How to cut the miters for a tetrahedron, using a sliding miter saw?
ttttt
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I want to make a tetrahedron from boards or sheet material, not a solid block, using a sliding miter saw. Festool Kapex – tilt is up to 47 degrees from vertical.
Tetrahedron is a pyramid made of 4 equilateral triangles – 60, 60, 60 degrees. I will leave one side open; think of a hollow 3-sided pyramid with the base being open. This means I need mitered edges on only 2 of the 3 sides of each triangle board.
The angle between sides, the dihedral angle, is 70.52 degrees. Half that, 35.26 (let’s say 35.3) degrees would be the miter angle I need to cut on the edge of my 3 equilateral triangle boards.
Question is: How to cut that 35.3 degree angle, since the smallest angle I can cut on a board laying flat on the saw base is 43 degrees (90 – 47 = 43) from horizontal. I can cut the edge as sharp as up to 43, but I need to cut it to 35.3
I’ve pictured first cutting the triangle to 60, 60, 60 with square edges, then laying the board horizontal and shimming it up about 7.7 degrees, then setting the saw’s tilt at 43 and the saw’s horizontal miter at 60 from the fence. I then cut the square edge to become 35.3 degrees. My cut would have to precisely meet the bottom corner of the board.
Another approach might be to tape the square-edge triangle board vertical to a square block, with the board’s square edge (and the block) against the saw’s base. Then the saw’s tilt can be 35.3, and the saw’s horizontal miter setting can be 90 from the fence. Again, the cut must come right at the board’s edge corner or else either the board’s miter will have a flat or the board’s dimension will become smaller.
Both of those solutions are pretty Rube Goldberg. I will appreciate any other solutions that are more direct and/or elegant. Ideas?
Big Domo,
TTTTT
Replies
I'm not sure exactly what the end result of your geometry is. What's the product?
It seems like a very dangerous process on a miter saw. There is no way to clamp a tetrahedron while cutting, and I wouldn't get my fingers that close to a complex cut.
It's an interesting academic exercise, but unless I'm missing something, I wouldn't do it.
As I mentioned, "I want to make a tetrahedron from boards or sheet material, not a solid block, using a sliding miter saw.” So there is no clamping of a tetrahedron. Only flat boards are cut.
Imagine that you cut 3 triangles from a 1” x 4” board, and want to join their edges to make a hollow pyramid with one side left open. You want to miter the board edges to join them. To do that, the boards have to have 35.3 degree angles on their edges.
Compare having 4 rectangular boards that you want to join into a square box using miter joints. To do that, the boards have to 45 degree angles on their edges. You could tilt a miter saw blade to 45 degrees to either initially cut the boards at 45, or you could take a board that has been cut with square edges and change those 90 degree edges to 45 degree edges.
The question here is - how do you get 35.3 degree edges on the boards, since the saw will not tilt to 35.3 as measured from the horizontal base (= 54.7 degrees from the vertical)?
Build a ramped base large enough to hold the parts and fasten it to your saw. Work out a solid clamping system for the funky shapes.
Your sir(madam) seem to have stumped the panel. I for one think you are asking too much of the Kapex and can't imagine a safe way to perform this cut.
My recommendation is to use a sled on the tablesaw with an appropriate support jig to easily and safely cut the needed angles. Leave the blade at 90° and simply make your jig at the required angle.
Stumped?
See _MJ_'s ramped base. Can be done safely and accurately.
You can cut any angle with any saw. Your only restricted to the length of your cut with a slide saw. The question is about a slide saw so we don't have to talk about table saws or cnc machines or any other tool that you may or may not have. You just need the proper jig or jigs. If I were doing what you are trying to do , I would draw it out and try to guess what would make a nice safe way to hold the piece in place and get the angles you want. Lots of scrap wood experiments,plenty of clamping arrangements and double stick tap. There is left hand and right hand and the first time around you most likely miss so you adjust and repeat until all sides match up then you can do it on the real wood. I've done similar thing, my guess is that you can get this done with the saw set at 90 degrees in both directions. Um maybe not I'm thinking this through thinking of using my RAS which has much more height adjustment than your saw. If the side angle is too steep then you either end up higher than the saws capacity or you'll bottom out on the deck so you'll possibly have to find the optimum angle to set the saw and in conjuction with an angled piece on the bottom get the proper angle for the slide cuts.. this whole process will probably occupy an entire day!
Theoretically it's possible. But using angled secondary fences on a sliding compound miter saw, and cutting angled and mitered pieces that small is very dangerous. Sorry, but I like my fingers. Just please, find another way.
“[Deleted]”
The material is solidly held in place in or on the jig using clamps or toggle type hold downs or something you make. It has to be in order to get a proper cut. I wouldn't attempt to do something like this if my hand was part of what was holding it in place. Properly done and everything secured there is no reason to have your hands anywhere near the cutting area. There are no fingers involved though if things aren't properly held you might get a face full! Personally I like it when it is a little bit scary because then you really pay attention.
Ummmm....no. Nope.
I think this can be done safely.
It will be hard to get absolute precision but it can be done.
You only need a 30 degree cut so you can set your saw to 30 degrees from vertical and straight and the angles will add up.
The first cut is easy - off the end of a long piece of sheet.
The second and third cuts will need a 30 degree angled fence and a hold-down of some sort.
As I understand it you are talking about the bevel cuts on the edges of the triangles, correct? And the triangles are to be cut from 1x4 (3/4 in. thick by 3-1/2 in. wide)? Those are pretty small pieces to handle at the miter saw. They'd be small at the table saw, too, but if you run the pieces standing on edge you could cut them. I would create a sled with a clamping arrangement to keep your fingers out of the way. Probably with a sacrifical clamping pad. I might consider making the sled to hold all four pieces at once.
The triangles in my sketch are 3/4 in. thick and 3-1/2 in. tall. It's evident that after the third bevel cut is made there's not much of a face left on the inside.
Maybe a fixture to run along the fence like this. Could also have a sled base to make it wider. Second image with clamping piece not shown. Screw the clamping piece in place or use trigger clamps or something. Depends on how many of these you want to make and how much time you have available.
My attempt yesterday to insert an illustrative photo after each paragraph failed, so I now try writing "PIC 1, PIC 2, etc." between paragraphs. The PIC numbers refer the the order in which the photos appear at the bottom. It seems there is a 5-photo limit for each post, so must do two posts. In second post, PIC 6 appears first.
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Thank you, wood persons, for all your efforts and understanding of my description. The safety cautions focussed the mind. I started with ten fingers. First project with a the new Kapex.
I went with my second plan, the vertical support block. First plan, ramp or shim was viable also, but it added an additional precision step in creating the shim.
I cut 3 triangles with square edges.
PIC 1
Cut an accurately square block, and stuck a triangle on it with double-stick tape. Bottoms of triangle and of block line up.
PIC 2
Lined the saw’s laser up with corner of triangle board's edge.
PIC 3
Clamped it, finger free.
PIC 4
The first cut. Did tiny sneaking up re-positionings of block relative to blade to get a sharp edge.
PIC 5
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Continued
Your photos didn't import. Try using the photo button on the bottom instead of dragging and dropping them into the comment as you type.
Dr. Strano,
I was worried about that. I inserted a pic after each paragraph to illustrate what I had said in each paragraph. I put in a total of 10 pics, using drag-drop. Did not work, right?
Question: Is there a way to achieve that using the “Add Attachment” button? So, can I alternate text-picture-text-picture, etc? Or would I have make 10 separate “Replies” to achieve that?
More basic question: It looks like more than one pic can be imported in a single post. Does the 3 MB max file size apply to each picture, or to the total file size of all pictures uploaded?
Domo
For starters, here is the final portrait:
Nice!
“[Deleted]”
Thank you. I use SketchUp for that sort of thing. Helps me to visualize things, too. For example it wasn't until I modeled out the sides for your tetrahderon that I realised the remaining inside face would be quite small.
{Part 2}
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Had to add anchor to block to pry triangle free of very strong tape, using reversed clamp.
PIC 6, PIC 7
Second cut. Recall that my pyramid will have open base (or top) so only two bevels per triangle.
PIC 8
Thar she is. A point-down, open top three-sided pyramid has symbolic meaning in Tibetan mysticism.
PIC 9
Or:
PIC 10
Joints came out pretty tight for a first try considering the limited ability to set a saw’s scale to tenths of a degree. Bevels need to be a tiny tiny fraction sharper to fit perfectly.
Thank you again for good brainstorming. Gave me confidence it could be done.
Terence T
{Part 3}
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Did micro-trimming of bevels' surfaces to make the angles a tiny fraction of a degree sharper. Pieces mate nicely now.
TT
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