# Easy-to-Make Polyhedral Kaleidoscopes

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Like a regular kaleidoscope, a polyhedral kaleidoscope (PK) uses mirrors to create a repeating pattern. But whereas a regular kaleidoscope creates flat patterns, a PK creates orb-like patterns. In addition, as the name implies, PKs are also very useful tools for recreating various polyhedra, and demonstrating their respective symmetries, and as such are useful for teaching spatial geometry. (Note: 2D photos and videos cannot do justice to what it's like to view objects in an actual PK; viewed live, with binocular vision, the results are fully dimensional and completely convincing.)

This Instructable describes how to easily make three different PKs. They have been designed to be easy to build, and don't require the use of any special tools, except a laser cutter. These three PKs, combined with their respective inserts (called fundamental domains), are capable of producing a wide variety of polyhedra, including all the Platonic solids, most of the Archimedean solids, most of the Catalan solids, and many other mirror-symmetric polyhedra. In addition, placing random shapes into a PK can result in the creation of very interesting and beautiful forms. As of this writing, nobody on the planet produces and sells PKs, so you have to make your own.

In order to function properly, a PK must be constructed with extreme precision. Historically, this has meant that the fabrication of a PK required considerable craft skills, as well as access to precision tools and machines. Consequently, very few people have ever seen--or even heard of--a polyhedral kaleidoscope. But the ever-increasing access to laser cutters and laser cutting services has created an opportunity for the do-it-yourselfer to create precision artifacts without being a skilled craftsperson. This instructable contains all the information, instructions, and cutting files you will need to easily create your own polyhedral kaleidoscope. Let's get started!

(see below)

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## Step 1: Materials

From WoodCraft.com:

Qty Part # Description

1 131406 Baltic Birch Plywood -- 1/4" x 12" x 30"

FromFirstSurfaceMirror.com: (choose mirror sizes based on which PKs you want to make)

Description Approx Price

For *532 PK: First Surface Acrylic Mirror -- 1/8" x 18" x 19.5" -- \$220

For *432 PK: First Surface Acrylic Mirror -- 1/8" x 10.5" x 20" -- \$121

For *332 PK: First Surface Acrylic Mirror -- 1/8" x 8" x 15" -- \$75

From McMaster.com: (Enter the part number in the "Find" box on their website)

Qty Part # Description

3 57455K71 Tapered Handle, Fluted, 1/4"-20 x 1/2" Insert 3-7/8" Handle Long

1 pk 7130K21 Standard Nylon Cable Tie, 17" Long, 50 lb Tensile Strength, White*

1 pk 92221A240 Flush Head Fanged Bolt with Nut, 1/4"-20 Thread, 3/4" Length

1 pk 91090A109 Large-Diameter Flat Washer, 1/4" Screw Size, 1-1/4" OD, .042" to .051" Thick**

The first surface mirror is by far the most expensive material in the PK. As such, you may be tempted to substitute regular (rear-surface) acrylic mirror as a cost-saving measure. Doing so would be a false economy, leading to vastly inferior results in the form of ghost images and misalignment in the image. You must use a first-surface mirror.

* Cable ties are also readily available at hardware stores. Be sure whatever ties you use are not wider than 0.2" or they won't fit in the slots on the PKs.

** The large-diameter flat washers are also available at hardware stores, where they can usually be purchased individually. You need one washer for each PK.

To make the fundamental domains to place inside the PKs you will need heavy duty cardstock in either A3 or 11x17 size.

From Amazon.com:

1 A3 Card Stock 300GSM - 100 sheets or

1 11x17 Card Stock 297GSM 250 sheet

## Step 2: Files for Laser Cutting

At the bottom of this step you will find the files used to cut the mirrors and mounts for the PK, and to cut the fundamental domains that go into the PKs. Currently, the files are all Adobe Illustrator files. (I'm working on providing SVG versions as well, which will be compatible with Inkscape. These should be available in a few days, so stay tuned.) Each of these files contains several layers. After unzipping, the files may be opened in Adobe Illustrator.

In order to make the files friendly for laser cutters that use color coding to indicate how lines are to be treated, the lines to be cut are red, the lines to be scored are blue, and the text to be rasterized is black. All lines are .001" thick.

What follows is a description of the contents of each file.

File: Mirrors & Mounts

This file contains cutting paths for the three different PKs. The three different PKs are distinguished by the use of *532, *432 and *332 (orbifold notation) in their layer names. These numbers represent the symmetries involved in each of the PKs.

*532 is the PK for polyhedra with the same symmetry as an icosahedron

*432 is the PK for polyhedra with the same symmetry as an octahedron

*332 is the PK for polyhedra with the same symmetry as a tetrahedron

(If you are only going to make one PK, I suggest you make the *532, since it has the most fundamental domains.)

There is one layer for each of the three PK's mirrors. The name of each layer includes the dimensions of the mirror required to make the mirrors in that layer. This information will help you when purchasing mirror stock. There is also a special combination layer that combines the *532 and *432 on a single mirror in order to be as efficient as possible in the use of mirror (however, as of 9/2019, combining the mirrors won't actually save you any money when ordering from FirstSurfaceMirror.com).

There is one layer for each of the three PK's handle mounts (to be cut out of plywood).

The layer *532_Domain_Guide_lc contains a minature version of the *532 PK. this is useful for forming materials (e.g. Sculpey) before placing them in the actual PK

Files: 532 Fundamental Domains, 432 Fundamental Domains, 332 Fundamental Domains

These files contain the cutting paths for the fundamental domains of the three PKs. Each of the files contain one layer for each fundamental domain. To allow for rapid cutting of sets of fundamental domains, each file also contains layers that combine the fundamental domains. These layers have the word "group" in their name. These group layers have been laid out to fit on both A3 and 11"x17" cardstock.

File: All Files.zip This file contains all 4 files in one zip file.

Here are the cutting files:

## Step 3: Cut the Mirrors and Plywood Handle

For this step, you will need to use a laser cutter or find an online laser cutting service (search "laser cutting service" on Google to find services nearby). If you have never used a laser cutter before, I encourage you to find a maker space and learn how to use this easy-to-use and handy machine.

All the files required to cut the mirrors and the plywood with a laser-cutter can be found at the end of step 2.

IMPORTANT: When cutting the mirrors, make sure that you orient the mirror so that the silvered side is facing up. Although both sides of the acrylic are reflective, only one side has the silver coating. In order to avoid double reflections, you must have the silvered side facing into the kaleidoscope, so it is very important that you properly determine which side is which. You can determine this is by holding something against the surface and seeing whether or not there is a gap between it and its reflection (see photos below). The side without the gap is the silvered side, and that is the side that should face up in the laser cutter.

Always handle the mirrors with care. The most reflective side is particularly vulnerable to scratching. The protective plastic should not be removed until you are ready to assemble the mirrors.

## Step 4: Assemble the Mirrors

Although the kaleidoscope can be assembled by one person, the process will will be easier if you have set of hands to help you.

Before assembling the mirrors, remove the protective plastic from both sides, and gently clean the silvered side of each mirror. (The silvered side must go on the inside of the kaleidoscope, which will make it harder to clean once the kaleidoscope is assembled.) I recommend using a microfiber cleaning cloth for this.

Use the indents in the mirrors to align them as you put them together, being sure to face the silvered sides inward. Once you have positioned the mirrors, secure them with the cable ties. Take note of the four sets of slots (next to the pointy edges sticking out) along the edges of the mirrors. The cable ties should pass through these slots as they wrap around the mirrors. Start by securing the cable ties on the large end of the kaleidoscope, and then secure the small end. Do not add the two central cable ties at this time.

Make sure the ties are pulled tight to keep the mirrors in position.

Note: For the large end, you will probably need to attach two cable ties together.

## Step 5: Create the Handle Assembly

1. Insert the bolt through the smaller hole in one of the wood panels.
2. Flip the panel and add the washer.
3. Screw the handle onto the bolt.
4. Put the two wooden panels together, and hold them in alignment as you perform the next step.

Note: the purpose of the second wood panel is to create clearance for the head of the bolt. The two panels will be held in alignment once they are attached to the kaleidoscope (in the next step).

## Step 6: Attach the Handle Assembly to the Kaleidoscope

The handle assembly is attached to the widest mirror of the kaleidoscope using two sets of cable ties. These cable ties also help hold the kaleidoscope together.

Align the tabs on the wooden panels with the pointy tabs on the kaleidoscope, and run the cable ties through the slots next to the tabs. Tighten the cable ties around the kaleidoscope and the handle as shown in the photos.

Once all four sets of cable ties have been fully tightened, trim off their ends.

## Step 7: Cut the Fundamental Domains

For this step, you will also need to use a laser cutter or find an online laser cutting service. If you have limited access to a laser cutter, you might find it more efficient to cut the fundamental domains at the same time as the mirrors and the handle mounts.

All the files required to cut the fundamental domains can be found at the end of step 2.

The fundamental domains should be made out of heavy duty cardstock in either A3 or 11x17 size. Sources for this cardstock are listed at the end of step 1.

## Step 8: Fold the Fundamental Domains

Once you have cut the domains, you can fold them by simply following the score lines. It's a good idea to individually crease each fold completely in order to overcome the bending resistance of the paper. For the simpler domains, there is no need to tape them; they will naturally settle into the proper form when placed in the kaleidoscope. For the more complex domains, you will need to tape parts of them in order to help maintain their shape.

Now it's time to slide your domains into the kaleidoscope and experience the magic!

Place the domain onto the larger mirror with the domain's identifying text facing the mirror. Orient the the narrow "tails" toward the small end of the kaleidoscope, and then slowly tip the kaleidoscope until the domain slides down to the small end. To help the domain get settled into place, you can pull the tails protruding from the narrow end of the kaleidoscope.

To remove a domain from the kaleidoscope, gently tap on the protruding tails of the domain.

## Step 9: Be Creative!

Experiment with coloring the fundamental domains to emphasize certain symmetries or to create interesting patterns. And don't limit yourself to using only the provided domains. Create different shapes and test them in the kaleidoscope. You can also insert all kind of objects and observe the shapes that result.

I hope you enjoy making, learning, and playing out with your polyhedral kaleidoscopes! Please share your results and any new ideas you have with the rest of us in the comments section below.

## Step 10: Acknowlegements

I am deeply indebted to Mathieu Penot, who provided invaluable assistance in creating this instructable, including producing the video.

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## 21 Discussions

Can you tell me why you need to cut the mirror in the ‘castle wall’ design?
why can you cut it straight and glue it together with either epoxy or a glue gun?
if the mirror edges were straight it would save the cost of the laser cutter and more people might try giving it a go, with junk shop mirrors.
i understand that you are going it like this so the parts line up, but could you 3D print something that holds the angle you need that you glue on the outside?

love the eye ball bit of the video!!

3 replies

Good questions!

My design goal was to ensure that the mirrors were accurately positioned (which is critically important), while eliminating the need for the fabricator to have any crafting skills. Thanks to products like the Glowforge, laser cutters are starting to become more commonly available to educators and the general public. I am hopeful that this this trend will continue.

I made a set of PKs for myself using the method you describe (straight edges with glue gun), and the process was very fussy.

By "Junk shop mirrors" I guess you mean glass mirror. That will require extremely accurate glass cutting skill, and would only give a somewhat reasonable result if you used the very thin mirror used in inexpensive mirrors (in order to minimize ghosting). Very thin mirror breaks very easily, resulting in a very fragile kaleidoscope, which would not be appropriate as a teaching tool.

Custom 3D-printed fittings might be an interesting direction to pursue, but beside requiring crafting skills to attach, there is the problem of gluing. Plastics are very challenging materials to glue, especially when trying to attach them to non-plastics.

Thanks for taking the time to reply to my question.
Living in rural Ireland later cutters are not exactly on your doorstep, so was looking for a way to build one without the need for one!!
Sorry if they are in the instructions but what are the exact angles you need?
Great build.

Another thought popped into my alleged mind. Many moons ago, I constructed a laser show device which required first surface mirrors to prevent the previously noted double reflections. The solution was to use ordinary acrylic mirrors, but to remove the painted surface on the back, using "gentle" paint remover. I think I used an organic or "green" paint remover, which resulted in the reflective coating being visible on both sides. The rear surface became the front surface and worked great.

I've also discovered that the big-box store sells self-adhesive mirror film, but in 17" widths!

Impressive results.

You're correct about the pricey mirror material! US\$350 for a single piece is astonishing.

I'm considering to create the mirror structure from front surface glass mirror salvaged from old projection televisions. It means a trickier assembly, but the price is much easier to handle. Of course, handling something so large made of glass has its own risks, but those can also be managed.

One note of caution. If the masking on the mirrors is plastic, it's probably vinyl. When vinyl is cut with a laser, dangerous chlorine gas is released. It corrodes almost instantly the equipment as well as any nearby lungs. It's probably a good idea to remove the vinyl when cutting. If it's necessary to protect the mirror, paper transfer tape from vinyl cutting supplies will do a good job and reduce the hazards.

4 replies

Actually, the price of the mirror for the largest kaleidoscope is \$220.

I see nothing on the web mentioning any problems with leaving the film on when laser cutting, and howtolaser.com specifically recommends leaving it on (scroll down to "Material Preparation". If you can find a reference that supports your fear that the film is made of vinyl, please share it with us.

I see the dimensions in the list have been changed to match the smaller, lower cost mirror. That's good to see. I've put out some feelers on the laser forum to pin down the vinyl matter. I have "ordinary" acrylic with masking and I'm going to run the green flame test on the material to see if it is vinyl.

I originally suggested a mirror size large enough to make two of the kaleidoscopes, assuming that it would reduce costs, but it ends up it does not; ordering separate mirrors costs essentially the same amount. I look forward to the results of your test!

An update on the vinyl question, although it is somewhat inconclusive. I have a piece of acrylic from the local big-box store, which is masked with a sheet of plastic on both sides. Using the test suggested here: https://en.wikipedia.org/wiki/Beilstein_test
I first used PVC pipe as a sample reference. As it is polyVINYLchloride, it's certainly going to qualify. The test resulted in a bright green flame.

The plastic sheet did not display any green, through three tests, suggesting that this particular portion of masking plastic is not vinyl based.

Even though I have a few sheets of first surface glass mirrors, I really like your suggestion to add mirror film to ordinary acrylic sheet as an economy measure to create these amazing works of art. If I'm able to accomplish something approaching your results, I'll be sure to post.

Very interested in this. Have you considered using window solar tinting film (over black cardstock/ply) as a first surface mirror replacement ?
You see this in many inifinite mirror instructables.

You would get a dimmer reflection which might be a visual problem, or benefit, as the domains would stand out a bit.
But the cost would be considerably lower.

That's an interesting idea! However, I wouldn't think you'd get very good results adding the film to cardstock or plywood, since they are not very smooth. But applying the film to acrylic sheet might work quite well if you use a film with high reflectivity. Perhaps even just using mirrored mylar with a spray adhesive. You might even be able to apply the film before laser cutting, so that it all cuts together. If you give it a try please report back with the results.

This is very cool, but why anyone would pay hundreds of dollars to make it is beyond me. Maybe for a classroom if you know someone who will give you a discount on the mirrors. I think your definition of easy somewhat varies from that of the general public as well. And even if it is easy compared to other instructions, it’s still fussy and labor intensive and the cost is extremely prohibitive. It amounts to buying an expensive kit with all the parts cut out for you, which you must then assemble, piece by piece. Like an IKEA loft bed, only more precise and you have to cut the pieces yourself.

Thanks for your feedback. Yes, it is indeed hard to appreciate the value of something one has never experienced. And they are not for everyone. But for the person who appreciates what these kaleidoscopes can do, and the fact that they are not available anywhere else, it might well be worth ~\$250 to have such a tool.

Could you please be more specific about where the construction process appears to be fussy and labor intensive? My intention was to have the laser do all the fussy work. Assembling the kaleidoscopes is certainly easier with second set of hands, but requires no craft skills.

Years ago I made a kaleidoscope, it was not as instructional as yours, more seat of the pants. I used a pvc pipe as the mechanism to keep the pieces of glass together. It made the glass more stable and protected and I decorated the pvc as part of my projects. I don't know if it would help with your project but for the people who don't need the specific shapes in the kaleidoscope it might be easier. I found an old kaleidoscope that I made but didn't decorate. Sorry about the dust, I found it in my garage.

Upon reflection, this is an awesome variation of a traditional kalidescope!

nice work, with the project, video, and write-up. i know from experience that some companies that sell sheets of plywood and plexi/plastic often have leftover pieces from full sheet cuts that they sell at sort of a discount. have never asked about mirror acrylic before. and your hint about local hackerspace did remind me of one in town so thanks for that.

What a wonderful build! Thanks for sharing. Looking forward to trying this as a family project. Cheers.

A great tweak on the classic! Thank you for sharing your work :-)