Articles and Tutorials

Atypical Symmetry Pattern Most of the time when you see a tessellation with only hexagons and triangles, there's only one hexagon and only one triangle and they alternate back and forth. But that's not the only way! Using the Hexagons and Triangles 6-fold Islands symmetry gets you a choice of a second hexagon too. You can choose an open or closed central hexagon, a triangle of any type on any side, and then a hexagon of any type on any side too! I figured out that all of the options work by playing with my crease pattern building block templates,...

One Space Away Groovy Triangles and Emergent Hexagons are one space away, yet feel worlds apart. The dominant feature in backlighting of Groovy Triangles is a Star of David made with open triangle twists on alternating sides, while the dominant feature of Emergent Hexagons is a honeycomb structure of solid dark bars. This is something I've found with other closely related tessellations too. In equilateral triangle tiling tessellations with clusters of four twists, there are several spacing considerations: between clusters, within clusters, and global lines.  In Groovy Triangles, the spacing within clusters is as dense as possible, with spacing between...

What are skew lines? Skew lines are the lonliest pairs of lines - they don't intersect at a single point, and don't maintain a constant distance from each other like parallel lines. They just pass near each other then continue out to infinity. It's pretty rare for a tessellation to have pattern elements align this directly when the twists are on opposite sides of the paper - much less have lines in two different directions on the two sides! How is this possible? Skew Lines is made up of clusters of four closed square twists, which are then mirrored all...

Oh the thinks you can think! So, it turns out that we have more choices available to us than we might suspect with Hexagon and Triangle 6-fold tilings! Instead of just having one choice for the next hexagon out from the middle, we actually get four hexagons to choose from - closed or open on either the front or the back. And that's after we choose the central hexagon (2 choices) and the triangle twist (also 4 choices)! Taking all of these options into account, we have 2*4*4=32 options for arranging hexagon and triangle twists in this extended symmetry and...

To start folding from crease patterns, we must first decide what part of the pattern to fold - what to put in the center, and how many repeats we want.

Next, we need to actually fold the grid.

Finally, we can start folding!