  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 distribution in 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 to the nuclear Equation-of-State and can be used to explore the EoS in more detail than is possible using only $v_n$. As an example to quantify the effect of the EoS, the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model is used to investigate 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