D)
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post #16 of 32 Old 03-07-2018, 07:38 PM
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OKAY....jay may have it BUT as a country boy I can't comprehend some of this and the bare basics is all I know....Jay you'll have to fill in the blanks in trig/geometry... I know A square + B square = C with that check mark thingy (LOL)

From altcar bob post # 3 pic I can tell you what to find BUT not when throwing in this in 3 planes.


Since all the sides are equal and basically won't change the angle even when changing size.... you'll need to determine your lil c to big C length, then get your length from the lil c to the intersections of ha, hb,hc.....use it in the formula as your A square, and the c to C will be the C with your check mark sign , that will get you the hieght of the new B square, once drawn you'll use the wider angle at the base (not 90 deg) will give you the cut bevel if you divide that in half.

sorry I don't know how (formula) to get the intersecting length. I just know what you need.

Jay or altcar I'm sure you know the formulas and how to write them....sorry I just find roof plane lengths.

Thanks up front to you both.

Woodnthings I think we typed at same time. edit
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post #17 of 32 Old 03-07-2018, 09:10 PM
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Quote:
Originally Posted by woodnthings View Post
This link has the trig involved and the angle arrived at of 54' 44" is the same as Jay C's.
http://www.nabla.hr/GE-AppTrigonomA2.htm
It may be difficult for folks to see (and/or covert) minutes and seconds to a useful decimal perhaps...Nor did this math model illustrate very clearly the actual angle to place on a saw blade...At least I did not think it did a good job of answering the OP's question? That's why (and Tennessee Tim suggested) providing a more empirical geometric example...Hope that explains my model and reasoning better?

The actual number from the reference linked information (see below) is: 54° 44' (aka minutes) 8"(aka seconds)...which actually reads in full value (or where I can do the math to decimaly...LOL) as 54° 44' 8.197142082"

To convert back to useful decimal we do the following:

44 + (8.197142082 ÷ 60) = 44.1366190347

(44.1366190347 ÷ 60) = 0.7356103172

54 + 0.7356103172 = (*rounded number) 54.736°

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post #18 of 32 Old 03-07-2018, 10:02 PM
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Thanks Jay!!! Yeah them numbers (formulas)( don't ask me to decipher them)
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post #19 of 32 Old 03-08-2018, 08:12 AM
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I worked it out the old fashioned way. I made a test piece out of foam core board by cutting 4 equilateral triangles, tacking the edges together with superglue then using a set square from the centre of the bottom edge to the peak I marked my bevels. Took it apart and carefully cut the bevels with a stanley knife and with a quick touch up with sandpaper to my great relief it all came together with only a couple of gaps were my knife wobbled off line. Then I realised I had glued it together and hadnt measured the bevel DOHH!!!!!. Managed to break it apart without too much damage and then realised I couldnt find my protractor but my workbench has a 30 and 45 degrees drawn on it and it looks to be slightly less than halfway between 30 and 45 degrees so I am guessing 36 degrees give or take a couple of degrees.

I know some people measure angles differently so its +36 degrees from the horizontal. I looked at my mitre saw to see if I could do the cuts but it only goes as far as 45 degrees and looked like it would be very awkward and dangerous to do the cuts even if it was possible.

All the different angles people have given might just be the same angle measured in different ways I couldnt work it out till I had made the cuts myself.

Measure twice, Cut once, Then force it to fit with a big hammer.

Last edited by AltcarBob; 03-08-2018 at 08:22 AM.
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post #20 of 32 Old 03-08-2018, 08:32 AM
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This might help the OP
http://sbebuilders.blogspot.co.uk/20...or-wooden.html

All this thinking about angles and dangles and swings on the wonk has given me a headache that can only be cured by lying on the floor in a darkened room at 45 degrees to the wall
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Measure twice, Cut once, Then force it to fit with a big hammer.
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