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We propose to extend the commonly known flow analysis in the transverse$p_x$-$p_y$ plane to novel flow coefficients based on the angular distributionin the $p_x$-$p_z$ and $p_y$-$p_z$ planes. The new flow coefficients, called$u_n$ and $w_n$ (in addition to $v_n$), turn out to be also highly sensitive tothe nuclear Equation-of-State and can be used to explore the EoS in more detailthan is possible using only $v_n$. As an example to quantify the effect of theEoS, the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model is used toinvestigate 20-30\% central Au+Au collisions at E$_\mathrm{lab}=1.23~A$GeV.

3-dimensional flow analysis: A novel tool to study the collision geometry and the Equation-of-State