Frameworks Symmetry and Rigidity

Symmetry equations are obtained for the rigidity matrix of a bar-joint framework in Rd . These form the basis for a short proof of the FowlerGuest symmetry group generalisation of the Calladine-Maxwell counting rules. Similar symmetry equations are obtained for the Jacobian of diverse framework systems, including constrained point-line systems that appear in CAD, body-pin frameworks, hybrid systems of distance constrained objects and infinite bar-joint frameworks. This leads to generalised forms of the Fowler-Guest character formula together with counting rules in terms of counts of symmetry-fixed elements. Necessary conditions for isostaticity are obtained for asymmetric frameworks, both when symmetries are present in subframeworks and when symmetries occur in partition-derived frameworks. 1 Supported by a London Mathematical Society Scheme 7 Grant. 1 

• Type: Journal
• Year: 2010
• Where: IJCGA
• Authors: John C. Owen, Steve C. Power
• Keywords: Bar-joint Frameworks, IJCGA 2010, Symmetry Equations, Symmetry Group Generalisation