In traditional magnetic resonance imaging (MRI) design, ideal coil overlapping is used to minimize coupling between nearest-neighbor coils, and low input impedance preamplifiers are used to isolate the relatively weak coupling. Modern-day MR systems use phased array coils constructed out of low impedance resonant loops. Inside such arrays, electrodynamic interactions between elements must be carefully balanced. However, to make the complex sensitivities of phased-array coils sufficiently distinct in parallel spatially-encoded MRI, needed an overlapping between coils. This electromechanical balancing act becomes increasingly difficult as the number of receive elements grows for optimal performance, leading to geometrical puzzles of profound complexity.