I want to draw the Cayley graph of $S_4$ with respect the rotations of the cube 90º with respect the y axis (is the one pointing up and I will call it $g_1$) and with respect the x axis (the one pointing right and I will call it $g_2$). If we call $G=<g_1,g_2>$ then this is the group of symmetries which turns out to be $S_4$.
Then my question this time is, How can I draw this graph?, I am stuck and I do not know how to begin, I know it has to have 24 nodes, but how to proceed in this?, Thanks for your help in advance :)