Stretched waterbomb base tessellation

H. A. Verrill

tessellated sheet of 8x8 units,
sheet side ratio 1: 1.414
single unit
completely flat folded.
number of rows of units for full circle: 9

download image (png)

Change side ratio: ratio 1:
Change scale of crease pattern: scale 1
Questions? Comments? Feedback? Let me know, hverrill,
Intending to put up more of these, and more features, so visit again sometime!

Moving and changing elements:

Use mouse to click on the dot at the corners (upper right or lower left) of the large square to change the size of the sheet. The sheet is divided into 8x8 units, by first folding a 16x8 grid, then adding diagonal creases. I take the large sheet as my fundamental object, since given a sheet of paper, you can see how it would look with this folding, whatever the side ratio. Diving into powers of 2, such as 8, is easiest. However, if you want this to fold flat into a complete circle, you would have to use a different number of divisions. The number of rows needed to form a complete circle when folded flat is indicated next to the flat folded image. However, this is the number only when completely folded flat. When opened out a little, the model is less curved, and so would need more rows of units. Each row of the tessellation corresponds to a different peak in the flat folded form.
You can move the single image by clicking near its middle, and you can move the folded flat picture by clicking on the dot at the fourth peak.
Currently I don't have this set up for touch screen, but with a touch screen you should still be able to use the slider to change the image.
Currently will not allow non flat foldable units, though these might be interesting to fold, and flatfoldability might possible with different fold directions or additional folds.
Note, I have only tested this page on safari on a macbook, it might not work on other systems.

Note on relative scales:

The units in the sheet are half the size of the single unit. The completely flat folded picture has units 1.25 the size of the single unit.

Historical notes and references:

The waterbomb base tessellation (with ratio of sides 1:1) was first convieved of by Ron Resch. There are many explorations of this tessellation unit, for example, Approximating 3D surfaces using generalized waterbomb tessellations by Zhao, Endo, Kanamori, Mitani.
I intend to improve this to a better list of references. I have been exploring waterbomb base variations since Autumn 2019, and have posted images of my folds on instagram @havtofold. I have a paper in the 2021 Bridges math art conference proceedings, a version is here. For more of my waterbomb base crease patterns and so on, see this page.