Here’s a basic crease pattern for a dodecagonal flagstone pattern, overlaid on top of a triangular grid.
The spacing between the hinges is not equal all around the dodecagon, but the actual tessellation itself is the proper dual of the 12.12.3 tessellation (two dodecagons and an equilateral triangle.)
What that means is we get two really big spiky 12-sided things and smaller triangular twists between them.
I haven’t tried it but if you actually squashed these they would probably overlap! I like them in their “uncollapsed” state, as I think they are more interesting as rigidly foldable constructs…
If you want to download the PDF version of this file, you can get it here:
Here’s the folded version:
This is so interesting… I remember doing so many paper plane models as a kid… Your tessellations really are a level above though, wow!