Designing crease patterns for polyhedra by composing right frusta

We propose an original and novel algorithm for the automatic development of crease patterns for certain polyhedra with discrete rotational symmetry by composing right frusta. Unlike existing algorithms, the folded product will conform to the surface of the target polyhedron without external flaps. The crease patterns of frusta are drawn first and then composed by the algorithm to draw the crease pattern of the rotationally symmetric polyhedron. The composition is performed by splitting creases that were folded on pleats from frustum crease patterns. A CAD program has been written to implement the algorithm automatically, allowing users to specify a target polyhedron and generate a crease pattern that folds into it.

► We fold rotationally symmetric polyhedral with origami by composing right frusta.
► Unlike other existing algorithms, the final products do not have external flaps.
► We develop a CAD program to automatically generate crease patterns of desired solids.
► Several test examples with varied structures are used to verify our own algorithm.