After leafing through Eric Gjerde’s “Origami Tessellations” I knew I had found the motherload of paper punishment:

This is the “Pinwheel” tessellation and it has a hidden beauty. I am learning that a tessellation is a regular repeating pattern, magically interlocking “molecules” that go together like tiles on a mosaic floor.

Usually based on a grid (at least initially), this one is based on a triangle grid, and features closed hexagon twists and open triangle twists that compliment each others vertices very neatly. Backlit they reveal an intense and curious but often completely different geometry.

I think the back side is more interesting than the front side – as a side-effect of folding the hexatwists and triangle twists you end up with deep interlocking gussets underneath that describe a perfect basket weave – quite lovely.

There are lots more to try, I pity the paper heading for this form of punishment.