2013/10/07 by Derek Kitson, S. C. Power, Kitson, D. +1
Engineering · #05C63 #52C25 #Advanced Materials and Mechanics #Combinatorics (math.CO) #Dielectric materials and actuators #FOS: Mathematics #Metric Geometry (math.MG) #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.1310.1860
openalex publication_date 2013/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A rigidity theory is developed for the Euclidean and non-Euclidean placements of countably infinite simple graphs in Rd with respect to the classical lp norms, for d>1 and 12 a countable graph which is rigid for generic placements in Rd may fail the stronger property of sequential rigidity, while for d=2 the equivalence with sequential rigidity is obtained from the generalised Laman characterisations. Applications are given to the flexibility of non-Euclidean convex polyhedra and to the infinitesimal and continuous rigidity of compact infinitely-faceted simplicial polytopes.