# BEVEL HELP for a tetrahedron



## PACHY (Mar 7, 2018)

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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## difalkner (Nov 27, 2011)

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.

David


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## AltcarBob (Jan 20, 2018)

I think the bevel angle would be 30 degrees as the internal angles of an equilateral triangle are 60 degrees.


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## woodnthings (Jan 24, 2009)

*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!


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## PACHY (Mar 7, 2018)

*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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## difalkner (Nov 27, 2011)

How large is this when finished? That's going to have some bearing on which tool is best for cutting.

David


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## PACHY (Mar 7, 2018)

*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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## AltcarBob (Jan 20, 2018)

woodnthings said:


> 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 :vs_laugh:


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## woodnthings (Jan 24, 2009)

*You might be right ...*



AltcarBob said:


> I think the bevel angle would be 30 degrees as the internal angles of an equilateral triangle are 60 degrees.





AltcarBob said:


> 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 :vs_laugh:


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. :smile2:


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## AltcarBob (Jan 20, 2018)

PACHY said:


> 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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## AltcarBob (Jan 20, 2018)

woodnthings said:


> 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. :smile2:


The Dihedral angle is something about 70 degrees if I remember it right from 45 years ago. Or was it the Bisector angle.


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## 35015 (Nov 24, 2012)

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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## 35015 (Nov 24, 2012)

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...*


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## 35015 (Nov 24, 2012)

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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## woodnthings (Jan 24, 2009)

*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


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## Tennessee Tim (Dec 15, 2010)

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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## 35015 (Nov 24, 2012)

woodnthings said:


> 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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## Tennessee Tim (Dec 15, 2010)

Thanks Jay!!! Yeah them numbers (formulas):wink don't ask me to decipher them:grin::grin


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## AltcarBob (Jan 20, 2018)

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.


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## AltcarBob (Jan 20, 2018)

This might help the OP 
http://sbebuilders.blogspot.co.uk/2013/03/making-wood-polyhedron-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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## 35015 (Nov 24, 2012)

AltcarBob said:


> T...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...



LOL...!!!


That simply made my day....:vs_laugh:

From my shared quotes...You and Tennessee Tim are those kind'a folks that:

"...I do, and I understand..."

Which is the most important finalization, and there is nothing wrong at all being an "empirical and practical person!!!"

:thumbup:


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## PACHY (Mar 7, 2018)

*54.736 is the consensus?*

Hello, and thank you all for your input! Jay your 3D rendering is exactly what I am talking about making. I appreciate the in depth explanation shown so clearly. Also great link AltCar. So I take from this that the angle the saw needs to be set at is 54.736? If so how can I actually cut that angle on a table saw? Don't most only adjust to around 45degrees? Also, my digital angle gauge only goes to the 1/10 of a degree. I am so glad I found this site with all this combined knowledge!


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## 35015 (Nov 24, 2012)

PACHY said:


> Hello, and thank you all for your input! Jay your 3D rendering is exactly what I am talking about making. I appreciate the in depth explanation shown so clearly. Also great link AltCar. So I take from this that the angle the saw needs to be set at is 54.736? If so how can I actually cut that angle on a table saw? Don't most only adjust to around 45degrees? Also, my digital angle gauge only goes to the 1/10 of a degree. I am so glad I found this site with all this combined knowledge!


Hi Pachy,

First...you are most welcome...:grin:...Glad you found it helpful and of use.

I have built tetrahedrons almost exactly as you have described for educational aids when teaching. Some still live in some elementary and middle schools.

If the format is not to large a piece of wood, or can be created as a "frame armature," you will work with the piece of wood in a vertical format with it aligned to the table saw fence. Like I have it in my illustration. Then your blade only needs to tilt to 35.264°

If you have something like my "Wixey" digital angle gauge, just set it to the closest decimal point rounded up. I then adjust (if really necessary) with my low angle block plane, but with a new/sharp blade on the saw, seldom is this nessary.

Does that make it clearer?

Regards,

j


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## PACHY (Mar 7, 2018)

*Wood sheets*

Hi Jay, I need to make it out of sheets of wood as opposed to the frame armature. So you are saying to take my precut equilateral triangles, put them on end and rip the bevels that way, with the saw at 35.264 degrees? Thanks again


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## 35015 (Nov 24, 2012)

PACHY said:


> Hi Jay, I need to make it out of sheets of wood as opposed to the frame armature. So you are saying to take my precut equilateral triangles, put them on end and rip the bevels that way, with the saw at 35.264 degrees? Thanks again


Yep..."By George...I think he has it!!"

If you give me the exact dimensions of you materials, there makeup (aka what they are), and over design plan; I should be able to provide you a picture here on your post thread of what you want to do to scale without much effort or bother...If that would help? Otherwise, I am about 98% sure you have a good mental picture already...

Good Luck, and look forward to some final project pictures...

j


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## AltcarBob (Jan 20, 2018)

Double post


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## AltcarBob (Jan 20, 2018)

PACHY said:


> Hi Jay, I need to make it out of sheets of wood as opposed to the frame armature. So you are saying to take my precut equilateral triangles, put them on end and rip the bevels that way, with the saw at 35.264 degrees? Thanks again


I wouldnt worry about going to 3 decimal points with timber or particle board, .2 or .3 degrees should be fine. A bit of damp in the air or central heating will change your measurments more than .264 of a degree.

I highly reccomend doing as I did and making a test piece out of foam core board first. Its really easy to cut with a sharp knife, its cheap (I got 5 x A3 sheets for £6), its sandable and you can check all your angles with a Bevel guage before you get to the table saw.


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## 35015 (Nov 24, 2012)

AltcarBob said:


> I wouldnt worry about going to 3 decimal points with timber or particle board, .2 or .3 degrees should be fine. A bit of damp in the air or central heating will change your measurments more than .264 of a degree.
> 
> I highly reccomend doing as I did and making a test piece out of foam core board first. Its really easy to cut with a sharp knife, its cheap (I got 5 x A3 sheets for £6), its sandable and you can check all your angles with a Bevel guage before you get to the table saw.


I agree...modeling always helps with a final design facilitation...

In this case it was (or like many things today) can be done in CAD...or in hand drawn form. The "math" is the back-check, and in this case is done already. As such, I was able to go directly to stock (white pine scrap) and cut one of the exact facets of the tetrahedron as in the CAD model image I shared below, without any "testing" to see if it would work...

The math was the "back check"...the CAD was the "testing" and the first attempt in material provided proof of concept...

I personally use whatever decimal point furthest I can get to with a tool setting...be it 1 or 3 decimal points. Just like I design to 0.5mm even on huge timber frames and layout the same way...As the old adage goes from days as a Marine..."...aim small...miss small..." It works and applies well in craft to...


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## AltcarBob (Jan 20, 2018)

Jay C. White Cloud said:


> I agree...modeling always helps with a final design facilitation...


It certainly helps with me I have a habit of reversing things when designing or marking out, I cant help it no matter how many times I measure something between my brain and my pencil gets back to front. Manys the time I have made two backs or two lefts but if I have a small 1/4 scale model made out of card, foam board or scraps to look at it almost always stops me from adding to the firewood pile. I dont know if its being able to look at a 3D model or the building of the model that helps.


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## 35015 (Nov 24, 2012)

AltcarBob said:


> It certainly helps with me I have a habit of reversing things when designing or marking out, I cant help it no matter how many times I measure something between my brain and my pencil gets back to front. Manys the time I have made two backs or two lefts but if I have a small 1/4 scale model made out of card, foam board or scraps to look at it almost always stops me from adding to the firewood pile. I dont know if its being able to look at a 3D model or the building of the model that helps.


Whatever is time efficient, economical and works for you should be employed...Be that a scale "touch model" and/or CAD modeling. 

For me, I keep a CAD open when working, as a piece is laid out, it is checked against the cad, when complete...that component is erased from the CAD and I move on. This creates a running inventory and is instantly clear what is left to achieve before completion. In the past, I relied exclusively on good isometric plans in the same fashion.


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## PACHY (Mar 7, 2018)

*Looking forward to making this!*

Thanks again to everyone for your help, Jay especially. I'm pretty sure you are probably the coolest person ever, far wiser and more experienced than I. And that is exactly what I was hoping to find by joining the forum. If I am ever on the opposite corner of the country I will come to thank you in person! Initially I am going to make this out of 1/2-3/4" melamine board, not a respectable wood but with clay we use it for its ability to repel water a bit, at least where it is coated. Most likely I will start with 12" sides on the equilateral triangles. I have family that has a table saw so hopefully if I have time this weekend I will try and get this made. This is the first of about 10+ steps in my process, so the final final piece is a ways away. I will however post pictures once I get the initial form made. I am sure I will have more questions in the future!


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## 35015 (Nov 24, 2012)

PACHY said:


> Thanks again to everyone for your help, Jay especially. I'm pretty sure you are probably the coolest person ever, far wiser and more experienced than I. And that is exactly what I was hoping to find by joining the forum. If I am ever on the opposite corner of the country I will come to thank you in person! Initially I am going to make this out of 1/2-3/4" melamine board, not a respectable wood but with clay we use it for its ability to repel water a bit, at least where it is coated. Most likely I will start with 12" sides on the equilateral triangles. I have family that has a table saw so hopefully if I have time this weekend I will try and get this made. This is the first of about 10+ steps in my process, so the final final piece is a ways away. I will however post pictures once I get the initial form made. I am sure I will have more questions in the future!


:vs_blush:

I doubt very much I am all that...but thank you deeply. I was glad to be of help to a fellow "maker of things!"

Blessings,

j

P.S.

I travel a lot...send me an email (its here on the forum) and I will set up a contact file for you...

Er...Ah...I missed something...!!!...Did I read clay...!!!

As in like maybe stoneware perhaps just maybe please...:vs_OMG:

I also work in traditional ceramics and would love to know more about your final design...do send me an email can't wait to see progress reports here on you post thread...


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