Generic rigidity with forced symmetry and sparse colored graphs
Justin Malestein, Louis Theran
TL;DR
This paper reviews recent advances in the rigidity theory of symmetric planar frameworks and introduces new combinatorial characterizations for minimally rigid periodic frameworks with fixed domain parameters.
Contribution
It provides a unified overview of forced symmetry rigidity and introduces novel combinatorial criteria for specific periodic frameworks.
Findings
New combinatorial characterizations for minimally rigid periodic frameworks
Unified treatment of rigidity with forced symmetry in planar frameworks
Insights into fixed-area and fixed-angle fundamental domains
Abstract
We review some recent results in the generic rigidity theory of planar frameworks with forced symmetry, giving a uniform treatment to the topic. We also give new combinatorial characterizations of minimally rigid periodic frameworks with fixed-area fundamental domain and fixed-angle fundamental domain.
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Taxonomy
TopicsStructural Analysis and Optimization · Advanced Materials and Mechanics · Supramolecular Self-Assembly in Materials