Embodiments of the present invention include dense, but accessible and well-interconnected component arrangements within multi-component systems, such as high-end multi-processor computer systems, and methods for constructing such arrangements. In a described embodiment, integrated-circuit-containing processing components, referred to as a “flat components,” are arranged into local blocks of intercommunicating flat components. The local flat-component blocks are arranged into interconnected, primitive multi-local-block repeating units, and the primitive local-block repeating units are layered together in a three-dimensional, regularly repeating structure that can be assembled to approximately fill any specified three-dimensional volume. The arrangement provides for relatively short, direct pathways from the surface of the specified volume to any particular local block and flat component within the three-dimensional arrangement.