Geometric Drawings · geometry and paper · geometry and paperfolding · origami

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.

How to fold a Pentagon from a Square
How to fold a Pentagon from a Square. For the Video of this that Tobias made, go to https://www.youtube.com/watch?v=4kJmJUQVbO0

 

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:

Lines for a Folded Paper Star
Lines for a Folded Paper Star

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 back of the paper sta
The back of the paper star

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.

36-54-90 triangles, with cutting lines on their tips
36-54-90 triangles, with cutting lines on their tips

These little beauties turn into:

Stars in Pentagons
Stars in Pentagons

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.

Find the Angles with degrees of 90, 45, and ~72, 18, 36, 54, and 108
Find the Angles with degrees of 90, 45, and ~72, 18, 23, 36, 54, 63 and 108

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/


addendum March 2018

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

Book Art · Box · origami

Terra Cotta and Green

Variations on Chinese Thread Book
two more Variations on Chinese Thread Book

My thought was that I would make a model based on the Chinese Thread Book, then make variations of said model using different papers. Turns out that using different papers resulted in creating many more questions than I anticipated. My next few posts will be showing how these questions got answered, one Zhen Xian Bao at a time.

Zhen Xian Bzo variation in Terra Cotta and Green
Zhen Xian Bao variation in Terra Cotta and Green

Whereas my previous thread-book-variation has a romantic feel to in, this one feels earthy to me, like it’s meant for keeping track of seeds, gardens, and planting/harvesting info. The green print is Chiyogami paper from The Paper Place, and the solid green on the left is Neeneh Classic Linen Cover, Augusta Green.

Variation of Chinese Thread Book in Green and Terra Cotta, Paula Beardell Krieg
Variation of Chinese Thread Book in Green and Terra Cotta

The pamphlet on the left is constructed with a five-station pamphlet stitch using waxed linen thread. The book block is Mohawk Superfine. The second tier box on the right is machine-made paper infused with flower petals.

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Both the pamphlet and the rectangular trays fold away to reveal a big rectangular tray as the bottom layer, made with handmade paper from India. You can also see in this photo a sleeve made from Metallic Stardream paper. underneath the second tier try.

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Inside the pamphlet is a small envelope that expands into….

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…a little box.

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Unlike my Indigo, Gold and Red version, I didn’t use the Chiyogami paper for the outside wrapper. I tried out lots of options, but this handmade terra cotta paper purchased long ago from Dieu Donne Papermill was the best choice. I still have just a bit of this paper left, so I can continue using this for a few more wraps, but just a few. It’s hard for me to use up a paper that I may never see again, but I remind myself that I have it so that I can use it.

It takes awhile to assemble these thread books, but what has taken me the longest is to mix and match my papers until I am happy –and I demand to be really happy– with my paper choices. I try to let the papers I start with suggest the rest of the paper choices.  Since this part takes so long, I am trying to make at least two of each paper/color combination, in an attempt to do at least a bit of streamlining.

One surprising discovering is realizing how well Stardream Metallics match the Chirogami. I’ll be showing more of this match in the next post, which, by the way, will feature a thread book that has a suede wrapper.  I didn’t see that coming, but it’s what worked. I feel like I’m just the messenger…

Book Art · Box · origami

Indigo, Gold and Red

Zhen Xian Bao with Red, Gold and Indigo
Based on Zhen Xian Bao with Red, Gold and Indigo, barely opened

I’ve been cutting up my stashes of beautiful papers to design/make structures that borrow liberally from what I’ve learned about the Chinese Thread Book structure that I’ve been posting about over the last few months.

based on Zhen Xian Bao,, with Ried, Gold, and Indigo
Unwrapped

Rather than strictly mimicking traditional Chinese structures, of which there are countless variations, I’ve been making variations of my own. Basically, I’ve been repeating one design with different combinations of paper, but mostly featuring Chiyogami papers. So far I’ve made five distinct compositions of papers. This one, with the indigo cover, and the red/gold paper inside, is the most romantic looking of them all.

based on Zhen Xian Bao,, with Ried, Gold, and Indigo
pamphlet and rectangular tray, opened

Inside, instead of going the traditional route and placing collapsible boxes on the verso and recto sides, I’ve chosen to place pamphlet on the left, and rectangular trays on the right.

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Still, inside the pamphlet there is a traditionally made, collapsed origami box.

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Here it is, that little box (a 2″ square), opened.

based on Zhen Xian Bao,, with Ried, Gold, and Indigo7

Next layer down is a machine-made paper, which contains real flower petals, a paper that is one of just a few pieces of paper I have left from the now extinct Kate’s Paperie.

Big Box layer
Big Box layer

Finally, here’s the big interior box, made from handmade paper from India, containing leave skeletons. Also, you can see there’s a copper Stardream Metallic on the right, which is a slim pocket.

 

Chinese Thread Book
Closed, with Gold

All closed up.

origami · Rubber Band Books · Uncategorized

Origami Lantern

I came across a video tutorial for this lantern, made it, then posted it on my Twitter account, @PaulaKrieg. Folks there showed such interest in it that I thought it would be good to post here as well.

Also, I am writing this post as an experiment, as I am attempting to write this using just my phone.

Here’s one of the tricky parts of doing post by mobile: trying to add this link to the SonobeCubeLamp tutorial. When I get back to my home computer in a couple of days I will fix that link if it doesn’t work.

If you try making this lamp, here’s a tip for assembling the modular origami units:think of the pieces joining together by creating tension, in other words, notice how when one corner slips under a joining unit then the other corner goes over an opposing joining unit.

Have fun folding!