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.



geometry and paper · holiday project · Ornament · Paper Ornament · Uncategorized

Round-up of Holiday Season Projects

A Bevy of Paper globes
A Bevy of Paper globes Directions at

Making things out of paper seems to be something we do during the holiday season.

Here’s some projects that I’ve written about with links to the full posts that explain them, that seem appropriate for the season.

This first one, the Spiraling Ornaments was surprisingly well-liked. All year, when I visited different places, I’d see ones that people I know had made.

Video tutorial (not mine) for Kaleidocycle



Here’s a template for a kaleidocycle. Not particularly holiday-ish, but fun and colorful, folds into something like the image below. More about this at



Next, directions for a six-sided snowflake. My big tip is to use paper napkins, as they already are the right shape: no extra prep needed! Also, paper napkins cut quite easily. They are perfect for snowflakes.

how to make a paper snowflake


If you want to understand how the cuts of your snowflakes affect the final design, see below:



Festive Jumping Jacks are quite fun. I’ve made these with kids just a few times, as all the knot tying makes this an intense project for anything more than a small group, but so worth the effort!

Jumping Jumping Jack

To work out how to make these you might have to look at a few posts, which are all listed at

The stars below are tricky to make, until you get the hang of them. I still have the ones I made on display from last year.

The original post contains a good bit of discussion about the geometry embedded in these shapes.

Finally, making little books with stories or messages is always worth doing.

Origami books made from a multiple folded papers, to create a Star Book and a Cascading Book, aka Origami Caterpillar Book
Origami books made from a multiple folded papers, to create a Star Book and a Cascading Book, aka Origami Caterpillar Book

Here’s a post that can get you started on some simple books to make with kids

For more an overwhelming amount of other book ideas, check out what I’ve tagged as making books with children

There you have it. Enough to do to keep you out of trouble at least until January.

design · Geometric Drawings · geometry and paper

What to do about Color Combinations


Steal them.

Since I started decorating my own papers with geometric designs (as well as decorating geometric designs) I’ve been flummoxed about color combinations. Some of the decisions I’ve made have been truly horrible. Sometimes they’ve not been so awful, but, even then, it takes way too long to come up with color combinations that look good to me.

I suppose I could take an on-line class about color theory, but somehow I’m just not drawn to do that just now. Abode has a palette-sharing site, but it’s not supported in the version I use. Recently, having spent way too much time having way too little success, it finally occurred to me to try out dipping directly into the palettes of painters who use color in a way that sing to me.

Geometry and Georgia O'Keefe
Geometry and Georgia O’Keefe

I probably wouldn’t write about this if  I could do this only in Adobe Illustrator, since this info would be totally useless to most people. I noticed, though, that more and more people in my circle are using Inkscape, which is a free graphics program, and it turns out that dipping into the palettes my favorite painters is even easier to do in Inkscape than Illustrator.

Fra Angelico
Fra Angelico

Here’s what to do in Inkscape. Find a painting you’d like to dip into. Save it to your computer. Drag and drop it into Inkscape. Select the shape or area that  you want to color. Press F7 or choose the eyedropper tool (second to the last tool from the bottom on the left side) and click on the color on the painting that you want to use. That’s it.

Vectorizing the Image in Adobe Illustrator
Vectorizing the Image in Adobe Illustrator

To do this in Adobe Illustrator, it’s bit more complicated. Place the image into the Illustrator file, then vectorize it  in Image Trace. I generally use the high fidelity photo setting in image trace. This separates the painting into regions, which if you zoom in really closely looks abstract and totally cool (in Inkscape, getting this close just looks blurry).

Up-close O'Keefe
Up-close O’Keefe

Just like in Inkscape, to harvest the color use the eyedropper tool, which has the key shortcut “I”. I’ve been using the live paintbucket tool (k) to fill in the areas that I want to color, but, like Inkscape, choosing the shape then the eyedropper works too.

Even more O'Keefe
Even more O’Keefe

Now, I just want to mention that even though this is the best method I’ve used to choose colors digitally, there’s still a bunch of trial and error. But instead of me doing trail and error with millions of colors, I’m using this more limited palette. Works for me. Am having lots of fun with this.


Harry O’Malley just pointed me towards, which looks like the internet’s free version of Adobe’s Kuler. Yay! Another color resource! (I can use all the help I can get.)

Addendum #2: ((2/18/2019)

Another color resource:




folding · geometry and paper · geometry and paperfolding

A Square of Your Own

Squares, scaled
Squares, scaled

Making a plain old square exactly the size that you want can be such a chore. Too much can go wrong.

Squares can become so many different things (think ALL origami) that it’s worth knowing how to make a square just the size you want without getting stressed out.

Here’s how to do it, via the photo essay, followed by the video tutorial.

plain piece of copy paper
plain piece of copy paper

Here’s a regular piece of copy paper. The first steps look like I’m heading towards folding a square whose side is already predetermined by the short edge of the paper, but no. Be patient. This is going to be a surprise. Trust me.

First Step
First Step

Fold that short edge to meet the long edge, making sure that your fold ends (or starts) exactly at that corner. What you are doing here is bisecting that corner angle. If you cut away that rectangular flap on the edge, and unfold the triangle you’d have a square, but this isn’t what we are doing now. (Doing that was a different post, )

Marking the size of the new square
Marking the size of the new square

Unfold the fold then make a mark to indicate size of the square you want to make.


What I’m going to write next sounds horribly complicated but it’s easy to see and do.

Curl over that corner that has the fold going through it, lining up that corner point with the fold line it is leaning towards, and also lining up the upper edge of the paper with that mark you made. Press the fold.

Here’s a closer to look:

Closer Look
Closer Look

Now draw a line that traces around that folded down corner.

Time to cut out the square
Time to cut out the square

There’s your square!

Confused? Here’s a video to watch:

Got it?

Origami Pockets
Origami Pockets

Now make cool stuff.

Addendum: here’s a post that shows what I showed, plus another great way of making a square.