note to self: waste no paper

when you want square flagstone aligned to the edges of your paper you can fold the pattern and then cut away the parts you don't need (see picture below). however, this means a lot of wasted paper and, even worse, a lot of wasted effort (although at one point this extra effort gave me a second model which was a nice surprise).

 

anyway, I figured it should be possible to rotate the tesselation grid such that it's off-set against the paper's edges. if I do it right then the pattern should be aligned to the paper edges, so no need to cut away, no wasted paper.

 

so I thought about it,

tried it,

errored,

thought some more,

tried again,

found another mistake,

thought even more,

tried again,

hooray!!

 

.

 

the idea is actually quite simple. imagine a line in the crease pattern between the centers of 2 square twists. note that its slope is -1:4. so rotate the paper with a slope of 1:4.

 

this rotated grid folds surprsingly well. you got some rather nice reference points. you can find a step by step diagram in this pdf.

 

interesting enough this rotated grid folds even more nicely from a 1:2 rectangle.

Done