This paper presents a novel tensegrity structure derived from the tensegrity triplex (also called the simplex or regular triangular prism) by using the linkage-truss transformation. In this paper, the tensegrity triplex is first transformed into a 6R linkage with vertical members as revolute joints and is coined the triplex linkage. With this, a novel 6R linkage was derived, whose joint axes are perpendicular to the joint axes of the triplex linkage and is coined the ortho-triplex linkage. Rigidity analysis based on screw theory demonstrates that both obtained linkages with infinitesimal mobility are prestress stable. Finally, transforming the ortho-triplex linkage to a truss, by using cables for tensional members and struts for compressional members, leads to a novel tensegrity that is coined ortho-triplex tensegrity. A non-dimensional quadratic form is further provided to analyze the sensitivity of prestress-stability in terms of the structural parameters. The process of derivation of this novel tensegrity presents a new way of designing tensegrity structures with prestress-stability analysis based on screw theory.