Abstract
Tensegrity structures are stable pre-stressed self-equilibrated systems composed of axially loaded elements. The Simplex is an iconic and well-documented spatial tensegrity system composed of three struts and nine cables, often considered the most basic three-dimensional tensegrity
structure. However, in this paper, it is shown that the Simplex is composed of two tensegrity cells. Tensegrity cells are elementary infinitesimally rigid tensegrity units of one self-stress state that have been mathematically proven to compose any tensegrity structure. The topology and self-stress
of tensegrity cells are presented along with their foundational mathematical theorem. The equilibrium of the Simplex is then analyzed and analytically derived through cellular composition. The constitutive cells of the Simplex are then combined in alternative ways through a novel bio-inspired
approach that combines topology identification and form finding to provide examples of other candidate design solutions while also providing an insight to their stability. Traditional form-finding methods are useful for exploring configurations based on a predefined topology. However, due
to the many possible combinations in the topology of a tensegrity system, design strategies that combine topology and form finding while also providing information on the self-stress states in a system allow designers to identify better solutions than traditional methods.