Inspired by the high mechanical performance of diagrid structures, the minimization of material consumption on braced tubes and the expressive potency of tensegrity modular structures, this work proposes an innovative three-dimensional system for tall buildings. A new modular structural system generated from the assembly of tetrahedral units is investigated. The paper integrates insights on the architectural implications and mechanical performance of the reticular system arranged in repetitive triangular-based modules. The impact of different geometric configurations of the structural members on the economic design is also discussed and recommendations for the optimal topology are made. Guidelines for the design and analytical formula for accessing preliminary member sizes are proposed on the basis of stiffness requirements.