Dropped out of school and don't remember what I did learn. I need to build one of these lamps and can't figure out all the angles I need to make it. I know a pentagon is 36* cuts but keep confusing myself on the 3D part of this. Any help will be appreciated.
I was being a jerk, papadan. 42 is the The Answer to the Ultimate Question of Life, The Universe, and Everything, from the The Hitchhiker's Guide to the Galaxy.
Seriously though, that's a dodecahedron. A prism with 12 sides. The one you show is a regular dodecahedron. I did a web search for "angles to cut a regular dodecahedron" and it returned a number of results that might assist you. Sorry, that's about all my brain can handle
I feel your pain buddy. It's a complicated compound angle, but once you nail it, you can cut them all day. I could do the math, but then I'd have to charge you for the answer
This looks helpful:
There are probably more, but a lot of them look like a solid surface solution, not a frame.
They tried to teach me how to use a slide rule. I quit school and got a GED. I finally learned enough algebra to get my degree in Creative Writing then promptly forgot all I had learned about math.
The interior angles of a pentagon are 108 degrees and they are mitered at 54 degrees.
A problem arises with the the angle of the faces to each other I believe this is called the dihedral angle and is 116.56 degrees. (check me on this) It is critical. You don't have to miter it, you just have to have it in the exact middle at the top of your stock for your frames to line up properly. You will miter stock upside down. This way when you cut the miters right and left, the space for the third side automatically happens.
(this keeps you from having to figure out the compound miter.)
You should be able set up a jig and get all your pieces right and the same. Make lots of extra stock you will burn through it getting your angles correct.
once you have the angles solved, you will need to have some kind of joinery in the miter so they will stay together.
If I wanted one of these I probably would buy it. My woodworking club came up with a one board challenge and gave me a Walnut board to use. We have to even take the scrap back to show how much of the board we used and can only use 10% of any other wood and any hardware we want. I am either going to make a double hanging lamp or a single Dodehedaron table lamp with an Edison bulb. Just have to figure out how many pieces I can stretch this board into.
I want to that everyone who replied. in the 80s I taught my Son Algebra and Geometry, throughout my career I used math to design and build cranes and control systems. Radiation and Chemo have a way of destroying brain function I guess, because I have trouble with what day it is. I just write down notes on whatever I need to know now like these angles and diagrams of which way to hold the wood to cut them. LOL
I'm with ya papadan my math is almost nonexistant as well
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