The generic minimal rigidity of a partially triangulated torus

2015/09/02 by James Cruickshank, Cruickshank, James, Derek Kitson +3
Engineering · Materials Science · #52C25 #Advanced Materials and Mechanics #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #Structural Analysis and Optimization #Supramolecular Self-Assembly in Materials

paper · pdf · doi:10.48550/arxiv.1509.00711

openalex publication_date 2015/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A simple graph is 3-rigid if its generic bar-joint frameworks in R³ are infinitesimally rigid. Necessary and sufficient conditions are obtained for the minimal 3-rigidity of a simple graph which is obtained from the 1-skeleton of a triangulated torus by the deletion of edges interior to a triangulated disc.

Related

• The generic rigidity of triangulated spheres with blocks and holes
• Rigidity of Frameworks Supported on Surfaces
• Projective plane graphs and 3-rigidity
• Noncompact surfaces, triangulations and rigidity
• Infinitesimal rigidity for non-Euclidean bar-joint frameworks