| Summary: | 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.
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