So I’ve been doing a little thinking and exploring about regular and irregular polygon tiling. I’m working right now on some different models depicting the various methods of tiling regular polygons, which honestly is pretty easy to do- I’ve already done quite a few like this so it’s not a challenge, really. I’m looking to have good examples of every type, and to fully depict the possibilities more than anything. I’ve also been trying to fold tessellations made up of arbitrary angles. I really shouldn’t call these tessellations, as they aren’t, but maybe something closer to aperiodic or chaotic tilings. there’s a LOT of math involved, most of which I don’t understand anymore, so it’s slow and irritating going. but I have found some interesting facts which prove and disprove some things for myself, so I figure that any increase in understanding is a good thing. I’m taking the next week+ off from work, so hopefully I’ll have a few quiet moments to sit back and think about some of these things and discover some …

tiled hex tessellation———————- 1st step: pre-crease paper to preferred level of crease width- I’d suggest 4 iterations of folding, minimum. (that’s 1/2, 1/4, 1/8, 1/16; 1/32 or higher will yield better results). 2nd step: identify “central” hexagon. it should have a two-pleat- width radius from the center of the hexagon. This “central” hexagon can be the exact center, or offset if that’s what you prefer. actual location is irrelevant to the final pattern, although symmetry is usually a preferred result. see illustration. What we are doing with this fold is creating a valley around every hexagon shape, which results in a tight grid of hexagons across the entire paper. we’re folding the extra “valley” paper into the triangular squash twist folds. see illustration. 3rd step: identify the two-pleat-wide “valley” that encircles your central hexagon. This needs to be folded into a one-pleat-high mountain fold all the way around; at the hexagonal vertex points, you will need to fold it into a 3-way intersection. This also requires that you fold the 3rd angle at the intersections …

I found this link while digging around trying to find out what happened to Helena Verrill’s site(s). it’s for Ralf’s Origamipage, at http://www.origami-online.de/index_de.html. Take a look at his tessellations- some of them are very, very complicated pieces of work! quite stunning. I really like all his folding with triangular creasing, as I think that the triangle/hexagon combo is really the way to go for great tessellation patterns.

Spread Hex Tessellation With Squashed Triangles Originally uploaded by gila o. Gila O. over at flickr took the spread hex tessellation and did a squash twist on all the 3-way crease intersections. it looks great, in my opinion. Gila is a one-woman tessellation folding machine!

I have a set of diagrams that I came up with for my tiled hexagon tessellation, which makes up the background of this webpage. It’s a fold that I always enjoy making, and it’s relatively easy to fold as well. I’m looking to have some folks go through it and let me know what’s easy/hard/needs to be fixed/etc. I have a few very nice people who are already doing this for me, and I’d like to get some more feedback so I can try to make a better template to use for future models. If you’re interested please drop me a line at origomi@mac.com and I’ll send it to you. Thanks!