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


508008
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/Calculator/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:

508019


And like this in use

508020
The dihedral angle between the planes is, as others have noted, 116.57o So you have to be able to cut the sides at half that, or 58.29o, which means setting your table saw blade to 31.7o. 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 72o.

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 (https://sawmillcreek.org/member.php?169877-Ted-Diehl)
https://sawmillcreek.org/images/statusicon/user-offline.pngMember



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."

[Steve Demuth]

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

Depends on what you think the project is. She is not trying to convince the admissions committee that she's an expert woodworker, but that she can bring energy, imagination, and skill to a project related to her desire to be an architect. So she could pitch it as: "Here's how I collaborated with an expert woodworker to make something that embodies the beauty-combined-with-construction that attracts me to architecture, and what I learned in the process."

[Steve Demuth]

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!

The interesting thing about this project is that while you need very good precision in execution to get a good result, there is actually only one shape of piece to construct, and that shape is completely defined by getting two cut angles (the half dihedral angle, and the included angle of a pentagon), and one linear measurement (the radius of the inscribed circle of the pentagon) right. So the problem from a woodworkers' point of view is simply how to create a cutting process or jig that does that repeatably. Once you understand that, it's actually it's a very simple woodworking problem.

[Michael Schuch]

Depends on what you think the project is. She is not trying to convince the admissions committee that she's an expert woodworker, but that she can bring energy, imagination, and skill to a project related to her desire to be an architect. So she could pitch it as: "Here's how I collaborated with an expert woodworker to make something that embodies the beauty-combined-with-construction that attracts me to architecture, and what I learned in the process."

I have an 18 yo daughter that starts her freshman classes in 2 days. I would never let her get away with coming to me with a project and then help her with it without her first researching and trying to come up with a plan first (You can ask her, she will drown you with examples and experiences... fondly, with a smile on her face). I believe that learning the process of how to solve a problem is more important than actually solving the problem.

I have helped enough kids in my field of expertise to know that teaching them how to work through a problem is a LOT more work on my part than just giving them a solution. To me, helping them learn is my responsibility as an adult... like my father, mother and other adults did with me when I was young. I think it is a disservice to a young adult to just give them a solution rather than challenging their brain to try to figure it out. Let her, or require her, to at least research what a dodechahdron is and the angles involved. Then challenge her to translate this knowledge to a 3 dimensional object... maybe make one herself out of paper?


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

My apologies if I was too blunt with my posts.

[Steve Demuth]

I have an 18 yo daughter that starts her freshman classes in 2 days. I would never let her get away with coming to me with a project and then help her with it without her first researching and trying to come up with a plan first (You can ask her, she will drown you with examples and experiences... fondly, with a smile on her face). I believe that learning the process of how to solve a problem is more important than actually solving the problem.

I have helped enough kids in my field of expertise to know that teaching them how to work through a problem is a LOT more work on my part than just giving them a solution. To me, helping them learn is my responsibility as an adult... like my father, mother and other adults did with me when I was young. I think it is a disservice to a young adult to just give them a solution rather than challenging their brain to try to figure it out. Let her, or require her, to at least research what a dodechahdron is and the angles involved. Then challenge her to translate this knowledge to a 3 dimensional object... maybe make one herself out of paper?


Congratulations to your daughter and you on her starting college. Watching our children take flight is the best possible reward for the project of raising them, which you've obviously thought through in detail.

I don't disagree with your approach, but I think it matters what you think the "project" is really about. In this case, the project is the college application, and the video or pictures of designing and building it is one component of the project. The twelve identical regular pentagons with a specific edge angle are one component the video project. Now, I obviously don't know enough about the OP's friend's daughter to say anything definitive about what she or hasn't done to prepare her request, but it's perfectly plausible that she has thought through what she wants to say (she certainly chose a dodecahedron for some reason, the OP didn't come up with that), and she's offered to be as much a part of the actual cutting and construction as he is comfortable with. If she hasn't thought through the "script" and probably already made a cardboard dodecahedron, and can't describe to her collaborator why that particular solid, and what that implies about the constituent shapes, then, I agree, she hasn't done her homework.

But I would not expect a student, unless they are already an experienced wood worker, to be in a position to think through the shop mechanics of making jig and safely cutting, and successfully gluing up, the pieces - any more than I would expect a woodworker to know the metallurgy and machining of brass hinges, when he or she selects them for a project. Sometimes an important part of the plan is getting the right help.

BTW, I am not a stranger to this business of balancing what you give your children vs what they must do to get it: my wife and I home educated two children from birth through age 18. One is now a professor at top-ranked national university and an internationally recognized author, and the other a research scientist at the hospital US News ranks #1 in the nation. The work is all theirs, of course, but I'd like to think we provided the right guidance along the way.

[Jimmy Harris]

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 made some hexagonal shelves recently. No where near as complex as a dodecahedron, but it taught me a few things.

One: You need to be absolutely precise with your miter saw angles. That means spending a lot of time setting up your saws and quadruple checking your math. Make a few out of scrap to make sure they complete the 360° round correctly. You don't need to make a 3D version, just a 2D made of square dowels will be fine.

Two: Understand your saws won't hold those angles. I don't care how expensive of a miter saw you have and how good you are with it, the blades will flex and vibrate just a hair, which will compound over multiple angles to whole thing off. 0.125° and 1/128" off will be very noticeable. It's not like most things you make with the miter saw where good enough is good enough. Good enough is not possible here. It's better to cut everything just a hair long and plane it back to fit. Which brings us to...

Three: Build a shooting board with a donkey's ear made for your angles. Spend an exorbitant amount of time making sure you get this angle precise. The whole point of your miter saw is to spend less time on the shooting board. You'll use the shooting board to actually cut your pieces by hand. I literally would sand one stroke at a time with 320 grit to get my angle precise. When you can trust this, the rest comes together much more easily.

Four: Don't use plywood. Plywood doesn't flex and you'll save yourself a lot of headache if you can use wood that you can flex and compress to fit. Also, since you'll be planning lots of edges, you'll save yourself a lot of time by not having to resharpen your plane blade every two minutes due to the plywood epoxy. Also, plan on using lots of wood filler. I'd opt for solid wood or MDF. Preferably solid wood.

Five: Make each piece to fit. You can use measurements or a reference piece to get your basic sizes, but you're going to want to shave every piece to within a thou to get it to fit. And because you won't be able to make any piece perfect, expect to compensate and sneak up on your joints by hand, one wispy shaving at a time.

Six: Label each panel with a number on the inside and label where and which panel attaches to it. And don't do your final planning and fitting until you're almost ready for glue up. Each piece will be off and unique. They won't be interchangeable, even though they'll all look identical.

Seven: Use blue tape instead of clamps when it comes time to glue it up. And glue up a full 360° rotation first, so that the tape holds everything together. Then come back later and glue in the remaining panels.

So, as you can see, this project is going to be a nightmare. That is, if you want it to look good. And it's going to take forever, even though it's small. But, if you take your time and don't rush it, it is doable.

[Steve Demuth]

I made some hexagonal shelves recently. No where near as complex as a dodecahedron, but it taught me a few things.
...
So, as you can see, this project is going to be a nightmare. That is, if you want it to look good. And it's going to take forever, even though it's small. But, if you take your time and don't rush it, it is doable.

I didn't find it a nightmare. There is after all only one shape to make, and you only need twelve of them, with a total of 60 final cuts. Your list correctly identifies the primary issue: you have to be able to set up the cuts accurately and precisely, and precisely replicate the 60 cuts and 12 pieces, because there is cumulative error potential at every mating surface. So you need tooling that takes advantage of the simplicity of the shape, and assures replicability. You're absolutely right about the tape instead of clamps (the dodecahedron is un-clampable by traditional clamps, period). As for the miter saw: if you are trying to make this with a miter saw, I agree it will be a nightmare. This is a job for a table saw, with a jig that guarantees that you establish each of three critical measurements (the dihedral half angle, the included angle of the pentagon, and the radius of the inscribed circle of the pentagon) exactly once, and then repeat using the same setup.

[Rich Engelhardt]

My apologies if I was too blunt with my posts.
No need for apologies to me.
Like I said - I was trying to think of a way to say it myself.

It's her presentation, she's the one that should be doing all the research.

[Michael Rutman]

I suggest you cheat. Cut the 11 of the 12 pentagons all to be the same size. Then screw hinges on each one. No need to worry about angles. At the end, using a different colored wood, cut the fillers using an angle tool. Anything that copies the angle will work fine. When you glue those on it will make the thing more stable.

The last pentagram, you can't screw it in, so the final edge is the base that it sits on, just glue it.

[Steven O Smith]

This guy has excellent detail on how to do things like this: https://www.spiralsbysteve.com/old-polyhedrons.php
Also see his Precision Polygon Jig.

Steve

[Randall J Cox]

Michael and Rich. Sorry, I did a poor job of explaining the situation. I'm not figuring it out for her, I'm doing the cutting. She came to me with some web sites that showed it. She has the info and has an idea how to make it from these sites but I have to tools to do it. Unfortunately her sites don't give enough info for anyone to make it (well, not me at least). That's when I started researching and ended up asking you all if anyone has made one. Lucky for us, Steve had. I have her making the heavy paper cutout of the pentagon, need it perfect I told her. I made the jig for my table saw as she doesn't have a table saw nor will I let her use mine - too dangerous.

And thank you Steve Demuth for that detailed example on how to, appreciate the time you put into your reply. Your info is what we are using to make this gizmo. Randy

[Steve Demuth]

Michael and Rich. Sorry, I did a poor job of explaining the situation. I'm not figuring it out for her, I'm doing the cutting. She came to me with some web sites that showed it. She has the info and has an idea how to make it from these sites but I have to tools to do it. Unfortunately her sites don't give enough info for anyone to make it (well, not me at least). That's when I started researching and ended up asking you all if anyone has made one. Lucky for us, Steve had. I have her making the heavy paper cutout of the pentagon, need it perfect I told her. I made the jig for my table saw as she doesn't have a table saw nor will I let her use mine - too dangerous.

And thank you Steve Demuth for that detailed example on how to, appreciate the time you put into your reply. Your info is what we are using to make this gizmo. Randy

A couple of things I'd suggest as you work with your student, given what you write above:

1. If she knows how to lay out and draw a "perfect" pentagon, consider building the jig I described, cutting the jig off with the angled blade, and then have her lay out her pentagon directly on the jig, using the saw edge as her reference point. Once she's done that, you can drill the center dowel.

2. I showed the 72 degree angle as fixed by two dowels, which works. But if you change the order of operations a bit, you can do something that's easier to "perfect" and more repeatable. Rough cut a pile of the pentagons you'll need (I'd make plenty of extra), then make the first cut on all of them. This one is by definition correct. Then instead of the two reference dowels, you can screw a block with slotted holes along the second reference line for alignment. Run a test pentagon all the way 'round the 4 additional sides, and see how close to perfectly regular you are, and adjust the block as needed. That'll allow you to zero in on a pentagon that is as close to perfect as your patience and supply of spare rough cuts permits. Again, the included angle of the pentagon is the one measurement you have to get dead nuts on. (The "radius" of the pentagon is right by definition - it just determines the size of the dodecahedron, which isn't a critical tolerance, as long as the jig makes all 12 identical, and the dihedral half angle leaves some room to fudge. If it's a couple tenths of degree too shallow upon assembly, you can just adjust the blade and recut all the pieces on the jig. If it's a couple of tenths steep, the resulting crack is on the inside of the dodecahedron and you can cover it up by using a space filling glue like epoxy or thick CA.

[Randall J Cox]

Thank you all for your comments, recommendations, etc. I have finally cut the 12 pentagons about as accurately as I'm ever going to get them. I had to quit using the pegs in the holes (Steve's method) as I knew I probably didn't get the holes drilled accurately enough. I wrapped tape around them to take up a tad of slack and probably had one thicker than the other. Anyway, after ruining the first two pentagons, gave it up for the day, went in and had a glass of wine! Knew I needed something to index the pentagons off of that did not move each time a cut was made and the pentagon was rotated around the glued in peg. Finally hit upon just drawing some parallel lines on the jig itself using my Starret ruler with protractor head, 108 degrees off the cut side of the jig. I then lined up the freshly cut side of the pentagon on the lines and, looking straight down, slowly moved my head to make the line disappear (with my eyes) so that I knew the edge was parallel to the line. Then locked it down so it could not move. Out of all the pentagons that I cut using this method, was only off maybe 1/32" in two to three of the 60 cuts over the length of the pentagons sides. And I know some of you are going to say that is not good enough. Guess I'll find out when I go to glue up this prototype. This has certainly been a challenge (and still is) and a humbling woodworking experience for someone who has been a woodworking hobbiest for the past 40 years. However, your comments and instructions and observations have been invaluable, as I was hoping they would be when I started. TBC Randy

[Tom M King]

This might be useful:

https://www.youtube.com/watch?v=HVN4QTCZgbA

[Jimmy Harris]

I didn't find it a nightmare. There is after all only one shape to make, and you only need twelve of them, with a total of 60 final cuts. Your list correctly identifies the primary issue: you have to be able to set up the cuts accurately and precisely, and precisely replicate the 60 cuts and 12 pieces, because there is cumulative error potential at every mating surface. So you need tooling that takes advantage of the simplicity of the shape, and assures replicability. You're absolutely right about the tape instead of clamps (the dodecahedron is un-clampable by traditional clamps, period). As for the miter saw: if you are trying to make this with a miter saw, I agree it will be a nightmare. This is a job for a table saw, with a jig that guarantees that you establish each of three critical measurements (the dihedral half angle, the included angle of the pentagon, and the radius of the inscribed circle of the pentagon) exactly once, and then repeat using the same setup.

That's good to know.

[Steve Demuth]

We'd love to see the results of your, and your student's work.

I'm not surprised about the problem with the dowels. The pentagon angle is the most critical element in getting this to work, and the fact that the reference edge you have to lock to is a knife-angle surface makes it even harder. Your solutions sounds like the right way for your situation.

[Randall J Cox]

I have the bottom 6 glued up and they turned and fit out much, much better than I thought they would. We're gluing up the top 5 tomorrow, leaving one off as this is going to be a cat box. I'll post some pics in a day or two, when done. Each time I cut a side to a pentagon, I put my protractor on it to see how accurate I was cutting. 95% were dead on. A couple I shaved off another hair to bring each angle to 108. I did it each cut as I didn't want to get cumulative errors as I cut. I am super pleased at how it all fits - so far. This whole exercise has ended up as a favor to the father of the girl. The only thing she has done so far is draw and cut out a couple of pentagons on heavy paper. I hear all of you that say "make her do it". She is not my daughter, so I defer to her father. Randy

PS the father just gave me a couple of 4x8 sheets of 3/4" oak plywood that he had cut at Lowes. The cuts are absolutely terrible, like its the same sawblade on their panel cutter that they started with over 25 years ago without replacing or sharpening. Almost criminal from a woodworking point of view. These $90 sheets are splintered back a full inch from the cuts!

[Randall J Cox]

OK it's finished, almost. Still needs some wood filler and sanding as the plywood is not great. This was just supposed to be the prototype but its now going to be the final product. The original plan was a prototype and two (!) finals. No way I'm building two more of these!! The young lady now realizes she did not know what she was really asking for - work wise. Even with three people installing the top 5 pentagons, I still needed to use my pin nailer to keep panels aligned as we added panels. Actually put them on and tweaked their fit all at once, then used pin nailer to keep them in place as glue dried as there was no practical way to clamp this. I plan to sand the knife edges just a tad so you can't get cut on them. Then give it to her and let her take it home and do the wood filler, sanding, sealer and painting. I will recommend grits, sanding sealer, etc. I did sand all the inside panels before we glued it up. She can now seal the inside as it will be a cat box. Again, thank you all for you recommendations and comments. Great forum and super help!! Randy

508553508554508555

[Tom M King]

Looks good, and good lessons all around, including for us. I'd frame that last picture and hang it in the shop. I expect it helped a lot not having to fit in that last piece.

[Steve Demuth]

I'd say it looks very good, notwithstanding the rough material you used. Great work.

[Randall J Cox]

I will say that I put all the crappy sides in and the best sides out, just in case. Glad I did that. Randy

[Christopher Charles]

Thanks for sharing the journey, very clear everyone learned from the journey and I too learned much. Hope the cat uses it-the cat box I built has been straight out ignored. Which is the way of cats I suppose.