Pinwheel tessellation, version 2

Originally uploaded by Ori-gomi.

A newer, more interesting variant on a previous design, folded from white unryu.

In the first version of this design, I had used a strange little squashed-triangle fold with an extra side flap as a way of filling a triangular hole between the spokes of the individual pinwheels. this closed the space, but left the pattern somewhat lopsided, as the various hexagonal twist points were unable to “rotate” in a clean direction (other than the central one). If the spokes of the pinwheel had been clean diamond shapes instead of an elongated parallelogram, it would have tiled cleanly, with hexagonal twists interconnected by triangular twists. due to the extra pleat length on the tiles, this didn’t work on the old design.

However, on the newer variant, I found that the triangular hole I was dealing with was the same as one Jane found a while back:

topside here
reverse here

you’ll notice that triangular void? she came up with an elegant workaround using a 3d single-spaced triangle shape, which bridged the sections together in a “3d version” of a offset triangular squash twist.

In the folding of version 2 of the pinwheel, I had contemplated doing this same 3d triangle of Jane’s, but I’m really fond of making things fold completely flat. So I worked out a way to cleanly squash the whole thing flat, which gives you a large triangle which spans the hole, with some curious angles involved. I think it adds something nice to the piece, and gives some added depth of light play.

It also functions the same as the “normal” triangular squash twist we all know and love, and allows the hexagonal twists to tie together in a functional manner. they all can rotate in the proper direction, free from having to interact with each other.

Unfortunately I can’t capture how wonderful the unryu paper looks- the thick white parts of the mulberry fiber shine against the light, while the thin layers of paper pick up whatever color is behind them. I laid it on some black paper to take a photo, which helps the detail to come through.

I have been slowly working my way up to larger pieces of unryu- this one was originally about 40cm x 20cm (16″x8″). I have a much larger sheet that I have been precreasing in my spare time, which I am hesitant to use- I’m still looking for a great pattern that will fold well on a large sheet of paper.

Looks like this when backlit:

UPDATE:

It would seem this tiling is an old traditional japanese kimono pattern. if anyone has some links to a real physical example I would greatly appreciate it.