Rigidity of packings

In Ludwig Danzer's Habilitatiionsschrift [L. Danzer, Endliche Punktmengen auf der 2-Sphäre mit möglichst grossem minimalabstand, Habilitationsschrift, Göttingen, 1963] he initiated a study of the local nature of the packings from the point of view of whether their density can be increased by a small perturbation of the packing configuration. This is an abbreviated biased introduction to the theory of such locally maximally dense packings of disks in various spaces from the point of view of the theory of tensegrity structures. This has applications to jamming of granular materials as well as leading to a better understanding of jammed packings.