Communication latency, now a dominant factor in computer performance, makes physical size, density, and interconnect proximity crucial system design considerations. The present invention addresses consequential supercomputing hardware challenges: spatial packing, communication topology, and thermal management. A massively-parallel computer with dense, spherically framed, geodesic processor arrangement is described. As a mimic of the problem domain, it is particularly apt for climate modelling. However, the invention's methods scale well, are largely independent of processor technology, and apply to a wide range of computing tasks. The computer's interconnect features globally short, highly regular, and tightly matched distances. Communication modes supported include neighbour-to-neighbour messaging on a spherical-shell lattice, and a radial network for system-synchronous clocking, broadcast, packet-switched networking, and IO. A near-isothermal cooling system, physically divorcing heat source and sink, enables extraordinarily compact geodes with lower temperature operation, higher speed, and lower power consumption.