http://en.wikipedia.org/wiki/Wallpaper_group this covers every regular and semiregular tessellation that we can fold, I think. or all the possible orientations. I haven’t thought through all the ramifications of this, but I’m pretty sure that anything that we can fold fits one of these models. things get a little more complicated topologically since the paper isn’t really “flat”, and there’s more dimensions to the folding, but that’s rather beyond me.

I found this through my technorati RSS feed for “tessellations”; it’s “Makoto Nakamura’s Tessellation World”. it has some really neat animated tessellation scenes, and some rather unique ideas. definitely worth a look. it’s all in Flash, so be forwarned if you are flash-free.

Christiane has a really slick new triangular tessellation online, as well as some great star models based on one of owesen’s puffy star shapes. check it out!

simple escher-style fish tessellation, v. 2 (backlit) Originally uploaded by Origomi. decided to try an escher-style tessellation again after some discussion on the Origami mailing list. this is, obviously, a rather simple model, but something more complex would take more time than I have right now. this model tessellates across the plane, although it requires two differently sized triangles to fill in some gaps. you can see the tiling pattern here. I know they don’t really look all that much like fish (more like goldfish crackers, if you’re from the US) but it’s what came to mind. I came up with some more complex figures made up of larger groups of shapes; I’ll try to give some of those a go at a later point in time. All my diagrams that exist are available online at: www.origamitessellations.com. I only have 4 documents up there currently, but there are more in the works. If I come up with some better fish tessellations I’ll make sure to diagram them!

folded curve Originally uploaded by Origomi. folding curves, made by the intersection of two radiating points in space.