Origami Tessellations

Owesen asks:

Or are you aiming for the full deal, with two-headed eagles galore?

to which I reply:

the full deal with two-headed eagles! that would just be insane. maybe in 10 years from now.

Right now, I’m looking at getting a good egg shape. I figure if I can get that working, everything else can be done from there. I’ve started playing around with an octagonal base, but I might need more points to do what I’m trying to do here… I’m thinking I can incorporate some swirls from a star-like base to give me the crossing grid on the egg. If I can get something on the intersections that looks like a diamond, hexagon, star, etc that’s a big plus. I plan on folding one and then making some patterned paper to give me the “look” of the egg. any extra details I can do are all just icing on the cake.

as far as the egg opening, I thought of using two pieces of paper and finding a way to link them together… trying to do it out of one sheet just doesn’t seem practical.

So, I have two challenges going on right now… there’s a challenge to reimplement the crossed box pleat to get more surface area out of it- I thought this would be relatively easy but I’m rusty at straight box-pleating, and it’s much trickier than I thought. after making some attempts I’m letting it sit for a bit to percolate in the back of my mind. I’m also looking to come up with a unique version of it, which I’m not going to talk about until I get further with it- I’m hoping it comes out like I’ve visioned, but we’ll see.

My other challenge is folding a representation of a Faberge egg. I have a friend here at work who is a huge fan of russian imperialism, especially the Faberge egg collection. She’s lent a nice photo book to me, so I’m having a go at folding a rather simplistic effort to start. If I can get a basic egg shape, I think I can go from there (with grafts and pleats and all manner of extra fripperies.) I haven’t really started that one yet, but it’s out there. I’m thinking of trying this one first, as I think the pattern might be conducive to folding (and hiding some extra material for the pleats). It’s going to require some spiral work, and that’s going to be new for me. I’m not sure I’ll be able to pull it off or not. but what’s the point of having a challenge if it’s not something difficult, right?

new triangle tessellation
Originally uploaded by Origomi.

I was fiddling around with triangles again, and I broke down and started using some 30 degree angles as well as the normal 60 degree folds. this was a bit of a change, as I had previously been operating in some sort of weird purist mentality- I was trying to find everything that I could do with a very restrictive set of limitations, and slowly build on that.

While I haven’t found every basic fold that I can do with 60 degree angles, I think I understand enough about what I can and can’t do with the folds to branch out a bit from here.

I personally find strict limitations to be a positive thing at times, as it keeps the whole continuum of possibilities at bay- and allows you to focus more on what you *can* do with what you have. I think it helps you to hone your chops, so to speak.

but anyhow, back to this fold- I folded the peaks on this in a new method (to me) by folding an extra set of side folds into them. this means that on each side of the peak, there are 3 mountain folds, and two valley folds- and the valley folds only go half as deep as a “normal” fold (due to the 30 degree angles at the vertex instead of 60). these are very easy to flatten out, as the two new 30 degree-based valley folds meet to make two sides of an equilateral triangle. and this, of course, allows us to make something like a rabbit ear fold from a triangle base and fold the sucker flat. nifty how that worked out.

this would look quite nice with some patterned paper in a hexagonal shape. or, combining it with some other patterns to make some seriously complex tessellated work.

patterned "spread" hex tile fold
Originally uploaded by Origomi.

I refolded my basic “spread” hex fold using some nice patterned paper. since the paper actually had hexagonal patterns on it, it basically was calling me. and it said “fold me already, never mind that the lines printed on me aren’t exactly even. it’s fine, it won’t be troublesome at all”.

…yeah. regardless, it came out nicely, although my photo skills leave a bit to be desired. but that’s always what you get when you do a bit of do-it-yourself.

I actually uploaded a pretty large copy of this image to flickr, and ate up 12 percent of my monthly usage limit. eek!

Star Tessellation – Detail
Originally uploaded by Owesen.

This was folded by an acquaintance of mine (also on flickr) that seems to be inspired by the same odd kind of thinking.

I think he has significantly more patience than me, though! I like his work quite a bit. take a look at his photostream sometime.