Symmetric isostatic frameworks with ${\ell }^1$ or ${\ell }^{\infty }$ distance constraints

Abstract

Combinatorial characterisations of minimal rigidity are obtained for symmetric 2-dimensional bar-joint frameworks with either ${\ell }^1$ or ${\ell }^{\infty }$ distance constraints. The characterisations are expressed in terms of symmetric tree packings and the number of edges fixed by the symmetry operations. The proof uses new Henneberg-type inductive construction schemes.

20 pages. Main theorem extended. Construction schemes refined. New title