Abstract The deformability of soft material robots provides them with the ability to transform between complex shapes and forms. This unique facilitates Modular Soft Robots (MSoRos) assemble reconfigure into different configurations, e.g., planar spherical. These topologies display widely locomotion modes that are desirable navigate environments, crawling or rolling for these cases. research pr...

Herein we describe some properties and the occurrences of a beautiful geometric figure that is ubiquitous in chemistry and materials science, however, it is not as well-known as it should be. We call attention to the need for mathematicians to pay more attention to the richly structured natural world, and for materials scientists to learn a little more about mathematics. Our account is informal...

A cluster of cycles (or (r, q)-polycycle) is a simple planar 2–connected finite or countable graph G of girth r and maximal vertex-degree q, which admits an (r, q)-polycyclic realization P (G) on the plane. An (r, q)-polycyclic realization is determined by the following properties: (i) all interior vertices are of degree q, (ii) all interior faces (denote their number by pr) are combinatorial r...

In this paper we study the Platonic Bell inequalities for all possible dimensions. There are five solids in three dimensions, but there also with properties (also known as regular polyhedra) four and higher The concept of three-dimensional Euclidean space was introduced by Tavakoli Gisin [Quantum 4, 293 (2020)]. For any solid, an arrangement projective measurements is associated where measureme...