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Super-Apollonian circles and lattices of Gaussian integers

Super-Apollonian circles and lattices of Gaussian integers

Abstract We study the circles of the Apollonian band circle super-packing, which are also the images of the real projective line by all linear fractional transformations of the group PLS (2 ,Z [ i ]) . This super-packing takes place on the torus rather than on the plane. We focus …