How do I make a dodechahdron??

[Randall J Cox]

Back story. A friend of mine who knew I did woodworking asked me if I could make a dodechahedron for his "senior-in-HS" daughter who is applying to lots of colleges and wants to be an architect. She wants to help in whatever way she can in making it. Then she sends pics of us making it (I guess) to show she is interested in being an architect. Or something to that effect.

Anyway, I have watched every utube out there and done other internet searches trying to figure out the jig measurements. I did find out I have to set my table saw at 31.7 degrees for the mating angles and the outside angles on each pentagon are 108 (setting the fence to 18 degrees) on the 12 pentagon facets. She would like to have each pentagon at about 9", so this is obviously not a solid object. I played around on my table saw yesterday thinking I can figure this out with my very old geometry class knowledge (I'm 76) but so far just made more kindling for my cabin stove.

Has anybody out there ever made one? We plan to use either 5/8" or 3/4" oak or maple plywood plywood and I was going to use my biscuit joiner with the smallest biscuits, 0 I think. There's a couple of utube tutorials (that I watched over and over and over) that just don't give enough info for me to figure it out. If I can make just one pentagon with the right angles, then I just make 11 more and put it together. Will certainly make a prototype first out of lesser plywood given oak or maple plywood is $90 a sheet at Lowes. Know there are a lot of smart people out there.... Any help with any info on how to do this appreciated. Randy


dodechahedron.jpg
While typing this it just hit me that I should have her very carefully draw and cut out the size pentagon that she wants, then I will cut it out of plywood as I do know the correct angles. Then I can reverse engineer the jig to fit the pentagon to make the remaining pieces.... I find this challenging and still would like to know if someone has done these before and the jigs they used (in detail) or if there is any easier way to make these..

[andrew whicker]

Looks like the angle the planes meet at is 116.57 degrees. So you would have to set your table saw blade to half that (but using your table as reference so subtract 90 degrees somewhere along the way) while cutting your pentagon sides.

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

[Tom M King]

https://www.redcrab-software.com/en/...r/Dodecahedron

Zero margin for error. Less for anyone who has never built something even several factors simpler.

[Ted Diehl]

I think you can get vaccinated to protect you from that :-)

[Cameron Wood]

I'll bet Frank Howarth has done it.

http://www.frankmakes.com/

[Lee Schierer]

I would use painters tape on the joints and glue up three pieces to start. Then add one piece at a time to the glue up until it is complete.

[Mel Fulks]

Certainly there will be a picture in any of the dinosaur books !

[Edward Weber]

To keep it simple, I would cut a pentagon first, then cut the edge angles. For some, this is easier than cutting a complex angle all at once.
Pentagon, 5 sides at 72 degrees
Edge angles cut at 31.7 on the table saw

https://mathmonks.com/dodecahedron

[Steve Demuth]

Symmetry is your friend here. I did this a long time ago, and the jigs are long gone, so I can't post photos, but here is an outline of what I did.

My approach was to have a jig with exactly one setup, which means taking advantage of the symmetry of a pentagon about its center. I built a jig that could cut pentagons with angled sides from circles of flat wood large enough that you could inscribe the the pentagon you want in them.

The jig is a flat sled that fits entirely on the side of your saw table that the blade tilts toward. It's keyed to the table with a miter bar as with any sled. The sled is big enough that the circular cookies fit nicely on it.

The jig has a 1/4" dowel embedded in it at a distance from the blade equal to the distance from the center of your pentagon, to one of its points. So, roughly 4 1/2" in your case. This dowel is glued in.

The jig also has holes for two other 1/4" dowels, placed so they "lock in" one side of a pentagon whose adjacent side is the saw blade. These dowels have to be removable.

In use, you drill a 1/4 hole in the center of your circular blanks, partway through. Place the blank on the dowel on the jig, secure it well (you don't want it to try to rotate on the dowel when you're cutting) and cut one side. Rotate that side so it lines up with the two alignment dowel holes, place the dowels, and cut the second side. Rinse and repeat.

The jig looks like this:

Jig without blank.png


And like this in use

Jig with blank.png
The dihedral angle between the planes is, as others have noted, 116.57^o So you have to be able to cut the sides at half that, or 58.29^o, which means setting your table saw blade to 31.7^o. The closer you get this, the better your sides will fit, so it's worth some messing about to get it right. The more important thing, though, is that you get the angle of the locking dowels dead nuts on. You can assemble the thing if the dihedral cut leaves a gap. It plain won't go together if the pentagons aren't true regular pentagons, which means that angle has to spot on 72^o.

I would personally not use biscuits or dowels on the edges. Assemble the pieces into flat rollup (look up the wikipedia entry on dodecahedrons for what that looks like) using blue tape, or even something more permanent. Do a dry fit, and once you're satisfied, glue and roll up using a standard wood glue. It'll be more than strong enough for the purpose to which you're building it.

[Steve Demuth]

One other thing for your application: if your friend's daughter wants to get maximum mileage out of the video, have her explain as you're building how the use of a jig assures the identical pieces required for a regular Platonic solid, and how the use of the regularity of the pentagon vis-a-vis it's circumscribed circle means that getting the absolute regularity required is a matter of getting those two angles right. Just like in architecture, higher value (in this case, the fit and regularity of the Platonic solid) is a product of getting lower values (a couple of angles) right.

[Tim Janssen]

Ted Diehl
Member

Join DateOct 2016LocationGoodyear, AZPosts44

I think you can get vaccinated to protect you from that :-)

Wow, I didn't know that. Thanks

[Michael Schuch]

What is the point in you figuring it out for her? Have her do the research then come to you with how she thinks it should be built and the two of you can go from there.

[Dave Garrett]

I can recommend a piece of software called stella 4d. You can input some variables like edge length or circumfrence and it will output all other variables including dihedral angles etc.. It will help immensely in wrapping your head around some of the spatial data. there is no room for error here. also check out george hart. he is a sculptor/ mathematician who has made many wood (and other) polyhedral constructions. I believe he wrote a paper on the history of solid wood polyhedral models that you will want to check out if you are attempting this. Lots of time saving tips in there. good luck!

[Rich Engelhardt]

What is the point in you figuring it out for her? Have her do the research then come to you with how she thinks it should be built and the two of you can go from there.

+1
I was tring to think of a less direct way to put it - but - yeah..

[Tom M King]

Start with something many times simpler, like a pyramid, to see how easy it is not. I wonder how many people here giving advice have done something similar. There is zero room for error, which not only means that the measurements and angles have to be planned and laid our perfectly, but the tools have to have no errors built in to start with either.

I found the online calculators to be invaluable. https://www.blocklayer.com/pyramid-calculatoreng

I had to recut a roof panel on this one is spite of my best efforts, and that was accumulated error with just 8 cuts, plus it's not a closed volume. The roof is hinged so you can maintain the light in it. An old carpenter told me fifty years ago, "It's real easy to build something in your head."