Abstract
We introduce the notion of a “crystallographic sphere packing,” defined to be one whose limit set is that of a geometrically finite hyperbolic reflection group in one higher dimension. We exhibit an infinite family of conformally inequivalent crystallographic packings with all radii being reciprocals of integers. We then prove a result in the opposite direction: the “superintegral” ones exist only in finitely many “commensurability classes,” all in, at most, 20 dimensions.
Funder
National Science Foundation
Institute for Advanced Study
Simons Foundation
United States - Israel Binational Science Foundation
Publisher
Proceedings of the National Academy of Sciences
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