Le Lu

Distance-spectral classification of twelve-point kissing shells in three dimensions

Let D={1,2,8/3,3,11/3,4}, the set of squared distances realised between two points of one twelve-neighbour shell of a Barlow (close-packed) structure. Call a twelve-point subset of the unit sphere distance-spectral if all of its pairwise squared distances lie in D. We prove that...

Distance-spectral classification of twelve-point kissing shells in three dimensions

Let D={1,2,8/3,3,11/3,4}, the set of squared distances realised between two points of one twelve-neighbour shell of a Barlow (close-packed) structure. Call a twelve-point subset of the unit sphere distance-spectral if all of its pairwise squared distances lie in D. We prove that...