Conic Spirals

Joint work with Erik Demaine, Robert Lang, and Tomohiro Tachi.

We describe two exact geometric constructions of origami spirals obtained by creasing a flat sheet of paper along 2𝑛 curves, alternating mountain and valley, where the 2D crease pattern and resulting 3D folding are 2𝑛-fold rotationally symmetric about the center. Both constructions use conical developable surfaces and planar creases. Read more in our paper.

Conical spiral: All developed cone patches share an apex (the center).
Exploded vertex spiral: Multiple cones, whose developed apices are the vertices of a central regular polygon.

Gallery of examples

Spirals and their developments.
More complex spirals.
Spiral examples made from Hylite.