A processing method was developed to produce a composite architecture that consisted of polyhedra of one material separated from one another by thin layers of a second material. The materials used for this study were selected so that the material separating the polyhedra would develop large compressive stresses during cooling because of differential thermal contraction. This architecture was developed to determine if it could be used to produce a ceramic composite that exhibited an isotropic threshold strength; a threshold strength has been previously demonstrated for periodic laminates containing thin layers in residual compression. To produce the current architecture, spherical alumina agglomerates were produced by suspending aqueous slurry droplets in an upward flow of a hygroscopic liquid; during the suspension period, the water was absorbed from the droplets, thereby consolidating the particles within an agglomerate. The agglomerates were then coated with thin layers of mullite-alumina using methods commonly employed in the pharmaceutical processing industry. The coated agglomerates were then consolidated into compacts by a two-step process in which the agglomerates were first uniaxially pressed at low pressure and then isopressed at high pressure. The uniaxial consolidation introduced a small degree of anisotropy into the composite architecture. Edge-cracking was observed for compressive layers containing 55 vol% mullite, thereby confirming that the appropriate compressive stresses were developed within the architecture.