A breeze blew in
When I was working on the final steps of the Pentafleur⩘ lamp, which is in the shape of a rhombicosidodecahedron⩘ , I began thinking about a lamp in the shape of it's dual, the Catalan deltoidal hexecontahedron⩘ (a.k.a., trapezoidal hexecontahedron), which is made up of 60 deltoid-shaped faces.
I really love the deltoid shape; in fact, one of my earliest lamp shade projects was a pair of shoji screens in the shape of kites that I used as shades for a pair of bulbs hanging in the corners of a room. I still have one of them hanging in my workshop because its shape inspires me.
I like the way you can put three of these deltoids together to form an equilateral triangle, or five of them together to form a pentagon. Or 60 to form the deltoidal hexecontahedron! And, of course, I love the relationship the deltoidal hexecontahedron has to the icosahedron⩘ and dodecahedron⩘ .
I also like the way it contains decagons in its outline, and the playfulness of its 5-fold symmetry, as revealed in this illustration:
Designing the Windtraveler lamp
Pondering the numbers
Aha! It has been a few months since I finished the Pentafleur, and suddenly I find myself thinking about the Windtraveler more often. Guess it's time.
First step: figure out the numbers. I want to create a lamp similar in size to the Pentafleur, so the long edges should be 6″ in length. Since the ratio is 1.54:1, the short edges will be 3.9″ or just a sliver shy of 3-29/32″⩘ .
- Dihedral: 154.1°
Cut angle: 77.1° or 102.9°
- Between short and long edge: 87.0°
Cut angle: 43.5° or 136.5°
Using a 45° jig: 1.5° or 91.5°
- Between short edges: 118.2°
Cut angle: 59.1° or 120.9°
Using a 45° jig: 14.1° or 75.9°
- Between long edges: 67.8°
Cut angle: 33.9° or 146.1°
Using a 45° jig: 11.1° or 101.1°
- 60 faces
- 120 total shared edges
- 240 total frame edges: 120 long (6″) and 120 short (3.9″)
- 99 feet of frame
- 62 vertices:
12 with 5 shared edges meeting
20 with 3 shared edges meeting
30 with 4 shared edges meeting
Thinking about kumiko variations
The kumiko are the ¼″ × ¼″ inner frames that will hold the washi or rice paper (which is actually made from mulberry). The pattern created by the interplay between the kumiko and the frame in the first view reveals the hexakis icosahedron (a.k.a., the disdyakis triacontahedron⩘ ), a polyhedron made up of 120 faces. The pattern of the kumiko in the second view reveals the outline of the icosidodecahedron⩘ , and the interplay between the kumiko and frame in the second view reveals the Catalan pentakis dodecahedron⩘ (a.k.a., the kisdodecahedron) with sixty isosceles triangle faces.
Okay, now all that's left is to make it!
A while later
My friend Thomas and his daughter, Chiara, just helped me to see that you can also find the outline for the rhombic triacontahedron⩘ in the pattern revealed by the kumiko in the first view. I'm pretty sure this is the kumiko pattern I'll be using for this lamp, and the design I have in mind should very clearly reveal the rhombic triacontahedron. Thank you, Thomas and Chiara!
Things get underway
One thing I learned from the last project is that I need to be much more precise, beginning with the gluing jigs I create. So I started with Geometer's Sketchpad⩘ and created exact outlines for the frames and the kumiko, which I glued to the backside of acrylic sheets—they should provide a good surface to glue on.
I then mounted these on a section of oak stair thread, which should make a stable base. I added rubber feet so I can use both sides.
On one side I created the forms to glue up the deltoid-shaped frame pieces, two at a time. I used aluminum angle brackets aligned along the hairline outline. I figure that gives me fairly good tolerances.
On the other side I created the forms for the kumiko, the frames that will hold the washi (the shoji paper). The forms provide the flexibility to create either of the variations I mentioned previously (using horizontal or vertical cross pieces).
To make everything on the jigs even more impervious to the wood glue, I sprayed it all with Boeshield T-9⩘ .
My frame pieces will be ⅝″ wide on the outside face, with ¼″ rabbets cut into them for the kumiko, leaving ⅜″ showing. To adjust for that, I added ⅜″ UHMW strips that I get from Peachtree Woodworking⩘ to the aluminum angle brackets. (I keep the UHMW strips on hand for making jigs as they're cut to fit in standard miter slots.)
The kumiko forms also enable me to create the cross pieces of a traditional kite. I don't plan to use this variation, but it would be interesting to "weave" the kumiko cross pieces.
Dihedral angles: achieving better accuracy
Time to take the next step on the journey of (hopefully) achieving better accuracy. After realizing that I likely cut my dihedral angles too wide on the last project, I picked up a unique tool: the Bridge City Tools AngleMaster Pro⩘ . John Economaki, the master toolmaker who created Bridge City Tools, is in a league of his own, which one look at the AngleMaster Pro will certify.
When paired with a precise caliper (I'm using a Starrett 798⩘ ), the AngleMaster Pro provides insanely precise readings, much more precise than my tools, eyes, and hands can take advantage of. But I learned a lesson a long time ago: while I realistically can't get more accurate than 1/32″ with my cuts, even with my finest saw blades, I still think about my cuts in a more accurate way and keep in mind one of three adjectives as I cut—dead on, plus, or minus—and I think that might give me a slightly better opportunity to get it right.
In a similar way, while I really can't get more precise than 1° with my angles, I think keeping tenths of a degree in mind as I set my angles also might give me that better opportunity to get it right. If my dihedral angles are spot on, life will be great. If they're a hair wide, as I think they were with my previous project, then things will get out of whack really fast. If they're a hair narrow (which is what I'm aiming for), I should be good: the outside edges will align, and I can fill any hairline gaps on the inside edges.
Because the AngleMaster Pro's arms are magnetized, I've got the orange aluminum extrusion arm mounted on it so that I can more easily transfer the angle to my trusty Starrett 47 stainless steel sliding bevel gauge. I'll then use the bevel gauge to transfer the dihedral angle to my bandsaw for cutting the frame pieces.
Now it gets real. Next step is to cut enough correctly angled maple to end up with 100′ of frame pieces. I'll cut the dihedral angles on my bandsaw and the 90° cuts on my table saw. Last time I cut the rabbets using my table-mounted router, but this time I'm going to experiment with cutting them using my table saw, which I think might be faster and produce cleaner rabbets.
First cuts and more jig making
After cutting the first few pieces of frame pieces—using the table saw to cut the rabbets worked well—I spent a few hours making a miter jig to cut the angles into the frame pieces. The angles between the long pieces and between the long and short pieces are less than 45°, so I created a jig with 45° guides so that I can use my Nobex Proman to cut the angles.
[After working for a while with the pictured jig, which is made from pine, I decided I needed one that was even more precise and sturdy, so I made a second one, this time from oak and maple, and with more care getting the angles exactly right. The new jig made it much easier to get the cuts right, but it looks very similar to this one, so I'll leave this image up.]
Then I cut maple angle setters so I can accurately reproduce the correct angles … I'll need to cut 480 miters for the frame pieces alone: 120 for long:long joints, 120 for short:short joints, and 240 for short:long joints.
One tool that has been helpful is a 12″ disc sander. It enables me to finely adjust the length of the frame pieces I'm cutting.
Here's a shot of the first deltoid-shaped frame piece, as well as two more that are in my gluing jig. Seems to be working as intended.
I'm not ready to start gluing up the frame itself, but did a quick test of the first three deltoids, and they seem to fit pretty well. That's no guarantee—I'll need to glue up quite a bit of the frame before I know whether all the angles are good—but at least it's a promising start. This is an exciting moment because this is the first glimpse of the transition of the lamp to 3D.
With the cutting jig finished, the pace will now pick up.
I watched a video from Bridge City Tool Works the other day called Accuracy in Woodworking⩘ where they showed how a thousandth of an inch can make a difference. Whoa. That's just so far beyond my current level of skill. But there's no reason not to aim for the best I can do, right?! When I tested joining three deltoids together, I got pretty good results, but when I tested joining five deltoids together, it was evident that my dihedral angle was off.
So I adjusted my jigs by a fraction of a degree and used my Ridgid Oscillating Edge Belt / Spindle Sander⩘ to reset the angles on the deltoids I had already created. That got me to the point where things started to fit more nicely. Now I'm still not in the territory of thousands of an inch precision, but I'm close enough to get some decent results. I'm now pretty confident that this frame it going to come together without the kind of issues I encountered when I created the Pentafleur.
The latest test fitting with nine deltoids; not perfect, but fitting together fairly well without having to force things:
Years ago, when I was first starting on this path of making lamps, I wrote something about perfection that still holds true today:
My lamps aren't perfect. They're a bit crooked, there are little flaws here and there.
You know, I try to make each lamp as perfect as I am able to. But for me the more important qualities are the light itself, the warmth of the wood, the artistry of the paper, and the playfulness of the design.
And yes, I somehow also appreciate these little imperfections, I feel they are a part of what breathes life into the lamp.
Perhaps, in the end, perfection is found in imperfection. Maybe in the striving for perfection and always achieving imperfection, and in the acceptance, even celebration of that imperfection can be found true contentment.
Striving for precision
After I glue up each deltoid and allow the glue to set for 24 hours, I reinforce the joints with mini-dowels that are made from bamboo toothpicks (in my experience, the bamboo toothpicks seem to have a bit more resistance to breaking than the birch ones do).
My next step is to sand the dihedral angles to make the toothpick dowels flush and to ensure I end up with the right angle on each piece after the gluing up process.
As I mentioned perviously, I use a Ridgid Oscillating Edge Belt/Spindle Sander with a belt on to accomplish this. One challenge with this is that It's really difficult for me to set the table on the Ridgid to the exact angle I need (102.9°). If you look at the locking knob for the table, you can see why this is challenging: with one hand I'm holding the bevel gauge against the table and the sanding belt, with my other hand I'm fine tuning the angle of the table and trying to hold it steady, and with my third hand I'm trying to turn the knob to lock in the angle!
I tried this so many times, but could never get the angle exactly right. So I decided I needed to finally create a jig for making the fine adjustments to the table angle of this tool, something I had been thinking about on and off over the years. I also decided I'd try to make it out of only scrap wood as well as bits and pieces of hardware I had lying around in my shop. (I'm one of those people who, when I need to buy a bolt for some project, buys a few and tosses the extras in an odds 'n ends drawer or box. My shop has a lot of these drawers and boxes.)
I ended up making a mechanism that has rails that slide up and down in channels, uses table leg adjusters to set the height, and transmits the setting to the table via a homemade double hinge. Now, I'll be the first to admit that the whole thing is a bit crude—my friend Thomas, who is capable of making very precise parts and can even create working scale models of train engines, would probably make me do it over about a dozen times before calling it good enough—but hey, it works!
The precision pays off
Today I finished the first 30 deltoids, sanding all the edges on the oscillating belt sander, and then touching up the front and back faces with a palm sander. Then the moment of truth: dry assembling them to see if I got all the angles correct. I was very happy to find that all the attention to precision is paying off: everything fits together nicely without forcing anything.
If you read about my last project, the Pentafleur lamp, you'll know that the project nearly failed at one point because I had some slight imprecisions in my angles, so it's a big relief to have this shape coming together so well. Next step will be to actually glue these 30 pieces together, and then I'll start making the remaining 30. Long way to go, but it sure is good to know that I'm on the right track.
And now it gets real
After so long working in 2D space—cutting, sanding, routing, and gluing up flat lengths of wood into flat faces—it's so exciting, almost magical, when the 3D frame begins to take shape.
With 28 of the 60 deltoids glued in place, the initial ring is closed. I'm falling in love with this shape. I didn't think anything would ever top the shape of the Pentafleur lamp⩘ (a rhombicosidodecahedron) for me, but I'm starting to appreciate this shape even more. There is such purity and poetry in the way the shapes of the dodecahedron and icosahedron interweave.
Completing the frame
I've had a long stretch away from lampmaking. (I've been focused on emergency preparedness, including getting my ham radio license, KE0FHS⩘ , and figuring out how to put together my base station, mobile install, and so on.)
But now I'm back at my workbench, and the first thing I did was to assemble another third of the frame, including a triangular section of three deltoids that will be removable (attached with screws). That's where I'll create the base (or top, if it turns into a hanging lamp … still thinking about that). It went together pretty nicely, actually. The precision jigs are paying off. Of course, it's not perfect, but nothing I've ever done has been!
The next step was to cut the remaining pieces that will form the final 16 deltoids. My Nobex miter saw creates a bit of sawdust when I cut these pieces. One thing I haven't mentioned before is that I carefully collect all of this sawdust when it is from one type of wood.
I put all the collected sawdust through a strainer, and toss out the courser portion. What I end up is not actually dust, but very fine fibers. I save that, and then mix it with glue to make my own filler whenever there are small cosmetic gaps in between the pieces I'm gluing together. It works pretty well.