3.6.3.6 Waterbomb / Flagstone Tessellation, Crease Pattern

3.6.3.6 flagstone tessellation, Crease Pattern

If you are so inclined, I uploaded two different crease patterns for this design:

I’m really at somewhat of a loss on what to name these tessellations. If folded fully they become flagstone tessellations, ala Joel Cooper; if left three-dimensional, they are “waterbomb” style tessellations (although waterbomb is the wrong term for us to use here, but we’ll dispense with that argument for the moment.)

Regardless, this is a 3.6.3.6 tessellation- the old standard, triangles and hexagons together.

When you fold “normal” tessellations, the twists are always the dual of the tessellation you are folding. (For example, the 3.6.3.6 tessellation has a dual made up of rhombic stars- and the rhombic star tessellation, when folded, has hexagon and triangle twists, which most people actually think of as a 3.6.3.6 tessellation even though it’s really the dual of that…)

However, with these “waterbomb” tessellations, there seems to be a little bit of change due to the geometry involved. I still think they use the same “my twists are my dual” rule, but it’s a little different in how it folds out in the end, and I haven’t quite figured it all out yet.

This pattern (which I am currently folding) is really quite complicated to collapse. Much trickier than I thought it would be. However, I think the results will be quite interesting and worth the time spent.

It’s not really a full CP- many of the little creases for the hourglass shapes aren’t there- but I think you can figure it out if you fold these sorts of things.