After another long trip, here are some more tessellations. There’s an assortment here of designs folded from instructions, designs reverse-engineered from pictures of the folded models, and my own designs (which may be re-inventions of other people’s models).
Recently, I’ve returned to more purely geometric designs, exploring some new ideas.
Square vase with inset sides
This vase looks very clean from the outside, but the folds hidden inside are a bit more messy. I figured out what dimensions I needed for the insets and just hid the extra paper inside and used glue to hold everything in place. Since the angled lines on the main faces are at 45 degrees, the triangles wind up being equilateral.
Twisted stack of boxes
The second vase uses a bit different folding approach. Creating the twist is actually fairly straightforward – I would be surprised if it’s not a re-invention of someone else’s idea. I used the same angle between each box here, but any angle from 0 to 90 degrees would work with very minor changes to the crease pattern. It could also work for shapes with more sides, not just squares. Collapsing the stack of twists is a bit tricky and uses a lot of paper, so I’m not sure I would want to try a stack too much taller than this.
This piece is one I folded a couple of weeks ago using the same approach as my recent luminary. On the outside of the form, I drew a small spiral of a pattern in ink, which gives a hint of what is on the inside. The inside is painted and has two more patterned spirals.
Luminary 2 (lit)
The shape of this form creates interesting patterns of light and shadow when the model is lit. Near the middle of the model, the section just below the crease line that slopes away from the light appears much darker than the section just above – if the middle of the model flared out much more, the outer part would actually be in shadow. Also, the pattern drawn on the outside appears much crisper than the patterns drawn on the inside. Here is a close-up of the patterns:
I like folding tessellations while traveling because they are easy to transport (small and mostly flat) and relatively repetitive to fold because of the repetition in the grid and symmetry of the pattern (and so possible to do when I’m tired). All of these are folded from squares of Elephant Hide paper, some painted with acrylic paint. This paper is great for tessellations because it holds up through a lot of folding and unfolding without getting mushy, which many of the more complicated tessellations require.These models are all folded directly from or adapted from Eric Gjerde’s book Origami Tessellations.
Here are some close-up images of some of the tessellations:
Negative Space Stars, designed by Eric GjerdeStar Puff Tessellation, designed by Ralf KonradAztec Twist, designed by Eric Gjerde3.4.6.4, designed by Eric GjerdeLayered squares, adapted from Christine Edison’s Modern BlueReverse-engineered/adapted from Christine Edison’s Roundabout
For the past several years, I have been primarily folding curved-crease pleated designs where the pleats are vertical. In this piece, I changed the orientation of the pleats so I could create a different type of curvature of the piece. By using horizontal pleats that vary in width around the piece, I curved the vertical axis of the piece. This piece was primarily a test of a folding style I haven’t used much, but I’m hoping to explore this style of folding more.
I have designed a couple luminaries before (several years ago), but this time I decided to put the design on the inside. I started with plain white Elephant Hide paper and painted one side a mottled green/blue. Then, I drew the black pattern on the same side of the paper with a marker. Since the painted side is on the inside, the design only appears when the luminary is lit from the inside.
Here are a couple more views of the bottom of the piece to show how this works:
This is my Christmas design for this year, a variation on my ornament designs from the past two years. This year, I decided to record a video of the folding process. The video starts right after I finished scoring the creases (you can see the rulers and scoring tool on the desk). I start by pre-creasing along the scored (straight and curved) lines. I then glue the paper into a tube and collapse the form in stages, starting from the middle. I used a combination of tape and rubber bands to hold the form in shape. At the very end, I take the tape and rubber bands off an ornament I had folded earlier to reveal the final shape.
I was recently commissioned to fold a smaller version of my recent large Green Vase. I kept the same painted pattern, but I used a little yellower green, which is more the color I originally wanted.
Mini Green Vase
It’s fun seeing the two pieces together! Even though the smaller piece is almost 10 inches tall, it looks very little and cute next to the larger piece.
I recently posted photos of several large-scale origami pieces I folded. These pieces incorporate painted diagonal elements, but the folded patterns are not much more complicated than the ones from the series of tutorials I wrote a while back.
Here are the crease patterns for two of those pieces (and a few more comments below):
Turquoise VaseCrease pattern for turquoise vasePurple VaseCrease pattern for purple vase
In both of these pieces the painted regions have sinusoidally curved edges that in the folded form create the illusion of flat planes. This is all based on geometry: a plane that cuts through a cylinder at an angle creates a sine wave when the cylinder is unrolled. My forms are more complicated than just cylinders and there are places where the paper overlaps. That means a sine wave doesn’t create a perfect plane, but it’s close enough for the eye to follow.
The crease pattern for the turquoise vase is exactly the type of pattern I described in my earlier tutorials. The purple vase is similar – the top section follows the same type of pattern, and the bottom part is a simple corrugated pattern I previously used in my diamond vases. The corrugation requires some extra glue at the base, but it’s a similar level of difficulty to fold as the curved-crease pleats.
Over the past several weeks, I’ve been folding stars, fractals, and tessellations for fun. I bought some pretty papers several years ago that are too thin for my normal style of folding, but I finally used them for some models that don’t require as sturdy of paper. None of these designs are original – they include Chris Palmer’s Flower Tower, Evan Zodl’s EZ Star, Dasa Severova’s Star Mathilda, tessellations from Eric Gjerde’s book, and a few others. These models are on the wall in my room now, and they help fill up some space that has been empty for quite a while.