Abstract

Three-dimensional shells can be synthesized from the spontaneous self-folding of twodimensional templates of interconnected panels, called nets. However, some nets are more likely to self-fold into the desired shell under random movements. The optimal nets are the ones that maximize the number of vertex connections, i.e., vertices that have only two of its faces cut away from each other in the net. Previous methods for finding such nets are based on random search and thus do not guarantee the optimal solution. We proposed a deterministic procedure [1]. Our method allows not only to design the self-assembly of much larger shell structures but also to apply additional design criteria, as a complete catalog of the nets with the maximum number of vertex connections is obtained.
[1] N. A. M. Araújo, R. A. da Costa, S. N. Dorogovtsev, J. F. F. Mendes, Physical Review Letters
120, 188001 (2018).