geometry and paper · holiday project · Ornament · Paper Ornament

Paper Sphericon, a shape that wobbles



Just in time for the holidays, a shape that you probably never heard of. Maybe that’s just as well. If you want something that’s kind of awesome & easy to make, you are in the wrong place (go here instead). This shape is awesome and endearing, but takes more finessing than is comfortable for the average bear. I do not recommend making these with children. Or adults. Proceed at your own risk.

I was introduced to this shape by Vincent Pantaloni, who has a knack for distraction. Near the bottom of this post I will link some of our sphericon-related twitter threads.

Sphericons, nets and shapes
Sphericons, nets and shapes

What’s most endearing about this shape is that it wobbles as it rolls. You have to give it a flick right near one of its edges and it will roll like a drunken sphere. Its net (the flattened out version of the shape) reminds me of a duckbill platypus. I bet they wobble too.

If you have a template you can probably figure out how to make one of these without any help from me. Here are the templates, in black and white, in color, and in two different sizes. I’m pretty sure these will work with A3 and A4. (Let me know if I’m wrong about this!)

Spericon color 8.5 x 11 A4

Spherhicon B&W 8.5 x 11 A4

Large Sphericon B&W 11 x 17 A3

Large Sphericon Color 11 x 17 A3

After you fail a few times you can watch my video to see me struggle through making one. I do have a few good tips to offer.

Score and fold the curves and the edges
Score and fold the curves and the edges

I recommend printing these on heavier papers than standard copy papers. They don’t do their rolly-wobble really well when made from lighter papers. Really, who would want a non-rolly sphericon? I use 67lb cover paper.

Once you cut out the shape, score the curves and the straight lines within the net.

Adhesives matter
Adhesives matter

To get everything to stick together I recommend using some kind of double-sided adhesive.

I’ve tried regular tape and white glue and glue sticks: I do not recommend using regular tape because it messes up the rolling edge. I do not recommend using white glue or glue sticks because I have to hold everything together while the glue dries and this takes too long.

I had some big glue dots around. I like the way they worked, especially as I could stretch them over a larger area that one would expect. When I ran out of glue dots I discovered adhesive LINES. Very cool.

Stretching Adhesive LInes
Stretching Adhesive LInes

See the the adhesive line stretching in the photo above?

I put the adhesive on all the glue surfaces before I actually try to adhere anything to anything else.

The first sticking
The first sticking

I find that it’s best to stick the long tab to the one straight edge before doing anything else. You will likely disagree with me and try to glue one set of the teeth first, then the other set, then do the tab. Then you will realize that this was a mistake. Oh well. Told you so.

So Adorable
So Adorable

I think these look so adorable at this stage that I had to post both of these photos. Now you just have to somehow get those teethy things to stick to the inside edge of that arc (which, according to Vincent, is about about 127.3 degrees of a circle. About)

Getting these to stick together perfectly is just not possible. But good enough is actually good enough. You have to do a 3D print for perfection.

Here’s a video of me struggling through making this. It’s worthwhile to watch but there are some reaaaalllllly boring stretches. The whitish on the bottom of the video never goes away. Sorry.


Here are are some interesting twitter threads to look at. Click on them then scroll up.



2 thoughts on “Paper Sphericon, a shape that wobbles

  1. Dear Paula,
    I love your website – I home-educate my 2 children (aged 7 and 10 currently) and constantly refer to it – to see if we can incorporate any of your way of seeing maths and the world at large in our learning. At this end of year, I want to say “thank you” for all the learning and inspiration. Following your advice (when I commented on a previous post you made) and that of a few other’s encouragement, I have started an occasional blog about how we ‘see’ and so things at home. It is here
    There is a recent post on “Thinking Hands” which I think is what you do so beautifully!

    I’m going to place a link to your website soon – hope that is OK. I had no other way to contact you, so doing it through this message – don’t feel you have to post it up, it is a personal “thank you”. At some point, I’d love to ask you more about your approach and put it up as a blog interview. Warmest wishes for 2019! Navjyoat


    1. Naviyoat, thanks so much for this generous note! It means a great deal to be thanked, and am thrilled that you’ve started a blog. I’ve visited your site, and look forward to keeping up with you. Am happy to try to answer any questions that you have.
      best wishes for the New Year.


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