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?

kaleidocycleflag
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:

duffystirling-diamondsandsunrays
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 duffystirling@gmail.com.

Design Your Own

Foldplay

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.

Templates

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:

kaleidocycletemplate2
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. http://www.youtube.com/watch?v=kFUyXWlObLw

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.

Meanwhile

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 🙂

Later:

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.

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One thought on “Class Activity: Kaleidocycles

  1. Margaret Rietema February 18, 2016 / 6:25 am

    You can purchase Kaleidocycles by Esher from Fishpond.co.nz $29.45 $NZ

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