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

Computational Geometry