text: A “cuboct” cubic lattice of vertex connected octahedrons, similar to the perovskite mineral structure provides a regular polyhedral unit cell that satisfies Maxwell’s rigidity criterion and has a coordination number z of eight. The dependence of the relative density on the coordination number is small relative to the dependence on strut diameter. Winding the reinforcing fibers around the connection holes optimizes their load bearing capacity, while coupling them to struts which themselves retain uniaxial fiber orientation.