Class Activity: Kaleidocycles

In the evenings, while I devour Netflix, I’ll often have something engaging but brain numbing to help wind down. Generally it’s knitting or sewing, but recently it’s been ‘adult’ colouring in. Colouring in the latest relaxation-rage, dontcha know, and I’ve got the bug: I’ve spent far too many nights trawling through Pinterest for colouring pages (Islamic Geometry! Art Noveau! Zentangles! damnit!) and too much money splurging on Sharpies. Anyway, I discovered Hattifant’s Kaleidocycles and now I’m obsessed. Following a night spent colouring and constructing these geometric wonders, I found myself with unusually small Year 9 class to occupy. They’re easy to colour and construct, making them an ideal time filler and the kids flip out when they see the rotation. I bet there’s a decent Maths-last-lesson-on-a-Friday-afternoon in there.

M.C. Escher Kaleidocycle
Kaleidocycles = awesome

Kaleidocycles are paper tetrahedron rings which rotate endlessly and reveal, kaleidoscope-like, patterns (they are sometimes called ‘hexa flexagons’ or similar). They were a thing in the 70’s when the M.C. Escher Kaleidocycle book first came out. The most popular kind feature six tetrahedron segments (hexagonal) but as you can see at – the brilliant but under-designed geometric paper craft site – Korthal Saltes, there are multiple types. There is geometry involved which is fascinating – check out Mathematische-Basteleien’s Kaleidocyle Page or this PDF report on the mathematics – and the colouring is fun, but to tell you the truth, it’s all about how awesome they look when you rotate them. However, consider the possibilities for the classroom, besides a time filler activity. Obviously there’s a place as a maths activity, perhaps in compass skills. Consider what you could put on the template: vocabulary, equations, times tables, cheat sheet notes or a calendar:

Kaleidocycle Calendar: now that's cool
Kaleidocycle Calendar

How about flags for a geography assignment?

Kaleidocycles featuring flags

On this Wiki, a teacher has set a geography assignment whereby students create a Foldplay (see below) kaleidocycle to demonstrate their learning. Meanwhile, you could even make one out of fabric as per Ann The Gran’s machine embroidered felt one, this one out of quilting strips on Digipics’s Photography Weblog and this origami one out of felt.

Ann The Gran's felt kaleidocycles
Ann The Gran’s felt kaleidocycles

Ready to Colour/Construct Printables

There are hundreds of designs out there, as a quick Google Image search for ‘kaleidocycles’ will show. It is also relatively easy to design your own. These were worth a mention: Hattifant’s Flower Kaleidocycle was my first: print the printable (JPG), colour it in, and then follow the folding instructions on the website. There’s also a good YouTube instruction video. She also has a stripey animal one which some of my students didn’t mind, and links to a Frozen and superhero pre-coloured one.

Hallifant's Mandala Kaleidocycle: pretty!
Hallifant’s Mandala Kaleidocycle: pretty!

These stylish stripey kaleidocycles by Minieco can easily be printed from this PDF:

Minieco stylish kaleidocycle
Minieco stylish kaleidocycle

This coloured coral one by artist Eveline Kolijn is most spectacularly pretty:

Coral kaleidocycle by Eveline Kolijn
Coral kaleidocycle by Eveline Kolijn

I really liked the beautiful geometric design on this kaleidocycle from French site  ‘Math@ctivitie 3D’, but the painfully poorly designed website is just awful, so just download the template here without visiting it:

Math@ctivitie 3D
Math@ctivitie 3D Kaleidocycle

I had a go at creating some of my own; click on the image to download and print away:

Diamonds and Sunrays kaleidocycle
Squares and Sunrays kaleidocycle
Squares and Sunrays kaleidocycle
Art Deco Kaleidocycle
Art Deco Kaleidocycle

The stars and rays look quite pretty when it rotates:

Diamond and sunrays kaleidocycle
Diamond and sunrays kaleidocycle

If you make one of these, I’d love it if you could send a photo to see how they turned out! Email

Design Your Own


Foldplay Mandala Kaleidoscope
Foldplay Mandala Kaleidoscope

A quick Google search for kaleidocycles will bring you to the granddaddy of awesomeness that is Foldplay. Plug in your photos and Foldplay will make a kaleidocycle printable for you. I made this one from a collection of mandala colouring images I had saved: it took me a minute. You could add photos and diagrams of the topics you’re creating; or your students could choose which pictures they wanted to make their own.


Blank templates are easy enough to find, including this PDF from Minieco. Most are designed using tabs. Here is a template I drew up quickly:

Blank Kaleidocycle Template - 'net' method
Blank Kaleidocycle Template – ‘net’ method

And again without the fold lines:

Blank Kaleidocycle Template sans fold lines

Click on the thumbnails to open and save the larger JPG.

Folding Method

This YouTube video shows how to draw up and fold a kaleidocycle from scratch.

Pencil and Compass

If you’re going to deliver a maths lesson on compass and protractor skills, start your planning at Mathematische-Basteleien. Meanwhile this Instructable on Kaleidocycles shows you how to draw up a template from scratch. At first I thought I could get the correct dimensions of the base diamond by splitting a hexagon equally in three: this would make the individual diamonds easy to design by using a compass. However it turns out that kaleidocycles designed using diamonds of 60 and 120 degrees are too tight to rotate. Instead, the angles of the kaleidocycle tetrahedrons are slightly squatter:

Angles of the tetrahedron diamonds
Angles of the tetrahedron diamonds

Keep this in mind if you are drawing them using a compass and ruler (which I initially did).

Construction Tips

I found that ‘scoring’ the folds before folding made the kaleidocycles’ rotation smoother. The best kaleidocycles I made were printed on glossy photo paper which was 180gsm. the 220gsm card at school was somewhat clunkier. Paper glue seems to ‘grab’ the photo paper, making the bonds stronger: otherwise you generally need to rely on double sided tape to hold the joins. If you’re looking for construction instructions, I still quite like Hattifant’s Kaleidocycle page and the YouTube instruction video. Most kaleidocycle templates – including those on Foldplay – use ‘tabs’ to join the ring. I find that these tabs don’t quite cut it and often the ring breaks after multiple rotations. An alternative is to create a template with an extra row and column of triangles/diamonds to ‘glue over’ the opposing faces as per the templates on Math N Stuff (they call it the ‘net’ method):

Alternative template method which doesn't rely on 'tabs'
Alternative template method which doesn’t rely on ‘tabs’

The templates I provided above use this method.


I’d seriously like to get a copy of the M.C. Escher Kaleidocycles Book by Doris Wallace: if anyone spots it in Australia, let me know 🙂


Mostly because I could, I had a go making a fabric kaleidocycle:

It was pretty straight forward and quite successful! It worked quite well: if you make one I’d suggest avoiding packing the tetrahedron too tightly.


Recycling your teaching resources … literally.

Or: What I Did With 15,000 Sheets of Used A4 Paper and 100 Used Overhead Transparencies.

This summer has been the Summer of My Printer.

I bought it three or four years ago, attracted by the high efficiency, low running costs and auto feeder. After the joyful discovery that my it can scan and convert to PDF using the auto feeder, I saw a way to excavate the mountain of teaching resources (upwards of 20 lever-arch folders), inherited from an experienced retired English teacher. My two-bay desk had squeezed out to three-bays and was piled high: much to the polite chagrin of my Co-ordinator, who is a goddess of organisation. Due to a jaw injury, I faced several weeks during my summer break interned in my living room so I decided to start the laborious process of scanning those resources worth keeping. 20 lever arch folders packed full of A4 paper were reduced to four smaller folders. My Co-ordinator is going to be beside herself.

Excluding paper printed only on one side (over 15 standard reams worth, to be reused), I was left with four or five shopping bags full of useless paper, a thousand sheet protectors and a hundred plastic overhead transparencies. Oh what to do with all of that? Guess I could use it for kindling, or put it in the ‘recycling’ bin? Put it in compost?

Hey, why not take useless paper and make more paper!

Ever made recycled paper? It is so squishy messy and fun, I recommend everyone at some point in their life should try it. Wait till you are squishing your hands through strangely clean feeling paper pulp; sprinkling glitter and making confetti; being completely damp and wet from drips; and spray jetting the random particles of dried paper pulp which somehow manage to get everywhere. I’d always wanted to try it: as a kid I even got so far as getting my father to make me a frame and to pulping some paper with my mother’s old blender, but never got around to actually making the paper.

Google ‘how to make paper’ and you’ll find dozens of instructables and how-to’s, many quite comprehensive. This post is not a ‘how-to’ but rather a summary of my experiments: successful or failed.


Blending the pulp.
Blending the pulp.

I shredded, soaked overnight and blended the printer paper to make the pulp: I found the longer you soak the paper, and the more diligent you are at blending, the finer the final product. I separated bright white printer paper from yellowed or ivory: the white paper produced a slightly grey pulp which dries to a bright white with black specks; the yellowed printer papers and newspapers produced a speckled ivory paper that is lovely. One thing to note: the printing and colour stays firm on paper printed with laser or photocopiers, leading to paper which, depending on the thoroughness of blending, features small scattered text, colours and random letters. This looked somewhat very rock and roll eighties:

Rock and Roll Paper
Rock and Roll Paper

I have heard you can use food-colouring also to dye the pulp but I had quite a lot of coloured scrap paper that I was able to make pulp in various colours:

Soaking coloured paper reading for blending.
Soaking coloured paper reading for blending.


My ‘mold and deckles’ were made from recycled photo frames. I sifted through several op-shops looking for solid wood frames. I found solid wood is preferable as nailing the mesh is easier, and they withstand the water damage better. A few websites recommended sealing your frames with Estapol or similar to avoid water damage and warping, which I will do next time (my cheap MDF A4 frames are now soggy and warping). However, if you can only get MDF or plastic frames, a hot glue gun will attach the mesh: the glue seems to hold in the water.

I delighted in finding the ugliest pictures I could find to convert into molds.
I delighted in finding the ugliest pictures I could find to convert into molds. As long as it’s solid wood, it’s all good.

I bought cheap nylon fly screen from a discount store to make the deckle, but if I did it again I’d get a second hand open mesh curtain and cut that up. The mesh you use leaves a texture on the paper: imagine the patterns you could create!

My trusty A4 mold and deckle, which is now much more warped and soggy due to it's cheap MDF frame. I'm keeping an eye out for two identical A4 sized solid wood frames to replace it.
My trusty A4 mold and deckle, which is now much more warped and soggy due to it’s cheap MDF frame. I’m keeping an eye out for two identical A4 sized solid wood frames to replace it.
Two solid wood 5x7inch photo frames made my first (and still best) mold and deckle. This one has held its shape and is the easiest to use.
Two solid wood 5x7inch photo frames made my first (and still best) mold and deckle. This one has held its shape and is the easiest to use.


Standard paper making setup.
Standard paper making setup.

I had a typical setup: tray of water; mold and deckle; towels and cut up flannelette sheet; vinegar (which apparently whitens grey pulp) and liquid starch (which apparently ‘sizes’ the paper to prevent ink absorption); sponges; and of course pulp.

After several weeks of experiments this is the process I found the most successful:

Mold and deckle 'scoop' into the tray of water and pulp.
Mold and deckle ‘scoop’ into the tray of water and pulp.

The basic idea is frame with mesh (the ‘deckle’) is held together with the mold and ‘scooped’ under water in a tub full of pulp. I would scoop in from the side, submerge, shake, and lift the mold and deckle out as horizontal as possible (see other instructables on paper making to see how this is done). I’d then let the frame sit on the edge of the tub/tray to drain:

Draining: removing as much water as possible is the name of the game.
Draining: removing as much water as possible is the name of the game.

Then carefully remove the mold:

Removing the mold ...
Removing the mold …

Typically you would flip the deckle onto a waiting backing – usually cloth (in my case flannelette pieces cut up from an old sheet) – cushioned on a towel. Instead I found this process more successful:

Place backing over pulp-side:

Place cloth over pulp ...
Place cloth over pulp …

Press the soft pulp side flat and remove as much water as you can using a sponge:

Press and sponge off as much water as you can.
Press and sponge off as much water as you can.

Flip the frame onto a waiting bed of towel or blanket; sponge the ‘mesh’ side to again remove as much water as possible (and to reinforce the structure of the paper).

Sponge extra water from the mesh side
Sponge extra water from the mesh side

Carefully place on drying space (being careful not to let the paper fall away from the deckle surface too soon).

Place on drying space
Place on drying space

The tricky part of paper making is to release the paper from the deckle. I found after many tries that pressing in the corner of the mesh and then tugging on the backing allowed the paper to ‘peel’ away. If it doesn’t release automatically, go back and sponge again.

Press carefully in corner and peel backing away ...
Press carefully in corner and peel backing away …
... to release paper.
… to release paper.

While cloth is the standard backing used in paper making, I had heard you can get a very smooth surface using glass. I tried this out (conveniently the frames I’d bought came with glass … :)) but found the paper tended to stick.

The teaching resources I’d just trashed included several hundred plastic overhead transparencies which, in the age of Smart Boards and projectors, are near useless. I found that using them for backing worked surprisingly well:

Place overhead transparency on pulp side of deckle
Placing plastic on pulp side of deckle, overlapping as necessary
Press to squeeze out paper
Press to squeeze out moisture

Using the transparencies is also good as more moisture can be squeezed out.

The paper pulp tends to want to stick to the plastic which makes peeling the paper off onto the drying place much easier. They’re then easier to manhandle and move around. Because the paper constricts as it dries, the plastic curls up (which is a handy indicator to tell you when it is dry).

Wait until the paper is completely dry before peeling the backing away: otherwise it will stick and ruin the paper.
Wait until the paper is completely dry before peeling the backing away: otherwise it will stick and ruin the paper.

Avoid peeling the paper from the plastic until it’s completely dry: if still damp it will stick.

I also used old plastic sleeve protectors (of which I have thousands after going through these folders) which worked as well (though the overhead transparencies were nice and thick and sturdy).

The plastic creates a smooth, velvety surface which would be good for writing:

Smooth velvety flat side ...
Smooth velvety flat side …
Rough textured mesh patterned side.
Rough textured mesh patterned side.


On a side note, while I was doing paper making it was 35 degrees Celsius and very windy. In fact, it was the same time the Sampson Flat bush fires were terrifying the Adelaide Hills. While this meant very short drying times, it did mean several fluttering sheets of paper ended up scattered around my yard. With some clamps or clothes pegs, spare mesh (including garden netting, fly screen and lace curtains) I rigged up several portable  drying tables:

Drying table
Drying tables

In full sun the sheets of paper dried in two hours; in the shade it could take overnight. Sheets I brought inside took even longer to dry. Besides how wet you get, the drying time alone makes paper making a summer activity. It helps to have Catastrophic Fire Danger conditions (yes, that is a thing we have in South Australia).


I made a basic press using big bolts and wingnuts (new, from hardware store) and the sides of an old Ikea side table I had:

Just a big version of the flower press my Poppa made me.
Just a big version of the flower press my Poppa made me.

However, my cat, Maia, decided that sheets of recycled paper are oh so comfy so she assisted me in the pressing:



I was delighted to find that my beloved printer can also print quite happily on the recycled paper:

The absorbent paper soaks that ink-jet ink up, giving vivid colours.
The absorbent paper soaks that ink-jet ink up, giving vivid colours.

I haven’t experimented with a laser printer or photocopier yet, but provided the sheets aren’t too thin or too thick, the paper will make it through without clogging your printer.

Other experiments

The winner of the ugliest doily is ...
The winner of the ugliest doily is …

I experimented with creating textures on the deckles: in this case I found these dreadfully ugly doilies at an op-shop and hot gun glued it to the mesh.

The results were beautiful:

Doily art
Doily art

I might even frame some of these pieces. I’m experimenting currently with cutting stencils out of the plastic transparencies to create patterns.

I also tried adding confetti (or, in my case, coloured paper which had been hole punched), unblended paper, wool threads and glitter to the papers with varying levels of success.

Glitter and confetti were the best:

Confetti paper
Confetti paper
Colours featuring chunks of paper pulp which I didn't blend, leaving solid pieces of colour
Colours featuring chunks of paper pulp which I didn’t blend, leaving solid pieces of colour

The leftovers from making the confetti I soaked and then added to the pulp unblended, leading to paper with solid pieces of colour. Love the colours, not sure about the look of the paper though.

The best looking paper, though, continues to be the white and ivory sheets with the fewest ‘specks’ (and maybe some gold or silver glitter):

Peach, ivory and white
Peach, ivory and white
Blue and red pulp, yellow pulp, ivory, pastel green, and white with pink heart shaped confetti
Blue and red pulp, yellow pulp, ivory, pastel green, and white with pink heart shaped confetti

So …

The next time you have to clean out your teaching resources and you have a mountain of paper headed into the bin, think about how you could spend a nice summer in the sun getting soaked and covered in paper pulp. Raid some op-shops and thrift stores for ugly frames and uglier doilies. Get some kids involved. Cover your yard with fluttering paper. Make a year’s supply of scrapbooking materials.

And make your cat some comfy paper:

Seriously: I couldn't put a sheet down anywhere without her sitting on it.