# Pentagons, Paper Folding, Stars & Origami

I came across a lovely way of folding stars. It was in a youtube video by someone named Tobias.

As lovely as these stars are, what really caught my attention was the way Tobias showed how to use paper folding to make a pentagon from a square. This square-to-pentagon transformation was in a separate video, and since it will take me about two days to forget everything I saw in the video I drew out the directions.

After the novelty (but not the thrill) wore off of making a pentagon from a square I began to look at the angles that I was making and figured that I could make the star with less steps (and perhaps with more accuracy) if I just started out with the net of the shape, so I made this map of the paper star’s fold lines:

If you make Tobias’s stars, after you get the hang of which lines fold in which direction, I highly recommend printing out lines above, score the lines with an inkless ink pen, and make that same star using just its essential folds.

The photo above shows the backside of these stars. Quite a nice backside!

I’m sure that there are all sorts of things to do with pentagons, but something I want to mention is something that is fast and impressive, sort of the pentagon version of snowflake cuts. If you cut off an angled slice at the bottom of the folded up pentagon (step 12 in my tutorial drawing) there are all sorts of star possibilities.

These little beauties turn into:

The stars inscribed into these pentagons were made by cutting through all layers on the tips of the folded shapes.

And look, below there’s something extra for my friends who teach Geometry, and who might like a holiday themed angle activity. Part of the working out the folding pattern for the star was deciphering certain angles.

I had a good bit of help with the especially tricky parts of understanding the angle relationships. I’m sharing two twitter threads here, just because it was such a pleasure to get help from my friends.

and

That’s about it for now. Oh, and if you need to directions on how to fold a square from a rectangle, take a look at https://bookzoompa.wordpress.com/2014/12/10/paper-folding-squares-and-equilateral-triangles/

Here’s someone making this star. She makes it looks so easy! https://www.instagram.com/p/BfuSgYdnmY5/

## 12 thoughts on “Pentagons, Paper Folding, Stars & Origami”

1. Love this. Folding to 5 symmetry from a square is so intriguing, and the trig/geometry is sweet.

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1. ..I just finished up figuring out a paperfolding solution to show another, non–trig way, to make that first fold that results in that nearly 72 degree angle that is essential to this folding. But am heading out of the house so I will have to file this with Fermat;’s last theorem for awhile…..

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2. Thanks for this: best instructions ever for the four to five ratio! And of course I loved it because I have a thing about stars! ; ]

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1. Glad you like these stars. It took me quite awhile to get the hang of making these, but now, especially since I’m starting with the pentagon, they go quite quickly. I had been making some other really lovey stars from modular units. Take a look at this twitter thread for some images https://twitter.com/PaulaKrieg/status/927312314726076418 and here’s the link to the post that Clarissa Grande pointed out that contains the instructrions for this other great star. http://www.origami-instructions.com/easy-modular-5-pointed-star.html Yeah, this four to five ratio thing is so cool.

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3. The last ‘a little bit fiddly’ killed my star. But your pentagon works perfectly.

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1. I haven’t checked this out yet, but I suspect that if you use my net of the star, and cut out those 5 little rhombi near the middle, that the “little bit of fiddly” will give you less trouble. Also, the thicker the paper, the harder it is to make that last bit work.

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1. Came back to it today. Part of my problem was misunderstanding the points fold, which finally I really looked at. The other thing was an idea that helped. The first point I folded I then unfolded so it could be the last point already half done.

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2. Hey, I want some photo evidence of this! (please). I just got back to it today too, I tried out my thought of cutting out the little rhombi, and though it did make the folding easier, it also made it easier for the star to open up substantially in the middle…can be used as a cereal bowl now. Your solution to pre-fold is probably the best. Looking forward to pictures.

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