Auxetic Structures Based on Rhombic Tiling

Auxetic material using corner-connected kinematic tiles has been applied to different kinematic designs. However, existing works rely on the connectivity of regular polygonal tilings because of the overconstraining nature of kinematic tiling. This study proposes a new family of auxetic structures based on non-regular and aperiodic rhombic tiling inspired by the Tokyo 2020 Emblems. We convert emblem-like patterns on rhombic tilings into kinematic structures by regarding the rectangular figure as voids and the region between rectangles as rigid bodies. Due to the geometric properties of rhombic tiling, the structure forms a one-degree-of-freedom planar mechanism with a constant Poisson’s ratio of −1. The large combinatorial family of rhombic tilings provides design variations of kinematic structures with non-regular topology. Furthermore, we show a kirigami-based method for fabricating the structure as a compliant mechanism. This connection between math and art potentially broadens the range of architected materials based on folding, kirigami, and tessellation.

Productively sequential spaces

We characterize productively sequential spaces, that is, spaces whose product with every strongly sequential space is sequential, equivalently strongly sequential. It turns out that a regular topology is productively sequential if and only if it is sequential and bi-quasi-k.