This paper investigates the optimal number of faces for fast self-folding kirigami structures at the microscale, driven by thermal fluctuations. Through numerical simulations and analytical calculations focusing on regular pyramids, the authors demonstrate that the total folding time is a non-monotonic function of the number of faces (N), exhibiting a minimum at five faces. The folding process is modeled as a sequence of irreversible binding events between faces, described as Brownian processes. The first binding event is a 2D first-passage process, with a characteristic time decreasing with N. Subsequent binding events are 1D first-passage processes, with the last event's time growing logarithmically with N. The interplay between these timescales explains the non-monotonic behavior, offering insights for designing more complex self-folding structures.

H. P. M. Melo, C. S. Dias, N. A. M. Araújo