Geometry and arithmetic of crystallographic sphere packings.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 30587578.
- Also identified by DOI 10.1073/pnas.1721104116 and PMC identifier 6329941.
- No licence information is recorded for this record.
- Because redistribution is not established, this page shows the abstract only. Follow the links below for the full text.
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.