Rigidity of spherical codes
Author(s)
Cohn, Henry
Jiao, Yang
Kumar, Abhinav
Torquato, Salvatore
Date Issued
November 2011
Journal
Geometry and Topology
Publisher
Mathematical Sciences Publishers
Citation
Cohn, Henry et al. “Rigidity of spherical codes.” Geometry & Topology 15.4 (2011): 2235-2273. © Copyright 2011 Mathematical Sciences Publishers
Version
Final published version
Abstract
A packing of spherical caps on the surface of a sphere (that is, a spherical code) is
called rigid or jammed if it is isolated within the space of packings. In other words,
aside from applying a global isometry, the packing cannot be deformed. In this
paper, we systematically study the rigidity of spherical codes, particularly
kissing configurations. One surprise is that the kissing configuration of the
Coxeter–Todd lattice is not jammed, despite being locally jammed (each
individual cap is held in place if its neighbors are fixed); in this respect, the
Coxeter–Todd lattice is analogous to the face-centered cubic lattice in three
dimensions. By contrast, we find that many other packings have jammed
kissing configurations, including the Barnes–Wall lattice and all of the best
kissing configurations known in four through twelve dimensions. Jamming
seems to become much less common for large kissing configurations in higher
dimensions, and in particular it fails for the best kissing configurations known in
25 through 31 dimensions. Motivated by this phenomenon, we find new kissing configurations in
these dimensions, which improve on the records set in 1982 by the laminated
lattices.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.2140/gt.2011.15.2235
