# How might I make a tetrahedron?



## Bill Kahn (Nov 29, 2017)

OK.  I got making a cube now basically figured out.  I have a a PM25MV mill.  And some extra stuff (vise, end mills, caliper, clamps, angle plate, rotary table...).  And I finally can make a 2" cube that is good to .005 on any measurement.  I am thrilled.  (Was talking to my machinist brother-in-law over Thanksgiving--he mass produces to .0002" so he wasn't impressed.  I think he said he was doing .005" when he was 12 years old.  Did not dampen my excitement though.)

How might I machine a tetrahedron? (4 identical equilateral triangles as the four sides).  I am a good enough mathematician to work out any of the angles I may need.  But geometrically, how do you grab hold of it to machine it?  I don't want a hold down threaded hole in one side.  I can make an "extruded" triangle--e.g. --a  triangular "cylinder."  So, I have one of the four triangles. Then I can grab the two parallel sides in a small vise along just the edges, angle it up, and get the second side milled.

I just can't think of how to hold it from there.

Any thoughts/suggestions/references/youtubes?

Thanks.

-Bill


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## T Bredehoft (Nov 29, 2017)

Make the outside of a cavity, bolted together, cast one in the cavity.


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## 2volts (Nov 30, 2017)

Carefully.


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## magu (Nov 30, 2017)

Are you trying to make a tetrahedron just because, or is it meant to serve some purpose? 

Personally I would start with a bit of round stock and machine the top three sides of the tetrahedron on the end forming a pointy stick effectively. This can be done by setting the work at the appropriate angle then cutting, rotating 120 degrees, cutting again and rotating/cutting one last time. 

I would cut the sides all the way out to the bounds of the round stock the part it off at the appropriate "height" Preferably this is done on a lathe, but it is also possible to "part off" on a mill.


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## Eddyde (Nov 30, 2017)

Bill Kahn said:


> OK.  I got making a cube now basically figured out.  I have a a PM25MV mill.  And some extra stuff (vise, end mills, caliper, clamps, angle plate, rotary table...).  And I finally can make a 2" cube that is good to .005 on any measurement.  I am thrilled.  (Was talking to my machinist brother-in-law over Thanksgiving--he mass produces to .0002" so he wasn't impressed.  I think he said he was doing .005" when he was 12 years old.  Did not dampen my excitement though.)
> 
> How might I machine a tetrahedron? (4 identical equilateral triangles as the four sides).  I am a good enough mathematician to work out any of the angles I may need.  But geometrically, how do you grab hold of it to machine it?  I don't want a hold down threaded hole in one side.  I can make an "extruded" triangle--e.g. --a  triangular "cylinder."  So, I have one of the four triangles. Then I can grab the two parallel sides in a small vise along just the edges, angle it up, and get the second side milled.
> 
> ...


My approach would be to machine all but one side on the end of a larger piece and cut it off creating the final side. Then make a 3 sided "v block" jig to hold it in a vertical position (cut end up) and machine off the saw marks. You could use strong magnets in the "v block" to hold the work. Curious, Is this to show-off to your brother in law at Christmas dinner?


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## chips&more (Nov 30, 2017)

You can easily machine all but one side. For the last side/face, make a vacuum pod to hold the thing so you can machine the last surface…Dave.


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## Mitch Alsup (Nov 30, 2017)

Take a 6 sided collet holder big enough for the raw stock of the tetrahedron.
Take a 30º triangular reference and use it to position the 6-sided collet holder in the milling vise holding the raw stock.
Knock off 3 sides with this on the mill.
Take the 6 sided collet holder to the lathe and part off the tetrahedron.


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## RJSakowski (Nov 30, 2017)

This is an interesting problem in work holding.  I would machine three faces, leaving a long handle on the forth face.  If you are not concerned with final size, any cut for the fourth side will work as long as it is perpendicular to a line through the apex and equidistant from the first three sides.  Holding the work to make the cut could be an issue though.  You could hold by the handle to part off the work.  I guess that I would make a cylindrical handle, set up in the mill to cut the three faces, and part in the lathe.  This should get you within a few thousandths of your final size.

  I would make a fixture for the tetrahedron out of plaster of Paris, epoxy,  or similar castable material.  I calculate the taper angle to be 19.471º which is not locking taper so some means of hold down clamp would be required.  I would face one half, move the clamp(s), and face the second half.

If you are going to use a secondary operation for finishing (e.g.. lapping), it would eliminate the need for the fixture.

Let us know how it turns out!


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## JerryK (Nov 30, 2017)

I have a solid or wire frame model for your project.
Your welcome to both , let me know.
Good luck
Jerry


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## brino (Nov 30, 2017)

Hi Bill,

Check out some threads from @Fabrickator 

http://www.hobby-machinist.com/threads/a-diamond-is-forever.36780/
http://www.hobby-machinist.com/threads/soccer-ball-or-truncated-icosahedron.43936/#post-376170
http://www.hobby-machinist.com/threads/super-bowl-trophy.26504/
http://www.hobby-machinist.com/threads/4-hollow-sphere.61323/

There are many great ideas in those threads for work holding and positioning.

-brino


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## tq60 (Nov 30, 2017)

As suggested make 3 sides on end of round stock.

depends on what machines are available but the last cut is the critical one.

Our suggestion is as follows. 

Get the round stock with 3 sides finished in the lathe in a 4 jaw so it can be dead nuts centered and true.

Get some sacrificial material such as PVC that the part will fit in.

First clean part with acetone then coat it with a thin brushed on ) layer of epoxy. 

Give it another coat to insure no surface not covered.

Mix some bondo and fill the PVC and place it over the part and get it to run true as possible.

Let it cure fully and place a PVC cap on end and face it then center drill it.

Now make tiny cuts to get the PVC to run true.

Now use cutoff tool to remove part.

Hold by PVC and take tiny cuts until you get the correct face.

Finish polish then toss it in the freezer.

The part should break loose.

The epoxy usually will break off of a polished surface and can be cleaned up where the bondo will not let go and will be difficult to remove.


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## whitmore (Nov 30, 2017)

Bill Kahn said:


> OK.  I got making a cube now basically figured out.  I have a a PM25MV mill.  And some extra stuff (vise, end mills, caliper, clamps, angle plate, rotary table...).  ...
> 
> How might I machine a tetrahedron? (4 identical equilateral triangles as the four sides).



Four plate triangles should be easy enough, you have a mill and rotary table.   It'll take
some clamping, and shifting the clamps between edges.
Bevel the edges appropriately (angle plate UNDER the rotary table will help).
Assemble with superglue.


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## Bill Kahn (Dec 1, 2017)

WOW!  There is some absolute genius on this list.  Thank you all.  The weekend is here.  I have some round stock.  I am going to at least start making the pointy stick.  (Yeah, how hard can it be--every project seems to start with that feeling.). And then for goodness sake, how hard can cutting off the point possibly be?

Oh, and yes, no purpose to it.  I just make stuff that I find entertaining.  Shapes seem to be interesting to me.  I guess I am easily entertained.  Like the month of weekends to final make a cube that visually looked cubic. And, yes, also, to show off to remote family at Christmas--they have no interest, but if they can wear Christmas sweaters I can have a tetrahedron on the tree. 

Thanks again.

-Bill


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## Jimsehr (Dec 2, 2017)

I have never made one before so out to shop I went. After a few hours I have one almost done. Took longer then I thought it would. Now I plan on taking a threaded 
Piece of stock with a bore in it and a threaded cap with a hole thru end and facing 
End of part to finish it. Part is faced to length on outer part of triangle just need to face center cut off to blend to outer part of faced off end.



https://photos.app.goo.gl/g4nPlrxDc0xltCzq1


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## Wreck™Wreck (Dec 3, 2017)

If you like making things for the fun of it as I did at one time good on ya, I have very little interest in doing so today as 30 years working in the business dampens the enthusiasm.

However, one thing that I found to have very interesting properties and may be done in a home shop with VERY careful work is the Rolamite bearing.
I have built several in the past just for fun and they confuse most people. 
This is the the basic theory. 
Make one and report back (-:

https://en.wikipedia.org/wiki/Rolamite


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## JerryK (Dec 3, 2017)

Jimsehr said:


> I have never made one before so out to shop I went. After a few hours I have one almost done. Took longer then I thought it would. Now I plan on taking a threaded
> Piece of stock with a bore in it and a threaded cap with a hole thru end and facing
> End of part to finish it. Part is faced to length on outer part of triangle just need to face center cut off to blend to outer part of faced off end.
> 
> ...



Good thought for finishing the fourth side


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## JerryK (Dec 8, 2017)

Bill Kahn said:


> OK.  I got making a cube now basically figured out.  I have a a PM25MV mill.  And some extra stuff (vise, end mills, caliper, clamps, angle plate, rotary table...).  And I finally can make a 2" cube that is good to .005 on any measurement.  I am thrilled.  (Was talking to my machinist brother-in-law over Thanksgiving--he mass produces to .0002" so he wasn't impressed.  I think he said he was doing .005" when he was 12 years old.  Did not dampen my excitement though.)
> 
> How might I machine a tetrahedron? (4 identical equilateral triangles as the four sides).  I am a good enough mathematician to work out any of the angles I may need.  But geometrically, how do you grab hold of it to machine it?  I don't want a hold down threaded hole in one side.  I can make an "extruded" triangle--e.g. --a  triangular "cylinder."  So, I have one of the four triangles. Then I can grab the two parallel sides in a small vise along just the edges, angle it up, and get the second side milled.
> 
> ...


Hi Bill,
Doing any good with your Tetrahedron ?


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## Bill Kahn (Dec 16, 2017)

OK.  Made a tetrahedron.  (Well, a study piece really. Surface is ugly.  And smaller than I would have liked.)

2" Round aluminum.  Into my BS-0 dividing head on the mill. Angle up 19.47 degrees.  (arcsin (1/3). Was fun to work that out).  Mill a flat.  Rotate 120 degrees. Do again.  And again.  Now have sharp point on the end of the round stock.  To my surprise all pretty symmetric.  Now need to cut off.  Put on lathe.  Cut off tool.  Well, yeah it worked, but the surface finish of that 4th side is terrible.  Note though, I am easily amused.  the 1.7" a side tetrahedron is, indeed, on the mantle.  Maybe next I mount with clay/glue or such and get a safe pass on that last side with the mill.  I am more of a mechanical type so better machining through chemistry, while clearly smart, is not part of my intuition.  I will note that the cylinder I started with was a big chunk of material.  The tetrahedron waiting to come out was pretty small.  I think the respective volumes are 4.44 and .61 in^3.  I can't think of how to geometrically place a larger tetrahedron in a cylinder other than axially symmetric. And the real puzzle was the work holding challenge.  Thanks list for the idea of starting with a cylinder.  I am still puzzling too how to start with a cube and work hold a corner to be straight up.  Mill that flat off.  Repeat (ahh, but how hold?) for three more corners and get tetrahedron.  Lose just 2/3 of the material, much less loss than cylinder.

-Bill


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## Fabrickator (Dec 19, 2017)

brino said:


> Hi Bill,
> 
> Check out some threads from @Fabrickator
> 
> ...



Thanks for the honorable mention Brino.  I've certainly had to hold some impossible projects before!  I've found that using tenons is the best way, the trick being-how to lose the last tenon so no one can tell.

Advice to Bill: Always think 3-4 steps ahead on what you're doing to be successful.  I follow the 7-P's:
Proper Planning and Preparation Prevent ****-Poor Performance.  It's served me well.


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## Bill Kahn (Dec 19, 2017)

Fabrickator said:


> Thanks for the honorable mention Brino.  I've certainly had to hold some impossible projects before!  I've found that using tenons is the best way, the trick being-how to lose the last tenon so no one can tell.
> 
> Advice to Bill: Always think 3-4 steps ahead on what you're doing to be successful.  I follow the 7-P's:
> Proper Planning and Preparation Prevent ****-Poor Performance.  It's served me well.


Simply fabulous.  Thank you for sharing.  

After learning to make a cube (well, within ,005, which is visually a cube), I then figured out how to mount the compound angle and mill off each of the eight corners.   Octo-cube, but I think it has a real name too. This one in steel (have no idea what kind.) 

And then I put a square cross section on the lathe and played with the taper angle for the first time to observe that indeed, a plane parallel to the axis of a cone gives a parabola. Have done in brass, steel, and aluminum.  The one in the snapshot is magnesium.

Nothing at your level.  But the same general idea--geometry is beautiful.

Regarding planning ahead--I can't seem to do it.  I just sort of see a next possible step and do it.  Once there I puzzle on what the next step might be.  Sort of like chess--can puzzle on the next move options, but hard to see much past that.  Fortunately, as a hobby, the mess-ups are fine too.  (Though the broken drill bit/broken tap thing is getting old.  I need to develop some better skills.)

-Bill


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## Bill Kahn (Dec 19, 2017)

Bill Kahn said:


> OK.  Made a tetrahedron.  (Well, a study piece really. Surface is ugly.  And smaller than I would have liked.)
> 
> 2" Round aluminum.  Into my BS-0 dividing head on the mill. Angle up 19.47 degrees.  (arcsin (1/3). Was fun to work that out).  Mill a flat.  Rotate 120 degrees. Do again.  And again.  Now have sharp point on the end of the round stock.  To my surprise all pretty symmetric.  Now need to cut off.  Put on lathe.  Cut off tool.  Well, yeah it worked, but the surface finish of that 4th side is terrible.  Note though, I am easily amused.  the 1.7" a side tetrahedron is, indeed, on the mantle.  Maybe next I mount with clay/glue or such and get a safe pass on that last side with the mill.  I am more of a mechanical type so better machining through chemistry, while clearly smart, is not part of my intuition.  I will note that the cylinder I started with was a big chunk of material.  The tetrahedron waiting to come out was pretty small.  I think the respective volumes are 4.44 and .61 in^3.  I can't think of how to geometrically place a larger tetrahedron in a cylinder other than axially symmetric. And the real puzzle was the work holding challenge.  Thanks list for the idea of starting with a cylinder.  I am still puzzling too how to start with a cube and work hold a corner to be straight up.  Mill that flat off.  Repeat (ahh, but how hold?) for three more corners and get tetrahedron.  Lose just 2/3 of the material, much less loss than cylinder.
> 
> -Bill


Having learned from the little tetrahedron, did it all again.  But with a 4" cylinder rather than 2".  It is really not intuitive that you have to turn 6 times as much metal into chips as the final tetrahedron.  Lots of chip making.

And, that 4th side.  Yuck.  Parting off was an ugly finish.  I bandsawed the big one.  Not much better.  I have to try one of the chemical approaches--glue to bondo or something.  Strong enough to face on the mill.  And then find the magic (freezer?  Heat gun?) And presto chango the metal pops free without surface damage. That will take some playing.

But the raw geometry of a tetrahedron is really interesting.  While aware of the shape since a child, I don't think I have ever played with a big one.  It is not what I had thought.  It is actually much smaller than a cube.  (Hard to explain what I mean by that).  And very pointy. Dangerous points.  Much more pointy than a cube.  (And the point is straight up--not off to a side). The 6 edges are much sharper than the 12 edges of a cube (yes, I deburred them, but I did not round them)

"In theory there is no difference between theory and practice.  In practice there is." A real tetrahedron is surprisingly different from a drawing of one or the thought of one.

-Bill


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## brino (Dec 21, 2017)

Bill Kahn said:


> Though the broken drill bit/broken tap thing is getting old. I need to develop some better skills.



Bill, Many of your skills seem to be coming along very well!

There are a number of useful threads here on drilling and tapping. Let me know if you can't find them.
Much of it is:
-use sharp tools,
-keep brittle things straight (start taps in the drill press or mill)
-consider your materials (work and tools)
-manage the chips
-use appropriate lube if you should

I am enjoying the enthusiasm you're showing.

-brino


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