We find a.nd prove the maximum rectilinear crossing n1.1mber of the three-dimensional cube graph (Q3). We demonstrate a method of drawing then-cube graph, Qn., with many crossings, and thus find a lower bound for the maximum rectilinear crossing number of Qn. We conjecture that this bound is sharp. We also prove an upper bound for the maximum rectilinear crossing number of Qn.
Alpert, Matthew, Elie Feder, Heiko Harborth, & Sheldon Klein. The Maximum Rectilinear Crossing Number of the n Dimensional Cube Graph. Congressus Numerantium 195 (2009): 147-158.