Bespoke Folds

Hihi!

I took the day off because I’m a giant baby when I get sick. Well. Small sick. Big sick I’ll just try to soldier on through until I can’t take it. But as sinus infection? No ma’am.

SO, let’s talk origami. I made a few things recently that I’m proud of you. We’ll start with the boring one - the Sierpinski Tetrahedron.

It’s not the best view, but there it is - a small Sierpinski Tetrahedron. Just so’s you know, I used that same old stretched Rafaelita. It’s served me well.

NOW let’s talk fun stuff. 

This is a Menger Sponge. It took SO MANY business cards. SO MANY. Fortunately, I work for a company that believes upward mobility is a wonderful thing (true) and business cards are a must for every managerial position (false).

Hiya! It’s been a long time. Things are getting better, but. Anyways, lets talk origami.

So I took the Rafaelita unit and stretched it along both axes. The top two pictures are one way and the bottom the other. Interestingly, they’re obviously both edge units, but in one, they became face-joining and in the other, vertex-joining. The top is disassembled because hexagons, while beautiful and perfect and my favorite shape, are not terribly stable, and refused to cooperate.

Hi!

So, I think this post has been coming for months. I’m (hopefully temporarily) hanging up my tumblr hat. I still do origami, but not nearly as often, and not anything that pushes me. I’ll explain more after the jump cut - click it at your own risk, as it will include me whining and a frank discussion of health issues (that, as a person raised in the south, are uncomfortable to talk about even with my doctor.)

Before the jump quote, though, I wanted to say thank you to everyone who followed, encouraged, taught… you all meant a lot to me, and every time I fold, I fold better because of you. Thank you. I hope this is temporary, but as with so much else that I hope is temporary, who knows?

Thank you again - I love you.

A tiled Aztec Twist! (also some napkin-cranes I folded for brunch)

Before getting into the meat of the tess, I want to offer an insincere apology about the lighting in my photos. Sorry. I got a new desk so now I fold upstairs in my “bedroom” (it’s a loft-style apartment?). Anyways, because I work night shift, I have light blocking curtains and also because I’m incredibly lazy and not nine feet tall the light right over my bed, closest to my folding table has been out for several months. Doesn’t interfere with the folding though because I have a great desklamp which has the wonderful benefit of making night photographs have +1 harshness! It’s better for my folding, though, so pfft.

NOW this is folded from a 31 inch hex of Urban Metals. As you all know, this is my FAVORITE paper and - oh god, it’s time for a sidebar - until recently, I’d only seen three color combinations. NOW I FIND OUT THAT THERE ARE SIX???!!! And the place I buy my urban metals from isn’t planning on stocking anymore of the gold/gray and I’ve never seen the gold/black or the silver/black? If you know anything about the other colors, i.e. where to buy them, please PLEASE let me know.

Okay! I folded 64 divisions because when I folded it to 128 for this tess, there were a couple of pinholes. The Aztec Twist has a lot more folding than the Spreading hex, so I didn’t want to tax the paper. One of the things that I enjoyed about tiling it was the simple exercise in figuring out how to join the tiles. The regular pleats and off-grid pleats switched roles at the boundaries and it was fascinating.

I’ve said before how much I LOVE the transitional moments you see when you’re doing origami - this is one such.

It looks like a mess, but that’s because of the off-grid pleats and twists, not because I’m sloppy nononononono.

So this project was MONTHS old. See parts 1 and 2.

Eventually I’m going to learn to stop using scrap booking paper. It’s too. Soft. The Question Mark has a tear on each wing in the same place - luckily it’s in the back, so you can’t see it. On the plus side, I was able to make the pattern on the wings do what I wanted, unlike with the Origamido butterfly. Positive thinking, right?

Hiya! Here are two Buckyballs made with Lukasheva’s Rafaelits module! The one on the left is the version with triangular faces whereas the one on the right is composed of hexagons and pentagons.

I decided to make both because I hate myself there was something that felt weird about the triangular facet version every time I’ve made it. Well, except the first, but that was with PHiZZ units, and yearsyearsyears ago, so I’m not counting it. Please ignore the detritus on the desk and also the gaps - the Rafaelita don’t like sixes.

The problem I have with the triangular facet version of the buckyball is this: it looks like an icosahedron. I included an extra shot of the triangular one so that you could see the division into giant triangle faces. There are twenty of them. Each on of them is one hexagon on a normal Buckyball (of course) and 1/5 of the pentagon at each corner.

Here’s the difference. Towards the bottom of this page on Euler’s Theorem (one of many, I’m assuming), it states that you cannot have have the sum of three angles at a vertex equal 360° - that’d be flat. You’d be tiling the plane. Basically, you won’t have groups of three hexagons; the interior angle is 120°. When we’re using triangles, though, the interior angle is 60°, so the problem is triangles in groups of six. 

Now! The cool thing about the triangular facet version - there are clusters of six triangles EVERYWHERE. There are far more than twenty. Yes, they get used multiple times, that’s irrelevant. So, basically, you have would have a giant flat plane if there weren’t the clusters of five triangles that act as the vertex for the giant triangle faces. Planes can easily bend in one direction and when you complete your buckyball, you’ll see lines that form the edges of the triangles, running right through hexagons. It’s really neat.

Now, there are two conclusions to be drawn from this:

Because you’re making giant triangle faces, you’d get an octahedron if you exchanged the group of five triangles at the edge for a group of four, and a tetrahedron with a cluster of three.

And, since we’re not constrained against tiling the plane, we can actually make the faces have more or fewer triangles, as long as it follows a couple of specific rules.

Did you know that a Sonobe icosahedron fits inside of a PHiZZ dodecahedron?

I’m trying to be fold more contemplatively this year, to learn more from what I’m doing. 

Also, I think we can further divide edge units into: vertex-closure edge units, face-closure edge units, and edge units that can be either depending. I don’t know if that’s a useful distinction, but. For example, the Sonobe edge unit - I’d say that that’s a face-closure and because of that, we know it’s an icosahedron, not a dodecahedron (I know, obvious, but). Although the closures of the PHiZZ unit form little pyramids, I’d argue that that’s a vertex-closure and that’s why it’s a dodecahedron. Useful? I don’t know. Correct? I don’t know.

Tumblr, I’ve had an epiphany.

First, this is a Hydrangea Octahedron, inspired by the inimitable @origamipenguins‘ Hydrangea Cube. 

Now, the epiphany. If you’ve ever video chatted with a drunk me (<3 @foldswithinfolds & @paperloveaffair <3) and talked about origami, chances are I’ve expressed my feelings about the sonobe cube at least once. My epiphany may not mean much to anyone else, but it’s mine and I love it. When you use Sonobe units to make an icosahedron, octahedron, or Toshie’s Jewel, you have triangular faces. If you apply the same faces to the cube, it’s a stellated tetrahedron that just happens to look like a cube. That’s what I nattered on about, and, in some overly complicated view of the world, it’s not wrong. Here recently, though, I’ve been trying to critically think about my understanding of what I do and how my preconceptions of a model affect my execution. One of the ways the Mukerji categorizes modules in Exquisite Modular Origami is by the part of the polyhedron you’re folding: edge, vertex, or face. The Sonobe we use to create icosahedra and octahedra is an edge unit. I was laboring under the false assumption that the designation as an edge unit was fast, like the designation would be on the vast, vast majority of units. It’s not.

It’s not.

When making cubes, it’s a face unit. It’s the addition of the diagonal crease that turns it into an edge unit. That’s a beautiful thing. Especially when you can apply that same principal to other square face units, i.e., the hydrangea used in the hydrangea cube. In the cube, it’s a face unit. But pop one more crease in there (indeed, that crease is already there, you’re just reinforcing it) and it’s now an edge unit.

This is Sixfold Symmetry. I found a picture on Pinterest (no judgement please) and thought, I can do that. Couldn’t find a cp or diagram, so I just guessed. Fortunately, I guessed right. Unfortunately, the paper I used was a bit too clothlike. It’s not as sharp or neat as I would like, but eh.

I’ve been stressed out at work this week - twelve hour shifts, no one giving me credit card numbers, not fun - and I had a procedure done Monday, so forgive me if the tips are not great.

The top picture is what I made when I forgot how to make Lukasheva’s Igel. I knew the shape I was going for, and the connection, but I completely misremembered the steps. Considering it’s a very different unit now, I’m pleased with how similar it is. Made it for one of the gals on my team. Her desk was colorless and she was having a rough day, so.

The other two pictures are... I don’t know? The not-Igel got me thinking about connections, so I decided to blintz fold some kami and use the flaps as connectors. It’s not the strongest lock, but I’ve made kusudama with weaker locks. I enjoyed it not because it’s pretty (because it’s really not) but for two reasons. First, it’s a face unit - I don’t remember ever having done one before. Second because the connections are just from the triangles made by the blintz fold, the actual faces are one layer thick - it feels incredibly thin, like a drum. I tossed it on someones desk, though, and it stuck together. I see no reason why I couldn’t make a tetra-, octa-, or icosahedron if I used one of my reference folds for the blintz fold as a hinge, but that would make it an edge unit and not quite as fun.

I’ve been playing with this for a long time. As you can tell from the third photo, it’s a variation of a sonobe unit - my favorite! :D What I like about this is that, typically, I think about the thirty unit sonobe models as icosahedrons because of the triangular faces. This model, however, presents wavy pentagons - so I think of it as a dodecahedron. 

It’s not the tightest connection, but it’s stable, and I was able to put it together with no paperclips, a markéd improvement over the previous version. Unfortunately, it doesn’t seem to have the flexibility to form the octahedron or the tetrahedron (assuming a triangular face shape instead of the wavy pentagon).

There was a quote I saw FOREVER ago that I’ve not been able to find, but it was from Gjerde, and it was basically saying that if something you create has been created before, that’s okay. You still went through the process. I don’t know if anyone else has made this - I’m still happy because I did. If no one else claims it or can point me in the right direction, I think I’ll call it the Grace Sonobe.

Hey @team-erdos, it’s giant origami coffee mug.

Thomas Hull’s PHiZZ unit arranged in a torus. SUPER fun, highly recommend. The only downside is your friends WILL get tired of you sending them progress shots because it takes forever. It took me two days (plus a little more that I’m not counting because I only had to go to bed early because of doctor’s appointment, so just two days, really) of folding to do this. I’m incredibly pleased I switched to the 3″x3″ because the 1″x1″ were a nightmare. I can do PHiZZ icosahedrons with the teensy no problem, but the geometry there is much easier to force.

IF you’re going to make one of these, I have a few recommendations. As you can see in the fourth picture, I have a “Stand” for it - ABSOLUTELY FUCKING NECESSARY FORGIVE MY LANGUAGE. Your arms will get so tired of contorting to get to the connections if you don’t have one of these. Trust me. The other recommendation is to connect a cross section as soon as you’re able - good sense of accomplishment and much easier to continue on. 

Now lets talk size - It’s hard to know when to close it! Mine has more units in it than the one in the link earlier because... Well, I closed it when I felt like it. One of the shapes you make is pentagons and I have thirteen on each side of the coffee cup whereas the one in the link only has twelve. I’m confident you could do fourteen if you wanted too, so, you know, a full rainbow, not that purple nonsense. 

I’m drunk.