Frameworks with crystallographic symmetry

2011/10/20 by Ciprian S. Borcea, Borcea, Ciprian S., Ileana Streinu +1
Engineering · Materials Science · #52C25 #74N10 #Advanced Materials and Mechanics #FOS: Mathematics #Metric Geometry (math.MG) #Quasicrystal Structures and Properties #Structural Analysis and Optimization

paper · pdf · doi:10.48550/arxiv.1110.4662

openalex publication_date 2011/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in R^d. It is shown that natural parametrizations provide affine section descriptions for families of frameworks with a specified graph and symmetry. A simple geometric setting for diaplacive phase transitions is obtained. Upper bounds are derived for the number of realizations of minimally rigid periodic graphs.

Related

• Generic rigidity of frameworks with orientation-preserving crystallographic symmetry
• Crystal frameworks, symmetry and affinely periodic flexes
• The almost periodic rigidity of crystallographic bar-joint frameworks
• Generic rigidity with forced symmetry and sparse colored graphs
• Non-Euclidean Crystallographic Rigidity