Finite element modeling and linear elastic fracture mechanics are used to model the residual stresses and failure stress of ceramic composites consisting of polyhedral alumina cores surrounded by thin alumina/mullite layers in residual compression. This type of composite architecture is expected to exhibit isotropic threshold strength behavior, in which the strength of the composite for a particular assumed flaw will be constant and independent of the orientation of tensile loading. The results of the modeling indicate that the strengths of such architectures will be higher than those of laminates of similar architectural dimensions that were previously found to exhibit threshold strength behavior for a particular flaw type. Flexural testing of the polyhedral architectures reveals that failure is dominated by processing defects found at junctions between the polyhedra. Fractography revealed the interaction of these defects with the residual stresses in the compressive layers that separate the polyhedra.