# Rigidity and symmetry

@inproceedings{Connelly2014RigidityAS, title={Rigidity and symmetry}, author={Robert Connelly and Asia Ivi{\'c} Weiss and Walter Whiteley}, year={2014} }

Volumes of Polytopes in Spaces of Constant Curvature (N. Abrosimov, A. Mednykh).- Cubic Cayley Graphs and Snarks (H. Ademir, K. Kutnar, D. Marusic).- Local, Dimensional and Universal Rigidities: A unified Gram Matrix Approach (A. Alfakih).- Geometric Constructions for Symmetric 6-Configurations (L.W. Berman).- On External Symmetry Groups of Regular Maps (M.D.E. Conder, Y.S. Kwon, J. Siran).- Variance Groups and the Structure of Mixed Polytopes (G. Cunningham).- Mobility in Symmetry-Regular Bar…

## 7 Citations

### Symmetry-forced rigidity of frameworks on surfaces

- Mathematics
- 2013

A fundamental theorem of Laman characterises when a bar-joint framework realised generically in the Euclidean plane admits a non-trivial continuous deformation of its vertices. This has recently been…

### On the asymptotics of volume for non-Euclidean simplices

- Mathematics
- 2017

1. Let ∆ be an n-dimensional simplex in one of the spaces of constant curvature E, H or S. One of the first results on simplex volumes is the Tartaglia formula, which expresses the volume of a…

### Branches of Triangulated Origami Near the Unfolded State

- Geology
- 2017

Origami structures are characterized by a network of folds and vertices joining unbendable plates. For applications to mechanical design and self-folding structures, it is essential to understand the…

### Infinitesimal Conformal Deformations of Triangulated Surfaces in Space

- MathematicsDiscret. Comput. Geom.
- 2018

The space of infinitesimal conformal deformations of a triangulated surface in Euclidean space can be parametrized in terms of the change in dihedral angles, which is closely related to the Schläfli formula.

### Infinitesimal Conformal Deformations of Triangulated Surfaces in Space

- MathematicsDiscrete & Computational Geometry
- 2018

We study infinitesimal conformal deformations of a triangulated surface in Euclidean space and investigate the change in its extrinsic geometry. A deformation of vertices is conformal if it preserves…

### Dionysian Hard Sphere Packings Are Mechanically Stable at Vanishingly Low Densities.

- Materials SciencePhysical review letters
- 2022

High strength-to-weight ratio materials can be constructed by either maximizing strength or minimizing weight. Tensegrity structures and aerogels take very different paths to achieving high…

### Crystal flex bases and the RUM spectrum

- MathematicsProceedings of the Edinburgh Mathematical Society
- 2021

A theory of infinite spanning sets and bases is developed for the first-order flex space of an infinite bar-joint framework, together with space group symmetric versions for a crystallographic…