When I began this project, a shoji lamp in the shape of the Archimedean rhombicosidodecahedron, toward the end of 2011, I wasn't sure I'd be successful. I also didn't imagine it would take more than two years to finish it, but life has its own pace.
Thinking about making the Pentafleur lamp
Where did that decade go? I actually began this project nearly ten years before I finally finished it. At that time, I made a model of a rhombicosidodecahedron, a polyhedron made up of 12 pentagons, 20 triangles, and 30 squares, from a Zometool kit. The model sat on my desk for a long time as I contemplated it.
For me, the rhombicosidodecahedron is one of the most beautiful polyhedra.
One night, I found myself staring at the rhombicosidodecahedron, trying to understand it better. I have books that tell me the angles and other essential facts of each of the common polyhedra, but something in me always wants to know these shapes more intimately than that. That night I had an epiphany.
It helped that my dodecahedron Luna lamp⩘ was sitting on my desk near the model of the rhombicosidodecahedron. A few feet away, in my line of sight, was the icosahedron-shaped Numinosity lamp⩘ frame that I was working on.
I realized that if the dodecahedron were exploded, moving each face outward until each vertex was as far from the two vertices it had originally touched as the length of one of the face sides, a rhombicosidodecahedron is revealed.
This means the dihedral angle between the pentagon and the square must be ½ the dihedral of the dodecahedron (116º 34'/2 = 58º17') + the 90º of the square = 148º17'.
So that left me wondering what the dihedral angle is between a triangle and a square in this shape. Then I saw that if I exploded the icosahedron in a similar way, the rhombicosidodecahedron was again revealed.
This means the dihedral angle must be ½ the dihedral of the icosahedron (138º11'/2 = 69º6') + the 90º of the square = 159º06'.
I know there must be a more elegant way of calculating these angles; however, my math abilities just aren't at that level, so I'm quite happy to have discovered this roundabout method. I feel like I own the rhombicosidodecahedron now, and from that moment on I looked forward to fashioning a lamp in that shape someday.
- Animation of dodecahderon and icosahedron to rhombicosidodecahedron transformation⩘
- ScienceU.com - basic info and Java model⩘
- ScienceU.com - pronunciation⩘
- Geometer's Sketchpad plan:
And then I put the project on hold for a couple of reasons. First, I needed to focus on remodeling our home and making furniture for it. Second, I knew my woodworking skills needed to be a lot better before I attempted to make a rhombicosidodecahedron.
Making the Pentafleur shoji lamp
Seven years later, in December 2011, I finally began working on this project again. What follows are the notes I made as I was working on it, as well as photos of many of the steps, and a few reflections on life itself that were provoked by the project.
There were many weekends of preparation work before I got to the point of these first photos: planing the maple that will make up the frame (because of the different angles between the pieces, the frame's triangles are slightly thicker than the squares and pentagons), initial sanding, cutting the strips on the table saw and bandsaw (the bandsaw for the angled edge), routing the rabbet into which the kumiko (the ¼″ × ¼″ inner frame that will hold the washi or rice paper … which is actually made from mulberry) will fit, and then a second sanding. The frame requires 100 feet of these rabbeted strips.
In the following photo, you can see the finished frame stock for the 12 pentagons and 30 squares (by the time I took this photo, I had already finished gluing up the 20 triangles, which you can see stacked behind my glue bottle). Of course, I spent some time tidying up before I took this photo; my workbench is typically in a state of chaos during assembly!
Next I created a gluing jig for each of the three components: triangle, square, and pentagon. I used ordinary prefinished pressboard shelving as the base because the finish is a kind of plastic that glue doesn't stick to well. Then I made reference shapes out of basswood, in this case 5″ on a side. Finally I screwed down maple holders for the three shapes, leaving gaps at the endpoints where the glue squeezes out.
In the following photo, you can see a closeup of my gluing jig, with one of each shape drying. I dry them long enough so that they won't separate, then pry the pieces out of the jig holders, and use a scraper and a sharp punch to scrape away any glue squeeze out. When they are completely dry, I sand them with my palm sander, which provides an initial glue joint test.
Here's the first assembled section. It's much more difficult than I had hoped it would be … or perhaps I should say that it is as difficult as I had feared. As much as I try to make perfect cuts and glue up perfect shapes, everything is always a little imprecise, and those imprecisions magnify quickly in a complex shape like this.
Still, it's encouraging to have gotten this far. I always despair a bit mid-project, thinking I'll never be able to successfully pull it off. But having been able to glue up a complete section means that there is at least the possibility that I'll be able to create a complete frame.
A few weekends later …
Finally had an opportunity to spend a few more hours in my shop. (Yes, work and life have been intense lately!) Thought I'd share a few more photos that show both the messy intensity that occurs during assembly—when the glue is dripping, it's all clamps on deck, and even my palm sander has been pressed into duty as a counterweight—and the more tranquil aftermath.
Then, after the chaos of assembly, harmony and order are restored to the benchtop.
Halfway point on the lamp body
Passed the halfway point on the lamp body today: 6 of 12 pentagons, 12 of 20 triangles and 15 of 30 squares. Maybe just maybe this thing is going to turn out okay. If it does, it's going to be a nice size for a standing lamp, 22″ in diameter.
One of the tools that is proving itself invaluable on this project is the Ridgid Oscillating Spindle Sander⩘ . The tilting table lets me make fine adjustments to the edges, and it's really easy to control my passes so that I can take off very fine amounts. While this doesn't rank up among the higher quality tools I enjoy using, it's good enough to get the job done. Here it is shown in the alternative belt sander configuration, but I use it primarily as a spindle sander.
I hit an impasse
Last weekend I was at the stage where the polyhedron was beginning to curve inward, and that's when the small imprecisions really caught up with me. I got to the point where I needed to glue in the final square between two pentagons in the top belt of shapes (the triangle and two squares beneath that square were also open), and everything was out of whack.
I'm now pretty sure that the dihedral angles I cut were a bit too shallow. This shape demands a precision measured in hundredths of a degree, which I could only approximate with the tools I had at the time, and since I cut all the dihedral angles using the same setting, my imprecision was magnified by the numbers of joints involved.
I ran big clamps from one side of the sphere to the other to try to pull the square and the pentagon into alignment. It seemed to be working when suddenly the leg of the pentagon glued to the square and the one along the top broke away from the rest of the pentagon, and there was no way I could think of to use clamps to pull everything back together again.
I felt fairly distraught and thought I should abandon this iteration of the project, start over, and try to achieve more precise dihedral angles using the Bridge City Toolworks AngleMaster⩘ I had recently acquired for just this sort of project. But it was quite disconcerting to walk away from the work of many months of weekends that I had already put into this lamp.
Garima and I were going to take a hike that afternoon, so I decided to get out in nature, clear my mind of the swirling emotions, and make my final decision upon return. While sitting on the shore of the reservoir, I lost myself in the beauty caused by the interplay of the sun, sand, reflections, and the crosshatching patterns of ripples from the shifting breeze.
In that gap, an idea popped into my mind: to use my picture frame strap clamps to try to pull the shape into alignment. I had picked up two of these clamps years ago, but had only ever used one of them. At times I had wondered if I'd been totally foolish to get and hold onto a second one, but it proved to be the answer to my dilemma this time. The lamp pulled into alignment and, with the addition of some spreader clamps inside, held in place until the glue dried properly. Now I'm fairly certain I'll be able to complete the polyhedron.
That said, I'm certainly not as happy with this project as I have been with others; too many of the joints aren't perfect, and I'm having to force things together. As imperfect as it is, though, it still may turn out well enough for a lamp in our living room, and this has been a very good, if somewhat painful, learning experience. If I ever create another one of these, I have several ideas for better ways to proceed, for example, instead of building the sphere up from the bottom, I'd create circumference bands running along the XYZ axes, and then fill in the remaining sections. I think that approach combined with more accurate angles would minimize the cumulative impact of imperfections.
Spent most of today in my shop
And what a day it was! The first aha! moment came when I began to close the top of the lamp. After the near failure of the previous weekend, it was a moment of giddiness.
It took some custom fitting, but by late afternoon I enjoyed the satisfaction of gluing in the last triangle. Then an hour or so of sanding, and the lamp body was finished. Of course, this is just the first step, and it will take many more months of weekends before this lamp is standing in our living room, but I think I'll take some time off this evening to savor the moment.
A year later, summer 2013
Shortly after I took the previous photo in the spring of 2012, we started having some serious wildfires here in Colorado. As you might imagine, that always freaks us out a bit, and prompts us to do more fire mitigation work around our home. This time around, we replaced all the wood chips in our garden beds and pathways around the house with pea gravel.
Thing about pea gravel is that it's really heavy! We moved tons of it one weekend with wheelbarrows and buckets. I wasn't surprised when every part of my body ached after that, but when one of my elbows remained sore to the point that it hurt to lift anything for several weeks after that, I suspected something might be seriously wrong. Still, I was stunned when a specialist I went to see told me the injury would take a year to heal. He was right, though, and while it was healing, I had to be careful not to re-injure it; among other things, that meant not being able to do woodworking.
Well, that year has passed, the healing has happened, and I finally got back into my shop about two months ago. Woo-hoo! I had a backlog of odds 'n ends house projects to catch up on, and then I spent several days doing a thorough "spring" cleaning of my shop, including adding some additional storage space (never enough!).
Then I was ready to start working on my passion again: shoji lamps; specifically, this current project. I finished the stand, which is made up of five thin pillars of maple with the electric cord running up inside one of them in a routed channel that is capped. Here's a photo of the lamp standing for the first time, near where it will go when finished. I was checking that the height is right. At 6½ feet tall, it fits the space perfectly (I had started with it a bit taller, but it didn't look right for the space, so I shortened it by several inches).
After that, I turned my attention to the internal components: a base in the shape of a pentagonal prism that fits into the bottom pentagon on the lamp face and is the electrical junction box. Then there are two smaller pentagonal prisms attached to the top of the base that hold the light bulb sockets and into which fit two frosted glass lamp covers. I worked on these components last weekend, then finished them this evening, after which I lit the new lamp for the first time.
This is, for me, such a magical moment when I'm making a lamp. I've been thinking about this particular lamp for many years, so it's even stronger this time: "Wow, it's really happening!"
Making the kumiko
The next step, another long one, is to make the 61 fitted kumiko, the latticework frames in the shape of pentagons, squares, and triangles that will hold the shoji paper (61 instead of 62 because one pentagon face holds the internal components).
The rhombicosidodecahedron has a relationship to three other polyhedra:
- The icosahedron, which is made up of 20 triangles.
- The dodecahedron, which is made up of 12 pentagons.
- And the Catalan deltoidal hexecontahedron, which is the dual of the rhombicosidodecahedron and is made up of 60 kite-shaped faces (deltoids).
The kumiko will trace the outline of all three of those other polyhedra.
A good 3-day weekend in the shop!
After putting the first two coats of finish on the lamp body and stand over the course of the first two days (sanding between coats took a crazy long time!), today I started working on the kumiko.
Most of the hours went into creating jigs to hold the pieces as I glue them up, and also into figuring out whether something new would work: this is the first time I'm going to try attaching the kumiko with magnets, specifically, 1/8" x 1/16" neodymium disc magnets⩘ . I drilled aligned holes into the front of the recessed rabbet in the frame and the back of the kumiko, and then glued in the discs using E-6000 glue⩘ . Again, I made little jigs so I could align the holes properly.
Here are my "fancy" scrap-wood jigs, with a square kumiko drying:
Note: I had some problems with the jigs for drilling the shallow holes for the magnets (the three little stepped maple pieces you can see in the photo). First, the guide holes rapidly got larger each time I drilled, no matter how precise I tried to be. Second, I had hoped to control the depth with a handmade vinyl tape stop collar on my ⅛″ drill bit, but that quickly deteriorated, too, so it was challenging to get the right depth. I have a variety of stop collars, but I never had one that small. I was able to remedy these issues by finding some ⅛″ drill bit guide bushings to insert into the maple jigs, and a clever ⅛″ no mar drill dit depth stop collar for the drill bit (SLIPSTOP Drill Bit Collars⩘ ). The stop collar incorporates a freely rotating polymer collar that eliminates wear friction when you hit the depth stop.
Post-project note: As I began preparing for my next project and keeping in mind how important precision is to a shape like this, I created a much better gluing jig. I was so happy with it that I decided to create a new gluing jig for this shape in case I decide to make another. I used the Geometer's Sketchpad app to create precise shape outlines, printed them on tough paper (tear resistant and waterproof), mounted the outlines on oak stair treads for stability, mounted acrylic above them so the glue won't stick, and then defined the boundaries with extruded aluminum. I added rubber feet to the jig so I could use both sides of the stair tread for the various gluing shapes. Should make it much easier to get the precision I need.
And it worked! I like this approach for a specific reason. I always want to be able to remove the kumiko in my lamps in case the shoji paper tears and needs to be replaced. For previous lamps, I had attached the kumiko with brass screws coming through from inside the frame. But the inside of this lamp is so beautiful that I decided I didn't want to have screws showing if you look inside, which will be easy to do by simply pulling off one of the magnetized kumiko.
The little disk magnetics are amazingly strong for their size, and hold the kumiko with no problem; in fact, they sort of snap into place as the magnets pull them in. Here you can see the magnets on the back of one of the pentagon-shaped kumiko, as well as on the lamp frame.
After I glue the kumiko initially, I drill holes through the joints and then reinforce them with "dowels" (bamboo toothpicks, actually, which are the perfect size of dowel for the ¼″ × ¼″ kumiko). For example, there are 12 of these dowels in each square-shaped kumiko. By the time the glue is fully dry, the kumiko are really strong, even though they look somewhat fragile.
In the following shot, taken later after I had oiled the kumiko and glued on the paper, you can see the ends of three of the dowels. You also can see my numbering system. I custom fit each kumiko to one place in the lamp in order to compensate for the small differences in sizing that emerge in a handmade object like this. To keep track, I use a Starret automatic center punch to create a pattern of holes on one edge of the kumiko, and a matching pattern on the face of the rabbet that will hold it. In this case, this kumiko is fitted to the third row's third square. The little notch on the left side helps me initially keep track of which side is the back.
The final step with the kumiko is that I pass them over a Sand-Flee drum sander⩘ to make their faces perfectly flat. To keep all the pieces of the kumiko pressed down with equal pressure as I pass it over the drum, I made a simple little jig that is basically just a flat piece of wood with a handle on the top and a hook lip in the back of the bottom to keep the kumiko moving forward over the spinning drum. I drilled a couple view holes in the jig so I can judge the alignment of the kumiko.
I have half of the 18″ drum covered with a medium abrasive cloth and the other half covered with fine; that way, I can make a couple passes over the medium to even everything up, immediately followed by a couple finishing passes over the fine.
Even though only 3 of 62 kumiko are done, this is a nice moment in the making of this lamp, because now every concept is proven and all the jigs are made. Now it's just a question of relaxing into the flow of making the rest of the kumiko.
Another good weekend!
The outlines created by the kumiko pattern are beginning to emerge. Takes an amazingly long time, though; I spent many hours in my shop on both Saturday and Sunday afternoon.
It's a strange thing to reflect upon: how we use time. We live in a time when incredibly complex objects are manufactured at blinding speeds with success measured by how many millions of these identical objects are sold within days or weeks, and by how many billions of dollars of profit this generates. In juxtaposition, I've spent so many hours over so many months working on this one relatively simple (at least compared to electronic gadgets) object.
The only way I can think of to measure the value of time in a world like this is to say something entirely subjective like "Another good weekend!"
Meditating on a snail's journey
After the last photo, I wasn't able to spend any time working on the lamp again for a few months due to the extreme rain and flooding in Colorado and its aftermath, which hit my community really hard. Finally, for the past couple of days I've been back in my shop actually working on the lamp again. Hours pass, and then Garima comes out and wants to see what I've been doing … and I don't have much to show her!
Each pentagon-shaped kumiko is made up of 15 pieces of ¼″ mahogany that I've sanded twice, precisely cut (and sometimes it takes me several tries to get the exact fit), glued up, and then let dry overnight. After that, I carefully drill 15 holes into the kumiko's joints, glue toothpick dowels into each, and then let that dry overnight, after which the kumiko are strong.
Next, using a little jig I made, I drill five shallow holes precisely in the back center of each side of the pentagon, and five aligning holes in the maple frame, glue magnets into each, and then let all of that dry overnight. Finally I sand each of the faces inside and out on a little drum sander. Similar story for the triangles and squares.
That all makes for a total of 705 pieces of mahogany to cut and glue up (one pentagon face holds the internal lamp components and connects to the stand); 705 holes to drill into the kumiko joints and glue dowels into; 470 holes to drill and fill with magnets; and finally, 122 faces to sand. Guess I shouldn't be surprised that it's taking so much time.
The wood in the kumiko is in addition to the 240 pieces of maple in the lamp frame, 23 pieces of maple in the stand, and another 22 pieces of maple in the internal lamp components.
Altogether, there will 990 pieces of maple and mahogany in this lamp, plus the 705 dowels, for a total of 1,695 pieces of wood. In addition, there will be 296 pieces of washi (paper) that I'll glue into place on the kumiko, which means there will be a total of 1,991 pieces of wood and paper material in the lamp when it's finished.
Finally, there are 570 pieces of hardware in the lamp, including the magnets, all the lamp parts, and the wood screws the hold all the main parts together. So the finished lamp will be comprised of more than 2,500 individual parts when it's finished!
Here's another way of looking at it: the project has involved a lot of different types of work including designing, calculating angles, building a variety of jigs, planing planks to the correct thickness, cutting strips lengthwise (including some crazy angles) with the table saw and bandsaw, crosscutting with power and hand miter saws, fine angle finishing with spindle and disc sanders, routing and drilling, gluing and clamping, sanding with power palm and drum sanders as well as by hand, and finishing.
For a glimpse of what all of this entails, here are two numbers: more than 1,200 holes drilled (with more than half of those 1/16″ holes drilled with a handheld electric drill lengthwise into ¼″ × ¼″ pieces of mahogany; in other words, very little room for error … thank goodness for the new Makita brushless drills, which are a bit lighter, so less fatiguing to use), and more than 2,000 miter cuts (with more than 1,400 of those cut by hand using my Nobex Proman miter saw⩘ , which is in the foreground in the following photo).
Wow, I'm kind of glad I didn't know these numbers before I began!
I almost can't believe it!
The holiday break presented me with lots of time to work on the lamp (lots!), and I finally finished the woodworking portion of this project. After imagining, thinking about, and working on it for so long, it was quite a satisfying moment to sit back and just look at it.
Next I'll oil the kumiko. Once they're dry, I'll start gluing on the paper. So close now!
Finishing the kumiko
This afternoon I oiled the kumiko with Mike Mahoney's utility oil finish⩘ , a wonderful penetrating walnut oil. Now they are drying under heat lamps. This oil takes a long time to dry thoroughly, but it has a nice fragrance and can be used without gloves or masks, which is especially welcome during the winter months when it's more challenging to ventilate. I'll leave the kumiko under the heat lamps for several days, perhaps a week, turning them morning and evening, and then they'll be ready for the final step, gluing on the washi.
Adding the washi
I'm using two types of paper in this lamp to achieve a subtle effect. Across the entire kumiko, I'm gluing on a lace paper called Mizutama, very white in color. Behind that, on all corner sections, I'm gluing on Furuta Chochin, a traditional, off-white, 100% kozo lantern paper made by Mrs. Sayoko Furuta, who has the title "National Living Treasure" and is from the Mino city region of Gifu prefecture, an area where highly praised papers have been made since the year 702. This makes those sections more translucent.
I've found this a bit challenging to capture in a photo; here are two that give an idea of what it looks like: one with light shining through the papers; another with light bouncing off them.
The end result is that the patterns of the other polyhedra related to this lamp are a bit more visible: the pentagons that make up the 12-sided dodecahedron, the triangles that make up the 20-sided icosahedron, and the kite shapes that make up the 60-sided deltoidal hexecontahedron.
Some photos of the finished lamp
Closeup - natural sunlight
Full view of lit standing lamp
And a peek inside the lamp
I've since swapped in LED lightbulbs, which are much cooler … not a bad idea in a lamp made with paper! The frosted lamp covers ended up being unnecessary.