Isigami: sheet reconfiguration driven by cone interactions*

A novel class of surfaces holds the possibility of reversible reconfiguration into a large family of distinct, stable shapes. This property stems in part from their topological defects–they have equal numbers of cones and saddles. Exploring these surfaces with an example constructed out of a graphene monolayer with the defects arranged in a kagome-like superlattice, we model its mechanical response with semiclassical molecular dynamics. The cones possess a two-fold degree of freedom in their up/down orientation, yielding a reconfigurable surface with a large number of metastable shapes. Enumerating a complete 'zoo' of such shapes for a small patch of this material reveals that not only are the interactions between these degrees of mechanical freedom long-range enough to produce a gaussian-like 'density of states' for given cone orientations, but also that the surface possesses other hidden degrees of freedom in certain orientations–further increasing the number of stable shapes it can hold. These shapes cover a broad range of physical forms and a scale comparable to important biomolecules, raising the possibility of biological applications.