Articles and Tutorials

What are twist blocks?   Whenever I look at tessellation crease patterns, I mentally  break them up into their component parts. With twist-based tessellations, those parts are twists and they're connected by pleats. The good news is that the same set of twists are used over and over again in different tessellations, which means that we can treat them like building blocks and drag and drop to snap them together! I made a set of digital twist blocks in both square and triangle grid for my Tessellations by Tiles students last fall and found that they really speed up the diagramming...

Fully Flexible   Sometimes when you're thinking about tessellations, often when you're looking at what someone else has folded, you have a flash of insight and see new possibilities for patterns that you hadn't considered before. That's exactly what happened when I was looking at Miguel Gañan's book, Twist and Tess, when I first got it. I was looking through the crease patterns for interesting tilings, and came across a pattern that used the hexagon-rhombus-triangle-rhombus loop (which is usually very restrictive) in an expanded form that has specific places where the spacing is very variable! Immediately, I thought of Lens...

I addressed this very question in this week's livestream, which you can see here:   Tilings are the roadmap for where pleats go and what they connect in a tessellation. They're also the level of analysis that's most beneficial for folding and designing. After all, if you know that a particular hexagon in a pattern is in a position of 6-fold rotational symmetry and you know one of the things that goes next to it, then you know all of the things that go next to it! Thinking in terms of tilings and symmetries allows you to generalize and describe...

Patterns in the Tessellation   You can see many things in any tessellation - here I'm seeing a close mimic of the purl knitting stitch, and also an Easter bunny. I'm also seeing parallel mirror symmetry lines with a string of twists between them, a sequence of triangle-rhombus-triangle that I use in many tessellations, and an unusual arrangement of rhombi and triangles. Which aspect I choose to emphasize varies with the lighting, the level of zoom, and who I'm talking to.   Details As we look closely at this tessellation, we can see that there's the zigzagging rhombi and triangles,...

There's plenty of tutorials out there for folding triangle grids on squares, but the translation to folding these grids on rectangles in the orientation of your choice isn't well known. That's why I went live this week to talk about these grids - and why you might want to use them.   We often think of triangle grid tessellations with 6-fold symmetry that work well on hexagons, but there's also tessellations on triangle grids with dominant 3-fold or 2-fold symmetries too! In the 2-fold case or cases with one direction of mirror symmetry a rectangle is often the shape that...