The Origami Forum

I keep running into these "tucking molecules", or "vertex-tucking molecules" all over the place, it seems; but what are they?

A few places I've seen them:
http://www43.tok2.com/home/meguro/cgi-bin/clip/clip.cgi
http://www.flickr.com/groups/origamites ... 481829468/
http://www.flickr.com/photos/tactom/363954260/

On Meguro's site in particular there seems to be lots of stuff about them thrown in amongst his other work, but I can't read japanese and it therefore isn't of any use...

Could anybody explain? Thanks in advance, it looks like it'll require a lot of explanation from what I've seen....

Oh, and it looks like they're also sometimes called "Voronoi Cells" or "Voronoi Folds", unless I'm mistaken...

Maybe you'll want to get Origami Design Secrets, it has a chapter about molecules...

Oh, how I wish I still had that book... But instead, I'm getting Works of Satoshi Kamiya!

wow good luck with that stuff cupcake. sometimes really hard stuff can make people frusterated and not enjoy the same things as they did before :shock:

I've gone through a lot of frustration so far involving origami, but look at me, I'm still folding. It makes me proud, considering so many people try origami, yet so few stick with it.

I'm not entirely sure what Meguro is talking about, unfortunately; it really makes me wish I understood Japanese!

I'm a big fan of voronoi tessellations, and how arbitrary pleats and twists can be created using these simple processes.

You can see some basic images made with voronoi cells here:

http://www.flickr.com/photos/origomi/tags/voronoi

They're pretty old at this point and not necessarily indicative of the state of such things now, but maybe they will be useful in some way.

I'm hoping to write a long article on this topic at some point this year; hopefully I can connect with Tomohiro Tachi and Meguro and discuss this with them in depth, somehow.

I find voronoi cells very interesting; with normal tessellations, we are limited in where pleats and polygons can go, because you need to adhere to the precreased grid. But by applying some techniques derived from the creation of voronoi cells, it's possible to dispense with the precreasing entirely and instead fold completely arbitrary and random pleats. This is useful not only for tessellations, of course, but anything else where you'd like to have a tiling, or extra paper, or to figure out how to put a graft into some spot that needs it, etc etc.

I'm sure others have already done this sort of thing but they call it something else. Being a tessellation folder, I tend to use terms that come from tessellation geometry :)

By the way, are those tucking molecule faces somewhat the same as the tesselation faces discussed earlier on the forum?