A few years back I published a crease pattern for my Origami Dual Color Stellated Octahedron on this very blog. Being a single sheet polyhedron with a color change, the layout is kinda complicated, with two superimposed grids. In order to make the folding easier I slightly fudged the relationship between the two, so one could start by folding a 13×13 grid and develop the other grid in the middle at on offset angle.
The other day I got an email from Akira Terao. He not only developed a method for folding a mathematically perfect layout, but he also published an article about it on the origamidraw blog. Very cool. His method is developed from first principles very elegant, and his article is very clear and explains it well. You can read it here:
origamidraw.wordpress.com/2019/03/20/drawing-a-cp-with-unknown-references-part-3
I hadn’t heard of Origami Draw before. It’s an app for making crease patterns. It has a lot of origami geometric logic embedded in it. From their web site (origamidraw.wordpress.com):
With Origami Draw, you can:
– Perform all folds possible with the 7 Huzita-Hatori/Justin axioms
– Divide segments and angles in any number from 2 to 8
– Compose with building blocks from rabbit ear to frog base
– Propagate new folds across existing folds, alternating mountain and valley folds (or not)
– Instantly find the missing fold to flatten the paper around a node
– Find and retain all references needed to replicate your model exactly
– Verify its flat-foldability, with clear indications if anything is missing
– Keep all your CPs in one place
– Create different versions as your design evolves or to show a folding sequence
– E-mail your CP to your desktop computer as an Oripa file
Very cool!