# Problem figuring out the angles

1062 Views 21 Replies 12 Participants Last post by  therealSteveN
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Hi Guys/Gals,

I'm wanting to build a Tetrahedron frame that's exactly like the photo. I see that it's 1/4" thick and probably 1" wide sticks but I can't figure out the bevels and how to get the 3 pieces in each corner to come together while maintaining the bevel. Anyone know a way to explain this to me that doesn't drown me in angles and confusion?

-Zak

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On the older Mitre Boxes…instead of degrees, they would display number of sides to a box…with the number 4 standing for 45 degrees = a Four sides box…...the number of sides they would display went all the way to 24 sided boxes…then you just set the saw to cut at the number of sides….no degrees needed.

As in an 12 sided box, set the saw to the Number 12..and saw away….
On the older Mitre Boxes…instead of degrees, they would display number of sides to a box…with the number 4 standing for 45 degrees = a Four sides box…...the number of sides they would display went all the way to 24 sided boxes…then you just set the saw to cut at the number of sides….no degrees needed.

As in an 12 sided box, set the saw to the Number 12..and saw away….

- bandit571
This is a Tetrahedron. I don't know how many "sides" it has since the pieces look to be beveled 40 degrees or so. I also use a Miter saw not a mitre box, so that isn't making any sense to me either. You see how in the photo the pieces are angled and still all meet up in the corners. I need to know what those angles would be to make the pieces sit at that angle and still come together perfectly. Is this making sense?
I think you could use this chart. You may have to manipulate it a bit but it should be able to give you a starting point so you can do some trial and error.

What is the angle going up? (spring angle)
calculating angles from parallel lines math program.

dont know if that helps you here, but there are other programs out there on interwebs.

and, a page of various angle calculator software programs.

https://calculate-angles.software.informer.com

There is also a program called: pyramid calculator, or somethin like that, might be helpful here.
Your pic appears to be a frame, inside of there are what appear to be wires. All I can point you toward on angles for a
Tetrahedron are for making a solid block, which makes what is known as a pyramid puzzle.

This page has some description, and an hour long video. Hope it isn't wasting your time, because if you are making just the frame, I don't think you'll get there from here.

Good luck
This link may be helpful to you. There are many others out there. http://cowboyplus.net/cmiter/
From what I can make out in your picture, the only thing that makes it a tetrahedron are 3 rods on the opposite side that makes a pyramid shape? Otherwise, it just looks like a splayed miter joint to me. Matthias Wandell has a tutorial and handy cheat sheet for figuring out how to cut them based upon the number sides.
Darrel, I clicked that cowboyplus link and Norton warned me that is an unsafe site. Be careful out there.
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Tetrahedron - four sided solid. Sits the same no matter how you turn it. You've got the bottom 2" or so of any one side.

There is trig in this no matter how you "cut" it - lol.

Fortunately the apex angle isn't needed to be precise since there's no apex. The corners are 120° so 60° reverse miters are the baseline measurements if everything was flat. These would be cut perpendicular to the face. As you raise the apex point the miter angles move from 60° to 90°. At the same time the bevel angle moving from 90° (straight up) to … less.

The angle to the apex can be fudged, but the math isn't simple.

Cut four identical 120° triangles using beta as your bevel angle ~70-1/2° to make one.

Or use the bevel angle on both sides of the frame pieces and miter the ends to fit with the fence at 60° and the bevels flat. It's hard to hold but should work.

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Couldn't have said it better myself! ;-)
PS: You can't safely cut the 60º reverse miter on a 45º chop saw.

Thanks for your detailed explanation! That's very helpful. I'm gonna try and understand it a little better before tackling this.

Thanks everybody else for your input as well! I love this forum.
Lazyman,

None of the over 40 security vendors used by virustotal.com flagged the cowboyplus site as malicious.

Perhaps Norton is flagging that the site is not HTTPS.

And I agree, be careful out there!

TonyC
The link Foghorn posted works good.
Confirmed my Sketchup results (for a 60 deg slope.)

or you could take a trig class…
Lazyman,

None of the over 40 security vendors used by virustotal.com flagged the cowboyplus site as malicious.

Perhaps Norton is flagging that the site is not HTTPS.

And I agree, be careful out there!

TonyC

- jacww
SSL is probably at least part of it but I think Norton has it flagged in their database as malicious, not just unsafe. Any company that isn't using SSL by now may have other security issues that make them ripe for hackers to exploit. Sometimes they are simply doing things like crypto mining without your knowledge, and maybe without theirs if they have been hacked, so at a minimum close the website (tab) after visiting.
When I need to calculate angles I draw full scales drawing and just take the angles off the drawing with my bevel gage.
Compound angles are the trickiest but the most rewarding. Cutting them is only the first hurdle clamping them when glue makes everything slippery that's another challenge.
That frame thing doesn't look wood friendly.
Good Luck
When I need to calculate angles I draw full scales drawing and just take the angles off the drawing with my bevel gage.
Compound angles are the trickiest but the most rewarding. Cutting them is only the first hurdle clamping them when glue makes everything slippery that's another challenge.
That frame thing doesn't look wood friendly.
Good Luck

- Aj2
Maybe I'm not smart enough, but to me, it would seem pretty hard to draw a compound miter without knowing the angles first?

Sketchup will do it easily though. (5-10 minutes at most)
I draw the angles that I like. When it looks pleasing to the eye.
I'm a reference builder for me it's the easy way.
I do see your point it's a little bit of the chicken/egg thing.
I'm a reference builder for me it's the easy way.

- Aj2
I've been there, sometimes it's just easier to hold it where you want it and make a mark or eyeball the blade angle.

Not trying to sell anyone on Sketchup (or other programs) but since I started using it it takes out all the guess work. I drew his frame in a couple of minutes, took a little longer to layout the angles but it doesn't lie when your done if you do it right.
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