The decomposition of double latticed 2- fold unit circle packings into three unit circle packings (Q1200963)

Let \(B\subset E^ 2\) denote the unit circle, let \(L\subset E^ 2\) be a lattice and \(t\not\in L\) such that \(P=\{B+x\mid x\in L\cup(L+t)\}\) is a 2-fold circle-packing of \(E^ 2\). Then \(P\) can be decomposed into 3 circle-packing of \(E^ 2\).