Symmetric frameworks in normed spaces

Abstract

We develop a combinatorial rigidity theory for symmetric bar-joint frameworks in a general finite dimensional normed space. In the case of rotational symmetry, matroidal Maxwell-type sparsity counts are identified for a large class of d-dimensional normed spaces (including all lp spaces with p not equal to 2). Complete combinatorial characterisations are obtained for half-turn rotation in the l1 and l-infinity plane. As a key tool, a new Henneberg-type inductive construction is developed for the matroidal class of (2,2,0)-gain-tight gain graphs.