When I was a child, my family had a classic Christmas tree topper in the form of a 3-D star made from perforated metal with clear plastic points. Somewhere along the way, I got rid of it and now I regret it, because it was beautiful.
Geometrically, it was a dodecahedron (12-sided solid) with clear plastic points on each edge, and a light bulb in the center.
I wanted to recreate that star, and with access to a laser cutter, it became possible to produce the 21st Century version, with frosted and mirrored acrylic plastic and color-changing LEDs.
This is a bit of a challenge for a number of reasons, mostly having to do with unusual angles preventing easy, attractive joinery.
Step 1: The Design, and a Lot of Head-Scratching
Warning: Geometry Zone!
The dodecahedron is one of the five Platonic Solids, defined as solids composed only of regular polyhedrons (i.e. having all sides and angles identical), and having the same number of faces meeting at each vertex. This makes the design somewhat easier, because there are only two shapes to consider: The faces and the points.
I designed this in Inkscape, a free vector design program and highly recommended. The pdf files can be opened and edited in Inkscape. The zip file contains all necessary files, in Inkscape's native svg format.
Since acrylic is expensive, and cardboard is cheap/free, I prototyped my design numerous times in cardboard, and decided that the dodecahedron somehow didn't look right. I wanted the points to be equilateral triangles, and since the faces of the dodecahedron are pentagonal, the points looked too small. I redesigned it to be an icosahedron (A 20-sided Platonic solid), since the sides of the icosahedron are also equilateral triangles, and that looked much better.
I decided on triangles with 2.5" sides, which will give a star about 7 or 8 inches high, depending on which set of points it's standing on.
I'm not good enough at geometry to figure out how wide the tab slots for the points should be, so I fiddled with the slot depth several times until I had a slot that was a snug fit for the 1/8" thick points.
Of course, it needs some kind of holes for the light to shine through, and a little ventilation for the light source never hurt, either. After considerable tinkering, I decided to cut a slender star pattern out of each face of the icosahedron; I had wanted to use a pattern of holes as my original star had, but the holes had looked better in metal than they did in plastic.
I've included the design files for both the dodecahedron and the icosahedron here. The points are the same for both, as both, coincidentally, have 30 edges.
Step 2: Figuring Out How to Actually Build It...
I probably could have designed tabs and slots into the face edges, but I wanted the star to have a clean appearance, so the reinforcement had to be internal. My first thought was small gussets placed internally in each joint; that didn't work out too well, because the gussets would have been too small.
An additional complication arose because I was using mirrored acrylic for the faces: I did not want to use the traditional solvent cement, because I was afraid it would ruin the silvering on the mirror parts.
I designed a simple jig, to be cut from cardboard, with the correct face angle. Bisecting the angle gave the angle from the faces to the points, and I cut a slot for aligning the points. Small cardboard tabs were glued to the jig to stabilize it on the faces.
Step 3: Beginning Construction
I cut the parts out of 1/8" acrylic on a Trotec 300 laser cutter. The red lines on the cut files are "cut first," the blue lines are "cut second." The faces are mirror acrylic, and the points are frosted clear acrylic. The mirror acrylic must be cut face down, to prevent dangerous reflections from the laser.
I had constructed my prototypes using hot-melt glue, but I knew that wouldn't be strong enough for the finished product. Since solvent cement was out because of the mirroring, it boiled down to epoxy or superglue. Superglue, because of it's strange (Krazy?) chemistry, has a tendency to fog clear plastics, so epoxy it was. I used 5-minute epoxy throughout.
Side note: Acrylic usually has a paper or plastic protective film on it. This film should not be removed until it's absolutely necessary. I did not remove the film from the faces until the icosahedron was completely assembled. When installing the points, I peeled back enough from the tabs to do the gluing, only completely removing it when the assembly was finished. (You don't want epoxy fingerprints on your project!)
Since I didn't have the patience to mill down my edges to a proper joinery angle, I had to join the parts in such a way that the internal edges were in contact. Obviously, this is an incredibly weak joint if just those edges are the only contact. My plan was to put epoxy fillets (no, not a cut of meat, in mechanical engineering, the filling of an interior corner) into the interior joints.
Each joint was first butted together flat and taped on the inside to form a "hinge," Then I placed epoxy in the corners, formed the correct angle with my jig, and held it with clothespins while the epoxy set.
Breaking down the design, and taking into account the need to access the interior for lighting purposes, the icosahedron can be viewed as two pentagonal caps - each having five faces - and a center ring made up of the remaining ten faces. This is the way I built it, intending to make one of the pentagonal caps removable, so I could change the lighting should it become necessary.
I built the caps first, which was fairly easy. I placed them open side down on a flat surface until the epoxy was hard (making sure my tape joints stayed together); this guaranteed they would be correct and symmetrical. I then beefed them up with a generous application of epoxy in the center joint, and set them upside down in a glass (to keep them straight) until the epoxy was set.
Step 4: Miserable Failure, Success on the Second Try
I knew I would need some internal reinforcement, especially where the removable cap was concerned, but my initial thought was to construct the ring first, then add two pentagonal reinforcement pieces on the sides. That didn't work out too well. Even the epoxy did not stick very well to the backs of the faces, since I also couldn't rough them up for better adhesion without destroying the silvering... So I got my ring of 10 faces almost completely built, and then it fell apart...
Never Give Up! Never Surrender!
Always have a Plan B, or C, or...
I had designed two sizes of pentagons to reinforce the interior; the smaller ones inside the caps, and the larger inside the ring. I roughed up the pentagons with sandpaper for better adhesion, then re-constructed the ring using one of the pentagons as a base, using lots of tape to hold it together, and lots of epoxy in each corner. This worked much better, and it was reasonably sturdy when the glue set. When the points are added later, they will provide much of the strength.
In the photo of the parts in step 1, you'll notice that one of the triangles in the ring was made open to aid installation of the lighting. The plan was to install a light socket on a smaller triangle and then glue the smaller triangle to the open triangle. Depending on how one installs lighting, that may not be necessary.
How to make the cap removable? I designed the laser-cut files for the pentagons with 1/4" holes in each side. These holes will be filled with small (1/4" diameter, 1/16" thick) magnets. The important thing here is to make sure all the magnets are installed with the same polarity. The only way to do this is test each magnet and verify that the magnet faces on the ring and cap are opposite polarities, so they'll grab each other.
The laser-cut holes are very slightly tapered, and this is useful for retaining the magnets. If the magnets are inserted from the "wide" side of the taper, they should be a very snug fit and can be further held in place with a drop of superglue. When I pressed them in, I did it with the acrylic on a flat surface so the face of the magnets would be flush with the face of the plastic.
After the glue was dry on the ring and first pentagon, I flipped the ring over and installed the second pentagon with it's magnets.
I installed the smaller pentagons (One with magnets) into the caps. The pentagons are sized so that when they are in place, they are flush with their respective parts.
Finally, I glued the cap without the magnets to the ring. This isn't hard because I now had the flat faces of the two internal pentagons to ues as joining surfaces. The cap with the magnets was temporarily set aside.
Step 5: Get the Point?
Once all those glue joints are dry, now I can install the points, which will provide much of the strength. First, I removed the masking from the faces. I peeled back enough of the masking on the points to be able to glue them (this way I can still hold them by the masked part, avoiding glue smears).
Neatness is essential here. I applied epoxy to both sides of the tabs, and into the "channel" between the faces of the icosahedron. After sliding the point into it's slot, I wiped away any excess glue with an alcohol-moistened rag, then slid my jig over the point to hold it at the correct angle till the epoxy had set.
The points around the opening will be a small challenge. They are glued to the main part, rather than the pentagonal cap. I temporarily installed the cap so alignment would be easier, but remember to only put epoxy on one side of these points, to avoid gluing the cap to the body.
I left the rest of the masking on the points until I was finished with the lighting phase.
Step 6: Electrifying!
Return of the Fail Whale!
We're now up to plan E, I think...
The original plan was a low-profile standard light socket with a small RGB LED "bulb" screwed into it. I had carefully measured my cardboard model and determined it would (barely) fit. Imagine my chagrin when I found out that there was no way, even with the most convoluted gymnastics, that I could fit a light bulb around the internal reinforcement! It was just too small, after all...
I'd been playing around with those inexpensive RGB LED strips from eBay (Link) for some time, and that provided the alternative. These come with a viariety of different controllers for many different effects, and are easy to work with. I chose one of the 24-key controllers, which gives 15 solid colors, adjustable brightness, and 4 color-changing effects (my favorite is the slow fade between colors). I was glad I had that open triangle, for now I could install a power jack for my RGB LED controller. I cut another triangle of black acrylic, and made two holes; one for the power jack and one for the small infrared sensor of my cheap eBay RGB controller.
I removed the case of the controller, both to make it less bulky and because I wanted to add a remote power jack on one face of the star. I removed the original power jack that was soldered to the board and substituted a jack that would screw into the hole I'd made in the face. The IR detector was already on a short wire, so I just led it out through another hole.
The RGB strip can be cut at 6-LED intervals, and I made three strips of six LEDs each, joined the ends, and arranged them into a sphere, hot-glued together. I soldered wires between them to join them all electrically, then connected the assembly to the controller board with 4 wires.
The sphere of LEDs was just the right size to gently squeeze and fit into the star. I screwed the black triangle containing the power jack and IR detector to the open face of the star and tested the thing with a 12-volt power adapter.
It looked beautiful, but there were some "hot spots" showing through the cutouts. I fixed that problem by the simple expedient of wrapping the LED sphere in a piece of Kleenex to give it some diffusion.
I don't know if this will ever wind up on a Christmas tree, because it looks just too cool as a tabletop accent lamp!
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