Multi-stable design of triangulated origami structures on cones of revolution

It is well-known that the Kresling pattern of congruent triangles can be arranged either circularly on a cylinder revolution or in helical way. In both cases resulting cylindrical structures are multi-stable. We generalize these arrangements with respect to cones revolution, where our approach allows construct structures, which snap between conical realizations whose apex angles serve as design parameters. this context we also figure out shaky realizations, intervals for self-intersection free and an interesting property related cross sectional area. Finally, analyze origami their capability by means so-called snappability index.