Bernd Schulze

Symmetric Versions of Laman’s Theorem

AbstractRecent work has shown that if an isostatic bar-and-joint framework possesses nontrivial symmetries, then it must satisfy some very simply stated restrictions on the number of joints and bars that are “fixed” by various symmetry operations of the framework.For the group

Symmetry as a Sufficient Condition for a Finite Flex

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Infinitesimal Rigidity of Symmetric Bar-Joint Frameworks

which describes 3-fold rotational symmetry in the plane, we verify the conjecture proposed by Connelly et al. (Int. J. Solids Struct. 46:762–773, 2009) that these restrictions on the number of fixed structural components, together with the Laman conditions, are also sufficient for a framework with

How does symmetry impact the flexibility of proteins

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Coning, Symmetry and Spherical Frameworks

symmetry to be isostatic, provided that its joints are positioned as generically as possible subject to the given symmetry constraints.In addition, we establish symmetric versions of Henneberg’s theorem and Crapo’s theorem for

Linking rigid bodies symmetrically

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Protein Flexibility of Dimers: Do Symmetric Motions Play a Role in Allosteric Interactions?

which provide alternate characterizations of “generically” isostatic graphs with

On the Symmetric Molecular Conjectures

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Point-hyperplane frameworks, slider joints, and rigidity preserving transformations

symmetry.As shown in (Schulze, Combinatorial and geometric rigidity with symmetry constraints, Ph.D. thesis, York University, Toronto, Canada, 2009; Schulze, Symmetrized Laman theorems for the groups

Lifting symmetric pictures to polyhedral scenes

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