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We use a new coloured multi-graph constructive method to prove that every2-tree decomposition can be realised in the plane as a bar-joint frameworkwhich is minimally rigid (isostatic) with respect to $\ell^1$ or $\ell^\infty$distance constraints. We show how to adapt this technique to incorporatesymmetry and indicate several related open problems on rigidity, redundantrigidity and forced symmetric rigidity in normed spaces.

Constructing isostatic frameworks for the $\ell^\infty$ plane