We use a new coloured multi-graph constructive method to prove that if the edge-set of a graph G=(V,E) has a partition into two spanning trees T₁ and T₂
then there is a map p:V→R², p(v)=(p₁(v),p₂(v)), such that |p_i(u)−p_i(v)|⩾|p_3−i(u)−p_3−i(v)| for every edge uv in T_i(i=1,2). As a consequence, we solve an open problem on the realisability of minimally rigid bar-joint frameworks in the ℓ¹
or ℓ^∞-plane. We also show how to adapt this technique to incorporate symmetry and indicate several related open problems on rigidity, redundant rigidity and forced symmetric rigidity in normed spaces.