A symmetry treatment of Danzerian rigidity for circle packing

A symmetry-extended mobility criterion that incorporates Danzer's concept of bar-and-joint assemblies is derived and applied to the spherical circle-packing problem. The known scalar counting rule for Danzerian freedoms is strengthened in an equation that predicts not only the number, but also the symmetries, of distortion modes that may be used to improve a packing. Relationships between alternative candidates for best packing are consequences of the co-kernel structure of the representation spanned by Danzerian mechanisms, and in several cases lead to new local optima.

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