I want to build a triangular pyramid as a decorative wall accessory. The pyramid base would be a triangle with one side about 30 inches long and the other two sides about 20 inches each and the pyramid would have a height of about 4-5 inches at its top point.
Do you know of any references that will guide me in such a design. I can use the trig functions to determine the exact lengths of the sides and the included angles of the three face triangles but I’m at a loss to determine how to compute the compound angles for the mating edges of each of the face triangles. I’m also at a loss in how to go about actually cutting the angles.
Would appreciate any leads.
Replies
Triangular pyramid
Just for information, but I think the proper name for the object is a tetrahedron. Sounds like a fun challenge. My trig is so far gone, don't believe I could be of much help.
I believe you'll find it's like building any mitered corner object. Example a square box ( 4) corners = 8 joints. 8 divided into 360 = 45. Same for tetrahedron 6 divided into 360 = 60. Base angle is another story, that will be dependent on base footprint and height. Have long since forgotten my trig. I would lay out the base on paper and use a combination Square to get height and a protractor to determine the angle from the base line to the desired height. You will have to measure from dead center of the base and you can find that with a compass. And you can bet the Engineers out there are busting a gut in laughter.Work Safe, Count to 10 when your done for the day !!
Bruce S.
I used Triangular Pyramid rather than tetrahedron because one of the sides of the base is going to be a lot longer than the other two sides are will equal each other in length.
A regular tetrahedron would be the classic 4-sided dice shape. A non-regular tetrahedron is the shape you're trying to build.
You're going to some really shallow miters, given the large base area and low vertex height.
Build it first with cardboard stock, see how that works out.
Good advice. Cardboard won't help much with the compound angles needed for the mating edges, but it will help me figure out the procedure for how to cut the pieces of the tablesaw. I'll be trying that.
Larry,
A couple of years ago there was an article in FWW featuring a NBSS technique that may have some use to you. In essence, they cut the inside of the outside shape...made a jig of the inside shape. Then used the miter guage and tilt of the saw blade to (and the jig) to make the cuts. It was a two cut process to make the sloped sides of the tray.
Cardboard won't help much with the compound angles needed for the mating edges..Oh yes it will... Just me though. When I made doors to fit OLD houses.. I used cardboard all the time. NOTHING was at the same angles it should be. Give it a try. Make you mock up. Set it down on a flat surface and check the angle with some sort of protractor. I have even used some coat hanger wire snipped off and bent to match the angles. (I don't think them new fangled plastic coat hangers will work though!)Anyway, it's amazing what you can do with hunks of stiff wire and cardboard!
Another link you may find helpfull.http://www.woodweb.com/cgi-bin/search/search.cgi
Larry, You may try the search engine on this site.
http://mathforum.org/
If that doesn't work, I think I have seen something covering this on woodweb.com.
The miter angle is one-half of the 'included' angle. Use trig to find the angle between the pieces, divide by two, and that is your miter angle.
As far as cutting them, use the miter saw to cut out the triangle shape, then use the table saw set to the appropriate miter angle, your miter fence, and complementary angled guide blocks to assist when cutting out the miter angles. That's if you don't have a sliding compound miter saw.
This would be a good point to include a picture or a diagram, because when I reread what I just wrote, it's gibberish.
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