A few times before, I’ve posted origami failures, outtakes and disasters.  This time I’ll focus on some failed experiments–design ideas that didn’t quite work out.

First, we have a failed prototype of ten intersecting triangular prisms.  This was after I had made four intersecting triangular prisms and six intersecting pentagonal prisms.  I thought it should be theoretically possible to create ten intersecting triangular prisms.  I wasn’t wrong!  However, I couldn’t quite wrap my head around how to construct it, so I made some prototype prisms and tried to fit them together.  I stopped at five prisms because I couldn’t quite get them to fit.  The dimensions of the prisms aren’t right, and it’s not possible to create a model from this prototype.

This model is an experimental variation on Ilan Garibi’s “Wave“.  “Wave” consists of overlapping horizontal and vertical pleats.  What if the pleats make an acute angle?  What if they make an obtuse angle?  Rather than trying to visualize it, I just tried folding it, and here is what I got.  The pleats interact in an unexpected way, collapsing into a sharp point.  I also tried the other way, using an obtuse angle, but the pleats collapsed into an overlapping mess and I didn’t even bother taking a photo of it.

This last model is a prototype for a particular shape I was trying to make.  I wanted a cube whose corners had been replaced with little cube-shaped holes.  I managed to make the shape, but it felt messy, inelegant to me.  And that’s before I even figured out how to connect the units together!  I decided not to continue with this particular design idea.  I’m sure there’s a better way to do it though.

These are the last of the “failure” photos in my files.  I’ve posted all of them now!  It’s not that I stopped making failures, it’s that I stopped photographing them.  Let me explain why.

I’m very interested in talking about the process of origami.  The process is very important!  A lot of what makes origami impressive is not the mere form of it, but the viewer’s knowledge that it was created with mere paper.  And so, when I started doing origami, I liked taking photos of the process.  I took photos of models mid-construction.  I took photos of paper selection, and of spare strips of paper left over.  Even photos of finished models were at first intended to be “raw”, sometimes photographed on top of the math textbooks I used as flat surfaces for folding, or next to diagrams I drew to aid in creation.

Failure is also an essential part of the process, and a particularly interesting part that is generally hidden from view.  So I took photos of the failures as well, and regarded them not with shame and disappointment, but joy and fascination.

But eventually, I suppose the novelty wore off.  Failure is an ordinary part of the process… so ordinary that I don’t feel the need to record it.  I’m not ashamed of the failures, they just stopped being noteworthy.

Many years ago, I designed the origami Arrow Illusion–an arrow that points in the opposite direction when viewed in a mirror.  It’s probably the biggest “hit” among my designs.  Recently, CFC (an Origami community) had a monthly challenge to create optical illusions, and it featured Arrow Illusion as an example.  So, I thought I’d design another.

I went through several ideas, but ultimately settled on the Reutersvärd Triangle.  It’s similar to the better-known Penrose triangle, but was actually created independently by Oscar Reutersvärd in 1934–before the Penrose triangle.

Like the Penrose triangle, the Reutersvärd Triangle is just an illustration–it’s impossible to actually make something shaped that way.  And yet, you can find many very convincing 3D-printed implementations of the Reutersvärd Triangle.  I felt this was a sign that I needed to origamize it.  (Note that the Arrow Illusion, too, was inspired by 3D printing!)

Actually designing the thing was fairly challenging, and I went through over half a dozen prototypes.  Even once I got the basic form down, I tried many ideas to optimize for simplicity and stability.  The end result is so elegant that its instructions fit on a single page.  Note: if you try to fold this, I suggest trying the “easy” version first, and make one with just 6 pieces of paper. It will look like this:

How does the illusion work?  The cubes are actually inverted.  Although it pretends to be a collection of cubes pointing outwards towards the camera, they’re actually internal corners pointing inwards.  It’s… not very convincing when you have the physical object right in front of you.  It’s most convincing when you take a photo in ambiguous lighting, and then sometimes it helps to turn the photo upside-down.  The lighting of the cubes doesn’t match the shadows behind the model, which may have caused some of you to see through the illusion already.  But in case you don’t see it, here’s a photo from the side:

I’m saddened to hear that Meenakshi Mukerji recently died.  I almost had an opportunity to meet her at a convention, but there was a pandemic and it never happened.  I’d give her a lot of credit for getting me into modular origami, and many of my earliest models were from her books.  I love her work.  This is a simple model that I have folded many times; it can be found in Ornamental Origami.

This iconic model is one that we folded at the East Bay Origami Convention back in March.  It takes inspiration from Boice’s Head Empty model, which is a person in a coat and tie, with a cube for a head.  Taking that same idea to the extreme, now we have a little doll with a giant cube for a head.  It’s pretty hard to get a photo of the thing, because from any view from above, the giant head eclipses the rest of the body.  If you could see it from above, you would see that the cube is open on the top and in the back.

Boice has a video tutorial.  It’s easier than it looks, but you may want to start with large paper.  I think it’s a good introduction to the box pleating method.

The tricky part was getting it to stand up.  I chose the fold the feet a bit differently from the instructions, giving it giant duck feet.

A lot of origami paper is colored on the front, and white on the back, so you can make patterns by carefully exposing the front and back.  I’m vaguely aware of a subdiscipline within origami all about making shapes just with color change.  But I have very little experience with it, and don’t understand any of the design principles!  As far as I’m concerned, it’s basically magic.  Perhaps one day I’ll give a shot at designing something like this.

The instructions for this model are available on CFC.

I feel compelled to mention that I am not a coffee drinker.  I drink tea.