Abstract: Woven structures must be made of materials that are sufficiently flexible that they can be woven together. This often results in a finished structure that is also flexible. Thus weaving has long been considered inadequate for the production of buildings and other objects requiring high levels of stiffness. The present invention relates to increasing the stiffness of triaxial-weave woven structural manifolds. The present invention provides for a new type of triaxial weave that allows for structural members of greater diameter and stiffness that are still flexible enough to accommodate the geometry of the weave. The result is structures having approximately eight times the structural stiffness of conventional triaxial-weave woven structures.